NuITP (alpha 30) ProofProved


Goal

(True = alter($1:List $2:List)) /\ (True = even($1:List $2:List)) /\ (True = opposite($1:List, $2:List)) /\ True = shuffle($1:List, $2:List, $3:List) → True = pairedList($3:List)

Script

set goal ((alter(L1:List L2:List) = True) /\ (even((L1:List L2:List)) = True) /\ (opposite(L1:List, L2:List) = True) /\ (shuffle(L1:List, L2:List, L3:List) = True)) → (pairedList(L3:List) = True) .
apply ufree* to 0 .
apply ni* to 0.8.2.1 on pairedList($6:NeList) .
apply cas! to 0.8.2.1.4.1.2.1 on $7 .
apply cas! to 0.8.2.1.6.1.1 on $7 .
apply cas! to 0.8.2.1.6.1.1.3.1 on $10 .
apply cas! to 0.8.2.1.6.1.1.3.1.3.1 on $11 .
apply cas! to 0.8.2.1.6.2.1 on $7 .
apply ns! to 0.8.2.1.6.2.1.3.1 on shuffle(black, black $11:NeList, black $10) .
apply cas! to 0.8.2.1.6.2.1.3.1.15.1 on $13 .
apply cas! to 0.8.2.1.6.2.1.3.1.15.1.3.1 on $12 .
apply cas! to 0.8.2.1.6.2.1.3.1.16.1 on $12 .
apply ni* to 0.8.4.1 on pairedList($6:NeList) .
apply cas! to 0.8.4.1.4.1.1.1 on $7 .
apply cas! to 0.8.4.1.6.2.1 on $7 .
apply cas! to 0.8.4.1.6.2.1.4.1 on $10 .
apply cas! to 0.8.4.1.6.2.1.4.1.4.1 on $11 .
apply cas! to 0.8.4.1.6.1.1 on $7 .
apply ns! to 0.8.4.1.6.1.1.4.1 on shuffle(red, red $11:NeList, red $10) .
apply cas! to 0.8.4.1.6.1.1.4.1.15.1 on $13 .
apply cas! to 0.8.4.1.6.1.1.4.1.15.1.4.1 on $12 .
apply cas! to 0.8.4.1.6.1.1.4.1.16.1 on $12 .
apply ni* to 0.8.5.1 on pairedList($6:NeList) .
apply cas! to 0.8.5.1.4.1.1.1 on $7 .
apply cas! to 0.8.5.1.6.2.1 on $7 .
apply cas! to 0.8.5.1.6.2.1.4.1 on $10 .
apply cas! to 0.8.5.1.6.2.1.4.1.4.1 on $11 .
apply cas! to 0.8.5.1.6.1.1 on $7 .
apply ns! to 0.8.5.1.6.1.1.4.1 on shuffle(red $11:NeList, red, red $10) .
apply cas! to 0.8.5.1.6.1.1.4.1.15.1 on $12 .
apply cas! to 0.8.5.1.6.1.1.4.1.16.1 on $13 .
apply cas! to 0.8.5.1.6.1.1.4.1.16.1.4.1 on $12 .
apply ni* to 0.8.7.1 on pairedList($6:NeList) .
apply cas! to 0.8.7.1.4.1.2.1 on $7 .
apply cas! to 0.8.7.1.6.1.1 on $7 .
apply cas! to 0.8.7.1.6.1.1.3.1 on $10 .
apply cas! to 0.8.7.1.6.1.1.3.1.3.1 on $11 .
apply cas! to 0.8.7.1.6.2.1 on $7 .
apply ns! to 0.8.7.1.6.2.1.3.1 on shuffle(black $11:NeList, black, black $10) .
apply cas! to 0.8.7.1.6.2.1.3.1.15.1 on $12 .
apply cas! to 0.8.7.1.6.2.1.3.1.16.1 on $13 .
apply cas! to 0.8.7.1.6.2.1.3.1.16.1.3.1 on $12 .
apply ni* to 0.8.6.1 on pairedList($6:NeList) .
apply cas! to 0.8.6.1.4.1.1.1 on $7 .
apply cas! to 0.8.6.1.4.1.2.1 on $8 .
apply cas! to 0.8.6.1.6.1.1 on $8 .
apply ns! to 0.8.6.1.6.1.1.1.1 on shuffle(black $7:NeList, black, black $11) .
apply ni* to 0.8.6.1.6.1.1.1.1.16.1 on pairedList($13) .
apply cas! to 0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1 on $12 .
apply cas! to 0.8.6.1.6.1.1.1.1.16.1.1.6.1.1 on $12 .
apply cas! to 0.8.6.1.6.1.1.1.1.15.1 on $12 .
apply ns! to 0.8.6.1.6.1.1.3 on shuffle(black $7:NeList, black $12:NeList, black $11) .
apply cas! to 0.8.6.1.6.1.1.3.7.1 on $15 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.3 on $13 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.3.4.1 on $14 .
apply cut* to 0.8.6.1.6.1.1.3.7.1.3.4.1.4.1 with (True = alter(black red $17:NeList red $18:NeList)) /\ (True = even(red $17:NeList $18:NeList)) .
apply cas! to 0.8.6.1.6.1.1.3.7.1.3.4.1.2.1 on $16 .
apply ns! to 0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1 on shuffle(red $17:NeList, red, red $18) .
apply ni* to 0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1 on pairedList($20) .
apply cas! to 0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1 on $19 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1 on $19 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1 on $24 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1 on $19 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.4 on $13 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.4.4.1 on $17 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.4.4.1.1.1 on $16 .
apply ns! to 0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1 on shuffle(black, black $14:NeList, black $18) .
apply ni* to 0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1 on pairedList($20) .
apply cas! to 0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1 on $19 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1 on $19 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1 on $24 .
apply cas! to 0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1 on $19 .
apply cut* to 0.8.6.1.6.1.1.3.7.1.4.4.1.3.1 with (True = even($18:NeList black $14:NeList)) .
apply cas! to 0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1 on $18 .
apply cas! to 0.8.6.1.6.1.1.3.8.1 on $14 .
apply cas! to 0.8.6.1.6.2.1 on $7 .
apply ns! to 0.8.6.1.6.2.1.4.1 on shuffle(red $12:NeList, red $8:NeList, red $11) .
apply cas! to 0.8.6.1.6.2.1.4.1.7.1 on $13 .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1 on $14 .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1.3.1 on $15 .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1.3.1.3.1 on $16 .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1 on $17 .
apply ns! to 0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1 on shuffle(red $13:NeList, red, red $18) .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1 on $19 .
apply cut* to 0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.4.1 with (True = alter(black red $13:NeList red $18:NeList)) /\ (True = even(red $13:NeList $18:NeList)) .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1.3.1.4.1 on $13 .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1 on $17 .
apply ns! to 0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1 on shuffle(black, black $16:NeList, black $18) .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1 on $19 .
apply cut* to 0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1 with (True = even($18:NeList black $16:NeList)) .
apply cas! to 0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1 on $18 .
apply ni* to 0.8.8.1 on pairedList($6:NeList) .
apply cas! to 0.8.8.1.4.1.1.1 on $8 .
apply cas! to 0.8.8.1.4.1.2.1 on $7 .
apply cas! to 0.8.8.1.6.1.1 on $7 .
apply ns! to 0.8.8.1.6.1.1.3.1 on shuffle(black $12:NeList, black $8:NeList, black $11) .
apply cas! to 0.8.8.1.6.1.1.3.1.7.1 on $13 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1 on $14 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1 on $15 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1 on $13 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1 on $17 .
apply ns! to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1 on shuffle(red, red $16:NeList, red $18) .
apply ni* to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1 on pairedList($20) .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1 on $19 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1 on $19 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1 on $24 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1 on $19 .
apply cut* to 0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.4.1 with (True = even($18:NeList red $16:NeList)) .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1 on $16 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1 on $17 .
apply ns! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1 on shuffle(black $13:NeList, black, black $18) .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1 on $19 .
apply ni* to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1 on pairedList($20) .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1 on $19 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1 on $19 .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1 on $24 .
apply cut* to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1 with (True = even($25:NeList black)) .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1 on $25 .
apply cut* to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1 with (True = alter(red black $13:NeList black $18:NeList)) /\ (True = even(black $13:NeList $18:NeList)) .
apply cas! to 0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1 on $13 .
apply cas! to 0.8.8.1.6.2.1 on $8 .
apply ns! to 0.8.8.1.6.2.1.2.1 on shuffle(red $7:NeList, red, red $11) .
apply cas! to 0.8.8.1.6.2.1.2.1.15.1 on $12 .
apply ni* to 0.8.8.1.6.2.1.2.1.16.1 on pairedList($13) .
apply cas! to 0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1 on $12 .
apply cas! to 0.8.8.1.6.2.1.2.1.16.1.1.6.2.1 on $12 .
apply ns! to 0.8.8.1.6.2.1.4.1 on shuffle(red $7:NeList, red $12:NeList, red $11) .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1 on $13 .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1.3.1 on $15 .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1.3.1.3.1 on $16 .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1 on $17 .
apply ns! to 0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1 on shuffle(red, red $14:NeList, red $18) .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1 on $19 .
apply cut* to 0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.4.1 with (True = even($18:NeList red $14:NeList)) .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1.3.1.4.1 on $14 .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1 on $17 .
apply ns! to 0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1 on shuffle(black $16:NeList, black, black $18) .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1 on $19 .
apply cut* to 0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1 with (True = alter(red black $16:NeList black $18:NeList)) /\ (True = even(black $16:NeList $18:NeList)) .
apply cas! to 0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1 on $16 .
apply cas! to 0.8.8.1.6.2.1.4.1.8.1 on $14 .

Rewriting Theory

fmod GILBREATH-ACU is
sorts Boolean Card List NeList .
subsort Card < NeList .
subsort NeList < List .
op False : -> Boolean [ ctor metadata "1" ] .
op True : -> Boolean [ ctor metadata "0" ] .
op __ : List List -> List [ assoc id: nil metadata "5" ] .
op __ : NeList NeList -> NeList [ assoc ctor id: nil metadata "5" ] .
op alter : List -> Boolean [ metadata "8" ] .
op black : -> Card [ ctor metadata "3" ] .
op even : List -> Boolean [ metadata "11" ] .
op neg : Card -> Card [ metadata "12" ] .
op nil : -> List [ ctor metadata "2" ] .
op opposite : List List -> Boolean [ metadata "7" ] .
op paired : Card Card -> Boolean [ metadata "6" ] .
op pairedList : List -> Boolean [ metadata "9" ] .
op red : -> Card [ ctor metadata "4" ] .
op rotate : List -> List [ metadata "13" ] .
op shuffle : List List List -> Boolean [ metadata "10" ] .
eq alter(C:Card) = True .
eq alter(nil) = True .
eq even(C:Card) = False .
eq even(nil) = True .
eq even(L1:List C1:Card L2:List C2:Card L3:List) = even(L1:List L2:List L3:List) .
eq neg(black) = red [ variant ] .
eq neg(red) = black [ variant ] .
eq opposite(L:List, nil) = False [ variant ] .
eq opposite(nil, L:List) = False [ variant ] .
eq opposite(C1:Card L1:List, C2:Card L2:List) = paired(C1:Card, C2:Card) [ variant ] .
eq paired(C:Card, C:Card) = False [ variant ] .
eq paired(black, red) = True [ variant ] .
eq paired(red, black) = True [ variant ] .
eq pairedList(C:Card) = False .
eq pairedList(nil) = True .
eq pairedList(C:Card C:Card L:List) = False .
eq rotate(nil) = nil [ variant ] .
eq rotate(C:Card L:List) = L:List C:Card [ variant ] .
eq shuffle(L1:List, C2:Card L2:List, nil) = False .
eq shuffle(nil, nil, nil) = True .
eq shuffle(nil, nil, C3:Card L3:List) = False .
eq shuffle(C1:Card L1:List, L2:List, nil) = False .
ceq alter(C1:Card C2:Card L:List) = False if paired(C1:Card, C2:Card) = False .
ceq alter(C1:Card C2:Card L:List) = alter(C2:Card L:List) if paired(C1:Card, C2:Card) = True .
ceq pairedList(C1:Card C2:Card L:List) = pairedList(L:List) if paired(C1:Card, C2:Card) = True .
ceq shuffle(nil, C2:Card L2:List, C3:Card L3:List) = False if paired(C2:Card, C3:Card) = True .
ceq shuffle(nil, C2:Card L2:List, C3:Card L3:List) = shuffle(nil, L2:List, L3:List) if paired(C2:Card, C3:Card) = False .
ceq shuffle(C1:Card L1:List, nil, C3:Card L3:List) = False if paired(C1:Card, C3:Card) = True .
ceq shuffle(C1:Card L1:List, nil, C3:Card L3:List) = shuffle(L1:List, nil, L3:List) if paired(C1:Card, C3:Card) = False .
ceq shuffle(C1:Card L1:List, C2:Card L2:List, C3:Card L3:List) = False if paired(C1:Card, C3:Card) = True /\ paired(C2:Card, C3:Card) = True .
ceq shuffle(C1:Card L1:List, C2:Card L2:List, C3:Card L3:List) = False if paired(C1:Card, C3:Card) = True /\ shuffle(C1:Card L1:List, L2:List, L3:List) = False .
ceq shuffle(C1:Card L1:List, C2:Card L2:List, C3:Card L3:List) = False if paired(C2:Card, C3:Card) = True /\ shuffle(L1:List, C2:Card L2:List, L3:List) = False .
ceq shuffle(C1:Card L1:List, C2:Card L2:List, C3:Card L3:List) = False if shuffle(L1:List, C2:Card L2:List, L3:List) = False /\ shuffle(C1:Card L1:List, L2:List, L3:List) = False .
ceq shuffle(C1:Card L1:List, C2:Card L2:List, C3:Card L3:List) = True if paired(C1:Card, C3:Card) = False /\ shuffle(L1:List, C2:Card L2:List, L3:List) = True .
ceq shuffle(C1:Card L1:List, C2:Card L2:List, C3:Card L3:List) = True if paired(C2:Card, C3:Card) = False /\ shuffle(C1:Card L1:List, L2:List, L3:List) = True .
endfm

Goals

Goal Id:  0
Generated By:  init
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter($1:List $2:List)) /\ (True = even($1:List $2:List)) /\ (True = opposite($1:List, $2:List)) /\ True = shuffle($1:List, $2:List, $3:List) → True = pairedList($3:List)
Goal Id:  0.1
Generated By:  UFREE
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(nil)) /\ (True = even(nil)) /\ (True = opposite(nil, nil)) /\ True = shuffle(nil, nil, nil) → True = pairedList(nil)
Goal Id:  0.2
Generated By:  UFREE
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter($4:NeList)) /\ (True = even($4:NeList)) /\ (True = opposite($4:NeList, nil)) /\ True = shuffle($4:NeList, nil, nil) → True = pairedList(nil)
Goal Id:  0.3
Generated By:  UFREE
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter($4:NeList)) /\ (True = even($4:NeList)) /\ (True = opposite(nil, $4:NeList)) /\ True = shuffle(nil, $4:NeList, nil) → True = pairedList(nil)
Goal Id:  0.4
Generated By:  UFREE
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(nil)) /\ (True = even(nil)) /\ (True = opposite(nil, nil)) /\ True = shuffle(nil, nil, $4:NeList) → True = pairedList($4:NeList)
Goal Id:  0.5
Generated By:  UFREE
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter($4:NeList)) /\ (True = even($4:NeList)) /\ (True = opposite($4:NeList, nil)) /\ True = shuffle($4:NeList, nil, $5:NeList) → True = pairedList($5:NeList)
Goal Id:  0.6
Generated By:  UFREE
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter($4:NeList)) /\ (True = even($4:NeList)) /\ (True = opposite(nil, $4:NeList)) /\ True = shuffle(nil, $4:NeList, $5:NeList) → True = pairedList($5:NeList)
Goal Id:  0.7
Generated By:  UFREE
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter($4:NeList $5:NeList)) /\ (True = even($4:NeList $5:NeList)) /\ (True = opposite($4:NeList, $5:NeList)) /\ True = shuffle($4:NeList, $5:NeList, nil) → True = pairedList(nil)
Goal Id:  0.8
Generated By:  UFREE
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter($4:NeList $5:NeList)) /\ (True = even($4:NeList $5:NeList)) /\ (True = opposite($4:NeList, $5:NeList)) /\ True = shuffle($4:NeList, $5:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.6.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1
Generated By:  CVUL
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(black, red, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.2
Generated By:  CVUL
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $7:NeList)) /\ (True = even(black red $7:NeList)) /\ True = shuffle(black, red $7:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.3
Generated By:  CVUL
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black)) /\ (True = even(red black)) /\ True = shuffle(red, black, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.4
Generated By:  CVUL
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $7:NeList)) /\ (True = even(red black $7:NeList)) /\ True = shuffle(red, black $7:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.5
Generated By:  CVUL
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even(black $7:NeList red)) /\ True = shuffle(black $7:NeList, red, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.6
Generated By:  CVUL
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even(black $7:NeList red $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.7
Generated By:  CVUL
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even(red $7:NeList black)) /\ True = shuffle(red $7:NeList, black, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.8
Generated By:  CVUL
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even(red $7:NeList black $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, red, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, black, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.6.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.8.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $6:NeList) → True = pairedList($6:NeList)
Goal Id:  0.8.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, red, black) → True = pairedList(black)
Goal Id:  0.8.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, red, red) → True = pairedList(red)
Goal Id:  0.8.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, red, black $7:NeList) → True = pairedList(black $7:NeList)
Goal Id:  0.8.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, red, red $7:NeList) → True = pairedList(red $7:NeList)
Goal Id:  0.8.2.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $8:Card) → False = True
Goal Id:  0.8.2.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $8:Card $8:Card) → False = True
Goal Id:  0.8.2.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ (True = paired($8:Card, $9:Card)) /\ True = shuffle(black, red $7:NeList, $8:Card $9:Card) → True = pairedList(nil)
Goal Id:  0.8.2.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $8:Card $8:Card $9:NeList) → False = True
Goal Id:  0.8.2.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $8:Card $8:Card) → False = True
Goal Id:  0.8.2.1.6
Generated By:  NI
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ (True = paired($8, $9)) /\ True = shuffle(black, red $7:NeList, $8 $9 $10) → True = pairedList($10)
Goal Id:  0.8.2.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ (True = paired($8:Card, $9:Card)) /\ True = shuffle(black, red $7:NeList, $8:Card $9:Card) → True = pairedList(nil)
Goal Id:  0.8.3.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, black, black) → True = pairedList(black)
Goal Id:  0.8.3.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, black, red) → True = pairedList(red)
Goal Id:  0.8.3.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, black, black $7:NeList) → True = pairedList(black $7:NeList)
Goal Id:  0.8.3.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, black, red $7:NeList) → True = pairedList(red $7:NeList)
Goal Id:  0.8.4.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $8:Card) → False = True
Goal Id:  0.8.4.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $8:Card $8:Card) → False = True
Goal Id:  0.8.4.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ (True = paired($8:Card, $9:Card)) /\ True = shuffle(red, black $7:NeList, $8:Card $9:Card) → True = pairedList(nil)
Goal Id:  0.8.4.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $8:Card $8:Card $9:NeList) → False = True
Goal Id:  0.8.4.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $8:Card $8:Card) → False = True
Goal Id:  0.8.4.1.6
Generated By:  NI
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ (True = paired($8, $9)) /\ True = shuffle(red, black $7:NeList, $8 $9 $10) → True = pairedList($10)
Goal Id:  0.8.4.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ (True = paired($8:Card, $9:Card)) /\ True = shuffle(red, black $7:NeList, $8:Card $9:Card) → True = pairedList(nil)
Goal Id:  0.8.5.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $8:Card) → False = True
Goal Id:  0.8.5.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $8:Card $8:Card) → False = True
Goal Id:  0.8.5.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ (True = paired($8:Card, $9:Card)) /\ True = shuffle(black $7:NeList, red, $8:Card $9:Card) → True = pairedList(nil)
Goal Id:  0.8.5.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $8:Card $8:Card $9:NeList) → False = True
Goal Id:  0.8.5.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $8:Card $8:Card) → False = True
Goal Id:  0.8.5.1.6
Generated By:  NI
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ (True = paired($8, $9)) /\ True = shuffle(black $7:NeList, red, $8 $9 $10) → True = pairedList($10)
Goal Id:  0.8.5.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ (True = paired($8:Card, $9:Card)) /\ True = shuffle(black $7:NeList, red, $8:Card $9:Card) → True = pairedList(nil)
Goal Id:  0.8.6.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $9:Card) → False = True
Goal Id:  0.8.6.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $9:Card $9:Card) → False = True
Goal Id:  0.8.6.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ (True = paired($9:Card, $10:Card)) /\ True = shuffle(black $7:NeList, red $8:NeList, $9:Card $10:Card) → True = pairedList(nil)
Goal Id:  0.8.6.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $9:Card $9:Card $10:NeList) → False = True
Goal Id:  0.8.6.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $9:Card $9:Card) → False = True
Goal Id:  0.8.6.1.6
Generated By:  NI
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ (True = paired($9, $10)) /\ True = shuffle(black $7:NeList, red $8:NeList, $9 $10 $11) → True = pairedList($11)
Goal Id:  0.8.6.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ (True = paired($9:Card, $10:Card)) /\ True = shuffle(black $7:NeList, red $8:NeList, $9:Card $10:Card) → True = pairedList(nil)
Goal Id:  0.8.7.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $8:Card) → False = True
Goal Id:  0.8.7.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $8:Card $8:Card) → False = True
Goal Id:  0.8.7.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ (True = paired($8:Card, $9:Card)) /\ True = shuffle(red $7:NeList, black, $8:Card $9:Card) → True = pairedList(nil)
Goal Id:  0.8.7.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $8:Card $8:Card $9:NeList) → False = True
Goal Id:  0.8.7.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $8:Card $8:Card) → False = True
Goal Id:  0.8.7.1.6
Generated By:  NI
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ (True = paired($8, $9)) /\ True = shuffle(red $7:NeList, black, $8 $9 $10) → True = pairedList($10)
Goal Id:  0.8.7.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ (True = paired($8:Card, $9:Card)) /\ True = shuffle(red $7:NeList, black, $8:Card $9:Card) → True = pairedList(nil)
Goal Id:  0.8.8.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $9:Card) → False = True
Goal Id:  0.8.8.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $9:Card $9:Card) → False = True
Goal Id:  0.8.8.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ (True = paired($9:Card, $10:Card)) /\ True = shuffle(red $7:NeList, black $8:NeList, $9:Card $10:Card) → True = pairedList(nil)
Goal Id:  0.8.8.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $9:Card $9:Card $10:NeList) → False = True
Goal Id:  0.8.8.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $9:Card $9:Card) → False = True
Goal Id:  0.8.8.1.6
Generated By:  NI
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ (True = paired($9, $10)) /\ True = shuffle(red $7:NeList, black $8:NeList, $9 $10 $11) → True = pairedList($11)
Goal Id:  0.8.8.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ (True = paired($9:Card, $10:Card)) /\ True = shuffle(red $7:NeList, black $8:NeList, $9:Card $10:Card) → True = pairedList(nil)
Goal Id:  0.8.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, red, $7:NeList) → True = pairedList(black $7:NeList)
Goal Id:  0.8.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, nil, $7:NeList) → True = pairedList(red $7:NeList)
Goal Id:  0.8.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $8:Card $8:Card $9:NeList) → false
Goal Id:  0.8.2.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.6.1
Generated By:  CVUL
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, black red $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2
Generated By:  CVUL
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, red black $10) → True = pairedList($10)
Goal Id:  0.8.2.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, nil, $7:NeList) → True = pairedList(black $7:NeList)
Goal Id:  0.8.3.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, black, $7:NeList) → True = pairedList(red $7:NeList)
Goal Id:  0.8.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $8:Card $8:Card $9:NeList) → false
Goal Id:  0.8.4.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.6.1
Generated By:  CVUL
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, black red $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2
Generated By:  CVUL
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, red black $10) → True = pairedList($10)
Goal Id:  0.8.4.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $8:Card $8:Card $9:NeList) → false
Goal Id:  0.8.5.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.6.1
Generated By:  CVUL
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, black red $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2
Generated By:  CVUL
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, red black $10) → True = pairedList($10)
Goal Id:  0.8.5.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $9:Card $9:Card $10:NeList) → false
Goal Id:  0.8.6.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1
Generated By:  CVUL
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, red black $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2
Generated By:  CVUL
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, black red $11) → True = pairedList($11)
Goal Id:  0.8.6.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $8:Card $8:Card $9:NeList) → false
Goal Id:  0.8.7.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.6.1
Generated By:  CVUL
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, black red $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2
Generated By:  CVUL
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, red black $10) → True = pairedList($10)
Goal Id:  0.8.7.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $9:Card $9:Card $10:NeList) → false
Goal Id:  0.8.8.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1
Generated By:  CVUL
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, red black $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2
Generated By:  CVUL
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, black red $11) → True = pairedList($11)
Goal Id:  0.8.8.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.3.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, red, black) → True = pairedList(black black)
Goal Id:  0.8.1.1.3.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, red, red) → True = pairedList(black red)
Goal Id:  0.8.1.1.3.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, red, black $8:NeList) → True = pairedList(black black $8:NeList)
Goal Id:  0.8.1.1.3.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, red, red $8:NeList) → True = pairedList(black red $8:NeList)
Goal Id:  0.8.1.1.4.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, nil, black) → True = pairedList(red black)
Goal Id:  0.8.1.1.4.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, nil, red) → True = pairedList(red red)
Goal Id:  0.8.1.1.4.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, nil, black $8:NeList) → True = pairedList(red black $8:NeList)
Goal Id:  0.8.1.1.4.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(black, nil, red $8:NeList) → True = pairedList(red red $8:NeList)
Goal Id:  0.8.2.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, black black $9:NeList) → false
Goal Id:  0.8.2.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, red red $9:NeList) → false
Goal Id:  0.8.2.1.6.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, $7:NeList, $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, $7:NeList, black $10) → True = pairedList($10)
Goal Id:  0.8.3.1.3.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, nil, black) → True = pairedList(black black)
Goal Id:  0.8.3.1.3.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, nil, red) → True = pairedList(black red)
Goal Id:  0.8.3.1.3.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, nil, black $8:NeList) → True = pairedList(black black $8:NeList)
Goal Id:  0.8.3.1.3.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(red, nil, red $8:NeList) → True = pairedList(black red $8:NeList)
Goal Id:  0.8.3.1.4.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, black, black) → True = pairedList(red black)
Goal Id:  0.8.3.1.4.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, black, red) → True = pairedList(red red)
Goal Id:  0.8.3.1.4.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, black, black $8:NeList) → True = pairedList(red black $8:NeList)
Goal Id:  0.8.3.1.4.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
True = shuffle(nil, black, red $8:NeList) → True = pairedList(red red $8:NeList)
Goal Id:  0.8.4.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, black black $9:NeList) → false
Goal Id:  0.8.4.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, red red $9:NeList) → false
Goal Id:  0.8.4.1.6.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, $7:NeList, red $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, $7:NeList, $10) → True = pairedList($10)
Goal Id:  0.8.5.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, black black $9:NeList) → false
Goal Id:  0.8.5.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, red red $9:NeList) → false
Goal Id:  0.8.5.1.6.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, red, red $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, nil, $10) → True = pairedList($10)
Goal Id:  0.8.6.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, black black $10:NeList) → false
Goal Id:  0.8.6.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, red red $10:NeList) → false
Goal Id:  0.8.6.1.6.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.7.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, black black $9:NeList) → false
Goal Id:  0.8.7.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, red red $9:NeList) → false
Goal Id:  0.8.7.1.6.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, nil, $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, black, black $10) → True = pairedList($10)
Goal Id:  0.8.8.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, black black $10:NeList) → false
Goal Id:  0.8.8.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, red red $10:NeList) → false
Goal Id:  0.8.8.1.6.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.1.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.1.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, $7:NeList, red $9:NeList) → false
Goal Id:  0.8.2.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black)) /\ True = shuffle(nil, black, $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(red)) /\ True = shuffle(nil, red, $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, black $11:NeList, $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red red $11:NeList)) /\ (True = even(red $11:NeList)) /\ True = shuffle(nil, red $11:NeList, $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black)) /\ True = shuffle(black, black, black $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(red)) /\ True = shuffle(black, red, black $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black, black $11:NeList, black $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red red $11:NeList)) /\ (True = even(red $11:NeList)) /\ True = shuffle(black, red $11:NeList, black $10) → True = pairedList($10)
Goal Id:  0.8.3.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.3.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, $7:NeList, black $9:NeList) → false
Goal Id:  0.8.4.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black)) /\ True = shuffle(red, black, red $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(red)) /\ True = shuffle(red, red, red $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(red, black $11:NeList, red $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black red $11:NeList)) /\ (True = even(red $11:NeList)) /\ True = shuffle(red, red $11:NeList, red $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black)) /\ True = shuffle(nil, black, $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(red)) /\ True = shuffle(nil, red, $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, black $11:NeList, $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black red $11:NeList)) /\ (True = even(red $11:NeList)) /\ True = shuffle(nil, red $11:NeList, $10) → True = pairedList($10)
Goal Id:  0.8.5.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, red, black $9:NeList) → false
Goal Id:  0.8.5.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black black red)) /\ (True = even(black)) /\ True = shuffle(black, red, red $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black red red)) /\ (True = even(red)) /\ True = shuffle(red, red, red $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black black $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, red, red $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black red $11:NeList red)) /\ (True = even(red $11:NeList)) /\ True = shuffle(red $11:NeList, red, red $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black black red)) /\ (True = even(black)) /\ True = shuffle(black, nil, $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black red red)) /\ (True = even(red)) /\ True = shuffle(red, nil, $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black black $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, nil, $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black red $11:NeList red)) /\ (True = even(red $11:NeList)) /\ True = shuffle(red $11:NeList, nil, $10) → True = pairedList($10)
Goal Id:  0.8.6.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, black $10:NeList) → false
Goal Id:  0.8.6.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, red $10:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red black)) /\ (True = even($7:NeList black)) /\ True = shuffle(black $7:NeList, black, black $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red red)) /\ (True = even($7:NeList red)) /\ True = shuffle(black $7:NeList, red, black $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red black $12:NeList)) /\ (True = even($7:NeList black $12:NeList)) /\ True = shuffle(black $7:NeList, black $12:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red red $12:NeList)) /\ (True = even($7:NeList red $12:NeList)) /\ True = shuffle(black $7:NeList, red $12:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black black red $8:NeList)) /\ (True = even(black $8:NeList)) /\ True = shuffle(black, red $8:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black red red $8:NeList)) /\ (True = even(red $8:NeList)) /\ True = shuffle(red, red $8:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black black $12:NeList red $8:NeList)) /\ (True = even(black $12:NeList $8:NeList)) /\ True = shuffle(black $12:NeList, red $8:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black red $12:NeList red $8:NeList)) /\ (True = even(red $12:NeList $8:NeList)) /\ True = shuffle(red $12:NeList, red $8:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.7.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, black, red $9:NeList) → false
Goal Id:  0.8.7.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red black black)) /\ (True = even(black)) /\ True = shuffle(black, nil, $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red red black)) /\ (True = even(red)) /\ True = shuffle(red, nil, $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, nil, $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red red $11:NeList black)) /\ (True = even(red $11:NeList)) /\ True = shuffle(red $11:NeList, nil, $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red black black)) /\ (True = even(black)) /\ True = shuffle(black, black, black $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red red black)) /\ (True = even(red)) /\ True = shuffle(red, black, black $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, black, black $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red red $11:NeList black)) /\ (True = even(red $11:NeList)) /\ True = shuffle(red $11:NeList, black, black $10) → True = pairedList($10)
Goal Id:  0.8.8.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, black $10:NeList) → false
Goal Id:  0.8.8.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, red $10:NeList) → false
Goal Id:  0.8.8.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red black black $8:NeList)) /\ (True = even(black $8:NeList)) /\ True = shuffle(black, black $8:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red red black $8:NeList)) /\ (True = even(red $8:NeList)) /\ True = shuffle(red, black $8:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red black $12:NeList black $8:NeList)) /\ (True = even(black $12:NeList $8:NeList)) /\ True = shuffle(black $12:NeList, black $8:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red red $12:NeList black $8:NeList)) /\ (True = even(red $12:NeList $8:NeList)) /\ True = shuffle(red $12:NeList, black $8:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black black)) /\ (True = even($7:NeList black)) /\ True = shuffle(red $7:NeList, black, red $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black red)) /\ (True = even($7:NeList red)) /\ True = shuffle(red $7:NeList, red, red $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black black $12:NeList)) /\ (True = even($7:NeList black $12:NeList)) /\ True = shuffle(red $7:NeList, black $12:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black red $12:NeList)) /\ (True = even($7:NeList red $12:NeList)) /\ True = shuffle(red $7:NeList, red $12:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.2.1.4.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black)) /\ (True = even(black)) /\ True = shuffle(black, black, red $9:NeList) → false
Goal Id:  0.8.2.1.4.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red)) /\ (True = even(red)) /\ True = shuffle(black, red, red $9:NeList) → false
Goal Id:  0.8.2.1.4.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $10:NeList)) /\ (True = even(black $10:NeList)) /\ True = shuffle(black, black $10:NeList, red $9:NeList) → false
Goal Id:  0.8.2.1.4.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $10:NeList)) /\ (True = even(red $10:NeList)) /\ True = shuffle(black, red $10:NeList, red $9:NeList) → false
Goal Id:  0.8.2.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, black $11:NeList, $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black, black $11:NeList, black $10) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black)) /\ (True = even(black)) /\ True = shuffle(red, black, black $9:NeList) → false
Goal Id:  0.8.4.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red)) /\ (True = even(red)) /\ True = shuffle(red, red, black $9:NeList) → false
Goal Id:  0.8.4.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $10:NeList)) /\ (True = even(black $10:NeList)) /\ True = shuffle(red, black $10:NeList, black $9:NeList) → false
Goal Id:  0.8.4.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $10:NeList)) /\ (True = even(red $10:NeList)) /\ True = shuffle(red, red $10:NeList, black $9:NeList) → false
Goal Id:  0.8.4.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(red, red $11:NeList, red $10) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, red $11:NeList, $10) → True = pairedList($10)
Goal Id:  0.8.5.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black red)) /\ (True = even(black)) /\ True = shuffle(black, red, black $9:NeList) → false
Goal Id:  0.8.5.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red red)) /\ (True = even(red)) /\ True = shuffle(red, red, black $9:NeList) → false
Goal Id:  0.8.5.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $10:NeList red)) /\ (True = even(black $10:NeList)) /\ True = shuffle(black $10:NeList, red, black $9:NeList) → false
Goal Id:  0.8.5.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $10:NeList red)) /\ (True = even(red $10:NeList)) /\ True = shuffle(red $10:NeList, red, black $9:NeList) → false
Goal Id:  0.8.5.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle(red $11:NeList, red, red $10) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(red $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle(red $11:NeList, nil, $10) → True = pairedList($10)
Goal Id:  0.8.6.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black red $8:NeList)) /\ (True = even(black $8:NeList)) /\ True = shuffle(black, red $8:NeList, black $10:NeList) → false
Goal Id:  0.8.6.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red red $8:NeList)) /\ (True = even(red $8:NeList)) /\ True = shuffle(red, red $8:NeList, black $10:NeList) → false
Goal Id:  0.8.6.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $11:NeList red $8:NeList)) /\ (True = even(black $11:NeList $8:NeList)) /\ True = shuffle(black $11:NeList, red $8:NeList, black $10:NeList) → false
Goal Id:  0.8.6.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $11:NeList red $8:NeList)) /\ (True = even(red $11:NeList $8:NeList)) /\ True = shuffle(red $11:NeList, red $8:NeList, black $10:NeList) → false
Goal Id:  0.8.6.1.4.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red black)) /\ (True = even($7:NeList black)) /\ True = shuffle(black $7:NeList, black, red $10:NeList) → false
Goal Id:  0.8.6.1.4.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red red)) /\ (True = even($7:NeList red)) /\ True = shuffle(black $7:NeList, red, red $10:NeList) → false
Goal Id:  0.8.6.1.4.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red black $11:NeList)) /\ (True = even($7:NeList black $11:NeList)) /\ True = shuffle(black $7:NeList, black $11:NeList, red $10:NeList) → false
Goal Id:  0.8.6.1.4.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $7:NeList red red $11:NeList)) /\ (True = even($7:NeList red $11:NeList)) /\ True = shuffle(black $7:NeList, red $11:NeList, red $10:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList black)) /\ True = shuffle(black $7:NeList, black, black $11) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ (True = paired(black, black)) /\ True = shuffle($13:NeList, black $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black $13:NeList, $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle($13:NeList, black $14:NeList, $15)) /\ (False = shuffle(black $13:NeList, $14:NeList, $15)) /\ (True = alter(black $13:NeList red black $14:NeList)) /\ True = even($13:NeList black $14:NeList) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $13:NeList, $14:NeList, $15)) /\ (True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle($13:NeList, black $14:NeList, $15)) /\ (True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = shuffle($13:NeList, black $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = shuffle(black $13:NeList, $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $12:NeList red $8:NeList)) /\ (True = even(black $12:NeList $8:NeList)) /\ True = shuffle(red $12:NeList, red $8:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.7.1.4.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black black)) /\ (True = even(black)) /\ True = shuffle(black, black, red $9:NeList) → false
Goal Id:  0.8.7.1.4.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red black)) /\ (True = even(red)) /\ True = shuffle(red, black, red $9:NeList) → false
Goal Id:  0.8.7.1.4.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $10:NeList black)) /\ (True = even(black $10:NeList)) /\ True = shuffle(black $10:NeList, black, red $9:NeList) → false
Goal Id:  0.8.7.1.4.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $10:NeList black)) /\ (True = even(red $10:NeList)) /\ True = shuffle(red $10:NeList, black, red $9:NeList) → false
Goal Id:  0.8.7.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, nil, $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
(True = alter(black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, black, black $10) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $10) → pairedList($10) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black black)) /\ (True = even($7:NeList black)) /\ True = shuffle(red $7:NeList, black, black $10:NeList) → false
Goal Id:  0.8.8.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black red)) /\ (True = even($7:NeList red)) /\ True = shuffle(red $7:NeList, red, black $10:NeList) → false
Goal Id:  0.8.8.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black black $11:NeList)) /\ (True = even($7:NeList black $11:NeList)) /\ True = shuffle(red $7:NeList, black $11:NeList, black $10:NeList) → false
Goal Id:  0.8.8.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $7:NeList black red $11:NeList)) /\ (True = even($7:NeList red $11:NeList)) /\ True = shuffle(red $7:NeList, red $11:NeList, black $10:NeList) → false
Goal Id:  0.8.8.1.4.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black black $8:NeList)) /\ (True = even(black $8:NeList)) /\ True = shuffle(black, black $8:NeList, red $10:NeList) → false
Goal Id:  0.8.8.1.4.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red black $8:NeList)) /\ (True = even(red $8:NeList)) /\ True = shuffle(red, black $8:NeList, red $10:NeList) → false
Goal Id:  0.8.8.1.4.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $11:NeList black $8:NeList)) /\ (True = even(black $11:NeList $8:NeList)) /\ True = shuffle(black $11:NeList, black $8:NeList, red $10:NeList) → false
Goal Id:  0.8.8.1.4.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $11:NeList black $8:NeList)) /\ (True = even(red $11:NeList $8:NeList)) /\ True = shuffle(red $11:NeList, black $8:NeList, red $10:NeList) → false
Goal Id:  0.8.8.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(black $12:NeList black $8:NeList)) /\ (True = even(black $12:NeList $8:NeList)) /\ True = shuffle(black $12:NeList, black $8:NeList, black $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black)) /\ (True = even(black $7:NeList)) /\ True = shuffle(red $7:NeList, red, red $11) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $11) → pairedList($11) ⇒ True
Goal:
(True = alter(red $7:NeList black red $12:NeList)) /\ (True = even(black $7:NeList $12:NeList)) /\ True = shuffle(red $7:NeList, red $12:NeList, red $11) → True = pairedList($11)
Goal Id:  0.8.2.1.4.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.4.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.4.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.4.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.6.1.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, black $11:NeList, black) → True = pairedList(black)
Goal Id:  0.8.2.1.6.1.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, black $11:NeList, red) → True = pairedList(red)
Goal Id:  0.8.2.1.6.1.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, black $11:NeList, black $12) → True = pairedList(black $12)
Goal Id:  0.8.2.1.6.1.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, black $11:NeList, red $12) → True = pairedList(red $12)
Goal Id:  0.8.2.1.6.2.1.3.1.1
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.10
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.11
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $12:NeList, $13)) /\ (False = shuffle(nil, black $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.12
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.13
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.14
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.15
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, black $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.16
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.2
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.3
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $12:NeList, $13)) /\ (False = shuffle(nil, black $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.4
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.5
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.6
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.7
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, black $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.8
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.9
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.1
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.10
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.11
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $12:NeList, $13)) /\ (False = shuffle(red, $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.12
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.13
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.14
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.15
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, red $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.16
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.2
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.3
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $12:NeList, $13)) /\ (False = shuffle(red, $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.4
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.5
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.6
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.7
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, red $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.8
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.9
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, red $11:NeList, black) → True = pairedList(black)
Goal Id:  0.8.4.1.6.2.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, red $11:NeList, red) → True = pairedList(red)
Goal Id:  0.8.4.1.6.2.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(red $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, red $11:NeList, black $12) → True = pairedList(black $12)
Goal Id:  0.8.4.1.6.2.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, red $11:NeList, red $12) → True = pairedList(red $12)
Goal Id:  0.8.5.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.1
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.10
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.11
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList red)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.12
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.13
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.14
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.15
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.16
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.2
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.3
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList red)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.4
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.5
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.6
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.7
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.8
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.9
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle(red $11:NeList, nil, black) → True = pairedList(black)
Goal Id:  0.8.5.1.6.2.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle(red $11:NeList, nil, red) → True = pairedList(red)
Goal Id:  0.8.5.1.6.2.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, red, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(red $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle(red $11:NeList, nil, black $12) → True = pairedList(black $12)
Goal Id:  0.8.5.1.6.2.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle(red $11:NeList, nil, red $12) → True = pairedList(red $12)
Goal Id:  0.8.6.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.4.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.4.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.4.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.4.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList red)) /\ True = even($12:NeList black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList red)) /\ True = even($12:NeList black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.5.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.6.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = shuffle($13:NeList, black $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.1.1.3.8.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = shuffle(black $13:NeList, $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($13:NeList, red $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.4.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $13:NeList, $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.4.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle($13:NeList, red $14:NeList, $15)) /\ (False = shuffle(red $13:NeList, $14:NeList, $15)) /\ (True = alter(red $13:NeList red $14:NeList)) /\ True = even(black $13:NeList $14:NeList) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.4.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $13:NeList, $14:NeList, $15)) /\ (True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.4.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.4.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle($13:NeList, red $14:NeList, $15)) /\ (True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.4.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle($13:NeList, red $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.6.1.6.2.1.4.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle(red $13:NeList, $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.7.1.4.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.4.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.4.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.4.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.6.1.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, nil, black) → True = pairedList(black)
Goal Id:  0.8.7.1.6.1.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, nil, red) → True = pairedList(red)
Goal Id:  0.8.7.1.6.1.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, nil, black $12) → True = pairedList(black $12)
Goal Id:  0.8.7.1.6.1.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, black, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle(black $11:NeList, nil, red $12) → True = pairedList(red $12)
Goal Id:  0.8.7.1.6.2.1.3.1.1
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.10
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.11
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList black)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.12
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.13
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.14
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.15
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.16
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.2
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.3
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList black)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.4
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.5
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.6
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.7
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.8
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.9
Generated By:  NS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($10)
Goal Id:  0.8.8.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.4.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.4.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.4.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.4.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ (True = paired(black, black)) /\ True = shuffle($13:NeList, black $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.3.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black $13:NeList, $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.3.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle($13:NeList, black $14:NeList, $15)) /\ (False = shuffle(black $13:NeList, $14:NeList, $15)) /\ (True = alter(black $13:NeList black $14:NeList)) /\ True = even(black $13:NeList $14:NeList) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.3.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $13:NeList, $14:NeList, $15)) /\ (True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.3.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.3.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle($13:NeList, black $14:NeList, $15)) /\ (True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.3.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle($13:NeList, black $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.8.1.6.1.1.3.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle(black $13:NeList, $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList black)) /\ True = even(black $12:NeList) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList black)) /\ True = even(black $12:NeList) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($13:NeList, red $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $13:NeList, $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle($13:NeList, red $14:NeList, $15)) /\ (False = shuffle(red $13:NeList, $14:NeList, $15)) /\ (True = alter(red $13:NeList black red $14:NeList)) /\ True = even(black $13:NeList $14:NeList) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $13:NeList, $14:NeList, $15)) /\ (True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = True) /\ (False = shuffle($13:NeList, red $14:NeList, $15)) /\ (True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle($13:NeList, red $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle(red $13:NeList, $14:NeList, $15) → True = pairedList($11)
Goal Id:  0.8.2.1.6.1.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.6.1.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.6.1.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, $11:NeList, $12) → True = pairedList(black $12)
Goal Id:  0.8.2.1.6.1.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.10.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.11.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.12.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.13.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.14.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.15.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, black $12:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.2.1.6.2.1.3.1.16.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black, $12:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.2.1.6.2.1.3.1.2.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.3.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $12:NeList, $13)) /\ (False = shuffle(nil, black $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.4.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.5.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.6.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $12:NeList, $13)) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.7.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, black $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.8.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.2.1.6.2.1.3.1.9.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.10.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.11.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.12.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.13.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.14.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.15.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, red $12:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red, $12:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.2.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.3.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $12:NeList, $13)) /\ (False = shuffle(red, $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.4.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.5.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.6.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $12:NeList, $13)) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.7.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, red $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.8.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red, $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.1.1.4.1.9.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $12:NeList, $13) → True = pairedList($10)
Goal Id:  0.8.4.1.6.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.6.2.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.6.2.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.2.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red $11:NeList)) /\ (True = even(black $11:NeList)) /\ True = shuffle(nil, $11:NeList, $12) → True = pairedList(red $12)
Goal Id:  0.8.5.1.6.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.10.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.11.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.12.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.13.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.14.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.15.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($13)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($13)
Goal Id:  0.8.5.1.6.1.1.4.1.2.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.3.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList red)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.4.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.5.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.6.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.7.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.8.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.1.1.4.1.9.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($10)
Goal Id:  0.8.5.1.6.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.6.2.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.6.2.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, red, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.2.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red $11:NeList red)) /\ (True = even(black $11:NeList)) /\ True = shuffle($11:NeList, nil, $12) → True = pairedList(red $12)
Goal Id:  0.8.6.1.6.1.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($13)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($13)
Goal Id:  0.8.6.1.6.1.1.1.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList red)) /\ True = even($12:NeList black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = paired(black, black) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.1.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($11)
Goal Id:  0.8.6.1.6.1.1.3.7.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = shuffle($13:NeList, black $14:NeList, black) → True = pairedList(black)
Goal Id:  0.8.6.1.6.1.1.3.7.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = shuffle($13:NeList, black $14:NeList, red) → True = pairedList(red)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = shuffle($13:NeList, black $14:NeList, black $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black $13:NeList red black $14:NeList)) /\ (True = even($13:NeList black $14:NeList)) /\ True = shuffle($13:NeList, black $14:NeList, red $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.8.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red black black)) /\ (True = even($13:NeList black black)) /\ True = shuffle(black $13:NeList, black, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.1.1.3.8.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red black red)) /\ (True = even($13:NeList black red)) /\ True = shuffle(black $13:NeList, red, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.1.1.3.8.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red black black $16:NeList)) /\ (True = even($13:NeList black black $16:NeList)) /\ True = shuffle(black $13:NeList, black $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.1.1.3.8.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red black red $16:NeList)) /\ (True = even($13:NeList black red $16:NeList)) /\ True = shuffle(black $13:NeList, red $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.5.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.6.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.7.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle($13:NeList, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle(red $13:NeList, $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.7.1.6.1.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.6.1.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.6.1.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black $11:NeList black)) /\ (True = even(black $11:NeList)) /\ True = shuffle($11:NeList, nil, $12) → True = pairedList(black $12)
Goal Id:  0.8.7.1.6.1.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, black, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.10.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.11.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.12.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.13.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.14.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.15.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($13)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($13)
Goal Id:  0.8.7.1.6.2.1.3.1.2.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.3.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList black)) /\ True = even(black $12:NeList) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.4.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $12:NeList, nil, $13)) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.5.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.6.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, black, $13)) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(black, black) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.7.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.8.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black $12:NeList, nil, $13) → True = pairedList($10)
Goal Id:  0.8.7.1.6.2.1.3.1.9.1
Generated By:  LSB
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(black, black)) /\ True = shuffle($12:NeList, black, $13) → True = pairedList($10)
Goal Id:  0.8.8.1.6.1.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.5.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.6.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.7.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle($13:NeList, black $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle(black $13:NeList, $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($13)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($13)
Goal Id:  0.8.8.1.6.2.1.2.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList black)) /\ True = even(black $12:NeList) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $12:NeList, nil, $13)) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = True) /\ (False = shuffle($12:NeList, red, $13)) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = paired(red, red) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.2.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($12:NeList, red, $13) → True = pairedList($11)
Goal Id:  0.8.8.1.6.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.5.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.6.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle($13:NeList, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.8.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black red $14:NeList)) /\ (True = even(black $13:NeList $14:NeList)) /\ True = shuffle(red $13:NeList, $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, $12) → True = pairedList(black $12)
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, $12) → True = pairedList(black $12)
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black black $13:NeList)) /\ (True = even(black black $13:NeList)) /\ True = shuffle(nil, black $13:NeList, $12) → True = pairedList(black $12)
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black red $13:NeList)) /\ (True = even(black red $13:NeList)) /\ True = shuffle(nil, red $13:NeList, $12) → True = pairedList(black $12)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, black $12:NeList, black) → True = pairedList(black)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, black $12:NeList, red) → True = pairedList(red)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, black $12:NeList, black $14) → True = pairedList(black $14)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, black $12:NeList, red $14) → True = pairedList(red $14)
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(black, black, $13) → True = pairedList($13)
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(black, red, $13) → True = pairedList($13)
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black black $14:NeList)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black, black $14:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black red $14:NeList)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(black, red $14:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, red $12:NeList, black) → True = pairedList(black)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, red $12:NeList, red) → True = pairedList(red)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, red $12:NeList, black $14) → True = pairedList(black $14)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, red $12:NeList, red $14) → True = pairedList(red $14)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(red, black, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(red, red, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red black $14:NeList)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(red, black $14:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red red $14:NeList)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(red, red $14:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, $12) → True = pairedList(red $12)
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, $12) → True = pairedList(red $12)
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red black $13:NeList)) /\ (True = even(black black $13:NeList)) /\ True = shuffle(nil, black $13:NeList, $12) → True = pairedList(red $12)
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red red $13:NeList)) /\ (True = even(black red $13:NeList)) /\ True = shuffle(nil, red $13:NeList, $12) → True = pairedList(red $12)
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, red, $13) → True = pairedList($13)
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, red, $13) → True = pairedList($13)
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red black $14:NeList red)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black $14:NeList, red, $13) → True = pairedList($13)
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red red $14:NeList red)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(red $14:NeList, red, $13) → True = pairedList($13)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, black) → True = pairedList(black)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, red) → True = pairedList(red)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, red, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, black $14) → True = pairedList(black $14)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, red $14) → True = pairedList(red $14)
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, $12) → True = pairedList(red $12)
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, nil, $12) → True = pairedList(red $12)
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red black $13:NeList red)) /\ (True = even(black black $13:NeList)) /\ True = shuffle(black $13:NeList, nil, $12) → True = pairedList(red $12)
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(red red $13:NeList red)) /\ (True = even(black red $13:NeList)) /\ True = shuffle(red $13:NeList, nil, $12) → True = pairedList(red $12)
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black black red)) /\ (True = even(black black)) /\ True = shuffle(black, black, $13) → True = pairedList($13)
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black red red)) /\ (True = even(red black)) /\ True = shuffle(red, black, $13) → True = pairedList($13)
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black black $14:NeList red)) /\ (True = even(black $14:NeList black)) /\ True = shuffle(black $14:NeList, black, $13) → True = pairedList($13)
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black red $14:NeList red)) /\ (True = even(red $14:NeList black)) /\ True = shuffle(red $14:NeList, black, $13) → True = pairedList($13)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1
Generated By:  RST
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $13:NeList) → True = pairedList($13:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(black black red black $14:NeList)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black, black $14:NeList, black $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(black red red black $14:NeList)) /\ (True = even(red black $14:NeList)) /\ True = shuffle(red, black $14:NeList, black $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(black black $17:NeList red black $14:NeList)) /\ (True = even(black $17:NeList black $14:NeList)) /\ True = shuffle(black $17:NeList, black $14:NeList, black $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(black red $17:NeList red black $14:NeList)) /\ (True = even(red $17:NeList black $14:NeList)) /\ True = shuffle(red $17:NeList, black $14:NeList, black $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black black red black $14:NeList)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black, black $14:NeList, red $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black red red black $14:NeList)) /\ (True = even(red black $14:NeList)) /\ True = shuffle(red, black $14:NeList, red $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black black $17:NeList red black $14:NeList)) /\ (True = even(black $17:NeList black $14:NeList)) /\ True = shuffle(black $17:NeList, black $14:NeList, red $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black red $17:NeList red black $14:NeList)) /\ (True = even(red $17:NeList black $14:NeList)) /\ True = shuffle(red $17:NeList, black $14:NeList, red $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.8.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.8.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red)) /\ (True = even($13:NeList)) /\ True = shuffle(black $13:NeList, red, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.1.1.3.8.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.8.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList red $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(black $13:NeList, red $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red black red $14:NeList)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red red red $14:NeList)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(red, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red black $16:NeList red $14:NeList)) /\ (True = even(black black $16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red red $16:NeList red $14:NeList)) /\ (True = even(black red $16:NeList $14:NeList)) /\ True = shuffle(red $16:NeList, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red black)) /\ (True = even(black $13:NeList black)) /\ True = shuffle(red $13:NeList, black, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red red)) /\ (True = even(black $13:NeList red)) /\ True = shuffle(red $13:NeList, red, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red black $16:NeList)) /\ (True = even(black $13:NeList black $16:NeList)) /\ True = shuffle(red $13:NeList, black $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red red $16:NeList)) /\ (True = even(black $13:NeList red $16:NeList)) /\ True = shuffle(red $13:NeList, red $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, $12) → True = pairedList(black $12)
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black red black)) /\ (True = even(black red)) /\ True = shuffle(red, nil, $12) → True = pairedList(black $12)
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black black $13:NeList black)) /\ (True = even(black black $13:NeList)) /\ True = shuffle(black $13:NeList, nil, $12) → True = pairedList(black $12)
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(black red $13:NeList black)) /\ (True = even(black red $13:NeList)) /\ True = shuffle(red $13:NeList, nil, $12) → True = pairedList(black $12)
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, black, $13) → True = pairedList($13)
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black red black)) /\ (True = even(black red)) /\ True = shuffle(red, black, $13) → True = pairedList($13)
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black black $14:NeList black)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black $14:NeList, black, $13) → True = pairedList($13)
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black red $14:NeList black)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(red $14:NeList, black, $13) → True = pairedList($13)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black $12:NeList, nil, black) → True = pairedList(black)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black $12:NeList, nil, red) → True = pairedList(red)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black $12:NeList, nil, black $14) → True = pairedList(black $14)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, black, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(black $12:NeList, nil, red $14) → True = pairedList(red $14)
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black black black $14:NeList)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black, black $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black red black $14:NeList)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(red, black $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black black $16:NeList black $14:NeList)) /\ (True = even(black black $16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, black $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black red $16:NeList black $14:NeList)) /\ (True = even(black red $16:NeList $14:NeList)) /\ True = shuffle(red $16:NeList, black $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black black)) /\ (True = even(black $13:NeList black)) /\ True = shuffle(black $13:NeList, black, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black red)) /\ (True = even(black $13:NeList red)) /\ True = shuffle(black $13:NeList, red, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black black $16:NeList)) /\ (True = even(black $13:NeList black $16:NeList)) /\ True = shuffle(black $13:NeList, black $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black red $16:NeList)) /\ (True = even(black $13:NeList red $16:NeList)) /\ True = shuffle(black $13:NeList, red $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red black black)) /\ (True = even(black black)) /\ True = shuffle(black, red, $13) → True = pairedList($13)
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red red black)) /\ (True = even(black red)) /\ True = shuffle(red, red, $13) → True = pairedList($13)
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red black $14:NeList black)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black $14:NeList, red, $13) → True = pairedList($13)
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red red $14:NeList black)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(red $14:NeList, red, $13) → True = pairedList($13)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1
Generated By:  RST
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $13:NeList) → True = pairedList($13:NeList)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red black black red $14:NeList)) /\ (True = even(black black $14:NeList)) /\ True = shuffle(black, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red red black red $14:NeList)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(red, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red black $16:NeList black red $14:NeList)) /\ (True = even(black black $16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red red $16:NeList black red $14:NeList)) /\ (True = even(black red $16:NeList $14:NeList)) /\ True = shuffle(red $16:NeList, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black red black)) /\ (True = even(black $13:NeList black)) /\ True = shuffle(red $13:NeList, black, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black red red)) /\ (True = even(black $13:NeList red)) /\ True = shuffle(red $13:NeList, red, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black red black $16:NeList)) /\ (True = even(black $13:NeList black $16:NeList)) /\ True = shuffle(red $13:NeList, black $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black red red $16:NeList)) /\ (True = even(black $13:NeList red $16:NeList)) /\ True = shuffle(red $13:NeList, red $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
True = shuffle(nil, red, $12) → True = pairedList(black $12)
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(red $13:NeList)) /\ (True = even($13:NeList)) /\ True = shuffle(nil, red $13:NeList, $12) → True = pairedList(black $12)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, $12:NeList, $14) → True = pairedList(black $14)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
True = shuffle(black, red, $13) → True = pairedList($13)
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $14:NeList)) /\ (True = even($14:NeList)) /\ True = shuffle(black, red $14:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red $12:NeList)) /\ (True = even(black $12:NeList)) /\ True = shuffle(nil, $12:NeList, $14) → True = pairedList(red $14)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
True = shuffle(red, black, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $14:NeList)) /\ (True = even($14:NeList)) /\ True = shuffle(red, black $14:NeList, $13) → True = pairedList($13)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
True = shuffle(nil, black, $12) → True = pairedList(red $12)
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(black $13:NeList)) /\ (True = even($13:NeList)) /\ True = shuffle(nil, black $13:NeList, $12) → True = pairedList(red $12)
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
True = shuffle(black, red, $13) → True = pairedList($13)
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $14:NeList red)) /\ (True = even($14:NeList)) /\ True = shuffle(black $14:NeList, red, $13) → True = pairedList($13)
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, red, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red $12:NeList red)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, nil, $14) → True = pairedList(red $14)
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
True = shuffle(black, nil, $12) → True = pairedList(red $12)
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
(True = alter(black $13:NeList red)) /\ (True = even($13:NeList)) /\ True = shuffle(black $13:NeList, nil, $12) → True = pairedList(red $12)
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $14:NeList red)) /\ (True = even($14:NeList)) /\ True = shuffle(red $14:NeList, black, $13) → True = pairedList($13)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $14:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $14:Card $14:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired($14:Card, $15:Card)) /\ True = shuffle(black $12:NeList, nil, $14:Card $15:Card) → True = pairedList(nil)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $14:Card $14:Card $15:NeList) → False = True
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $14:Card $14:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6
Generated By:  NI
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired($14, $15)) /\ True = shuffle(black $12:NeList, nil, $14 $15 $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ (True = paired($14:Card, $15:Card)) /\ True = shuffle(black $12:NeList, nil, $14:Card $15:Card) → True = pairedList(nil)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red black $14:NeList)) /\ (True = even($17:NeList $14:NeList)) /\ True = shuffle(red $17:NeList, $14:NeList, $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(red $17:NeList red black $14:NeList)) /\ (True = even($17:NeList $14:NeList)) /\ True = shuffle($17:NeList, black $14:NeList, $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.8.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.8.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $14:NeList)) /\ (True = even($14:NeList)) /\ True = shuffle(black, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $16:NeList red $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red)) /\ (True = even($13:NeList)) /\ True = shuffle(red $13:NeList, black, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList red black $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(red $13:NeList, black $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
True = shuffle(red, nil, $12) → True = pairedList(black $12)
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
(True = alter(red $13:NeList black)) /\ (True = even($13:NeList)) /\ True = shuffle(red $13:NeList, nil, $12) → True = pairedList(black $12)
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
True = shuffle(red, black, $13) → True = pairedList($13)
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(red $14:NeList black)) /\ (True = even($14:NeList)) /\ True = shuffle(red $14:NeList, black, $13) → True = pairedList($13)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, nil, $14) → True = pairedList(black $14)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle($7:NeList, black, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $14:NeList)) /\ (True = even($14:NeList)) /\ True = shuffle(red, black $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $16:NeList black $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle(red $16:NeList, black $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black)) /\ (True = even($13:NeList)) /\ True = shuffle(black $13:NeList, red, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $13:NeList black red $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(black $13:NeList, red $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
(True = alter(black $14:NeList black)) /\ (True = even($14:NeList)) /\ True = shuffle(black $14:NeList, red, $13) → True = pairedList($13)
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $14:Card) → False = True
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $14:Card $14:Card) → False = True
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired($14:Card, $15:Card)) /\ True = shuffle(red $12:NeList, nil, $14:Card $15:Card) → True = pairedList(nil)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $14:Card $14:Card $15:NeList) → False = True
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $14:Card $14:Card) → False = True
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6
Generated By:  NI
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired($14, $15)) /\ True = shuffle(red $12:NeList, nil, $14 $15 $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ (True = paired($14:Card, $15:Card)) /\ True = shuffle(red $12:NeList, nil, $14:Card $15:Card) → True = pairedList(nil)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(black $16:NeList black red $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, red $14:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black)) /\ (True = even($13:NeList)) /\ True = shuffle(red $13:NeList, black, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
(True = alter(red $13:NeList black $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(red $13:NeList, black $16:NeList, $15) → True = pairedList($15)
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.1.1.3.1.3.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, $14) → True = pairedList(black $14)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, $14) → True = pairedList(black $14)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black black $15:NeList)) /\ (True = even(black black $15:NeList)) /\ True = shuffle(nil, black $15:NeList, $14) → True = pairedList(black $14)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black red $15:NeList)) /\ (True = even(black red $15:NeList)) /\ True = shuffle(nil, red $15:NeList, $14) → True = pairedList(black $14)
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.16.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(black, red $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, $14) → True = pairedList(red $14)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, $14) → True = pairedList(red $14)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red black $15:NeList)) /\ (True = even(black black $15:NeList)) /\ True = shuffle(nil, black $15:NeList, $14) → True = pairedList(red $14)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red red $15:NeList)) /\ (True = even(black red $15:NeList)) /\ True = shuffle(nil, red $15:NeList, $14) → True = pairedList(red $14)
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.16.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(red, black $7:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.2.1.4.1.4.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.15.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, red, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, $14) → True = pairedList(red $14)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, nil, $14) → True = pairedList(red $14)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red black $15:NeList red)) /\ (True = even(black black $15:NeList)) /\ True = shuffle(black $15:NeList, nil, $14) → True = pairedList(red $14)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(red red $15:NeList red)) /\ (True = even(black red $15:NeList)) /\ True = shuffle(red $15:NeList, nil, $14) → True = pairedList(red $14)
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.2.1.4.1.4.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ red $12
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $12) → pairedList(red $12) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.15.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $13
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $14:Card $14:Card) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $14:Card $14:Card $15:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $14:Card $14:Card) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1
Generated By:  CVUL
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, black red $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.2
Generated By:  CVUL
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, red black $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red black black)) /\ (True = even($17:NeList black)) /\ True = shuffle(red $17:NeList, black, $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red black red)) /\ (True = even($17:NeList red)) /\ True = shuffle(red $17:NeList, red, $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red black black $18:NeList)) /\ (True = even($17:NeList black $18:NeList)) /\ True = shuffle(red $17:NeList, black $18:NeList, $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red black red $18:NeList)) /\ (True = even($17:NeList red $18:NeList)) /\ True = shuffle(red $17:NeList, red $18:NeList, $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(red black red black $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(black, black $14:NeList, $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(red red red black $14:NeList)) /\ (True = even(red $14:NeList)) /\ True = shuffle(red, black $14:NeList, $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(red black $18:NeList red black $14:NeList)) /\ (True = even(black $18:NeList $14:NeList)) /\ True = shuffle(black $18:NeList, black $14:NeList, $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(red red $18:NeList red black $14:NeList)) /\ (True = even(red $18:NeList $14:NeList)) /\ True = shuffle(red $18:NeList, black $14:NeList, $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.7.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, red $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $13:NeList red black $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(red $13:NeList, black $16:NeList, black) → True = pairedList(black)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $13:NeList red black $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(red $13:NeList, black $16:NeList, red) → True = pairedList(red)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red black $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(red $13:NeList, black $16:NeList, black $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(red $13:NeList red black $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(red $13:NeList, black $16:NeList, red $17) → True = pairedList(red $17)
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.1.1.3.1.3.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$12.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ black $12
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $12) → pairedList(black $12) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.15.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, black, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, $14) → True = pairedList(black $14)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black red black)) /\ (True = even(black red)) /\ True = shuffle(red, nil, $14) → True = pairedList(black $14)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black black $15:NeList black)) /\ (True = even(black black $15:NeList)) /\ True = shuffle(black $15:NeList, nil, $14) → True = pairedList(black $14)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(black red $15:NeList black)) /\ (True = even(black red $15:NeList)) /\ True = shuffle(red $15:NeList, nil, $14) → True = pairedList(black $14)
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.7.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $13:NeList black red $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(black $13:NeList, red $16:NeList, black) → True = pairedList(black)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $13:NeList black red $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(black $13:NeList, red $16:NeList, red) → True = pairedList(red)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black $13:NeList black red $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(black $13:NeList, red $16:NeList, black $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black red $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(black $13:NeList, red $16:NeList, red $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.2.1.15.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$13.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $13
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $13) → pairedList($13) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $14:Card $14:Card) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $14:Card $14:Card $15:NeList) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $14:Card $14:Card) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.1
Generated By:  CVUL
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, black red $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2
Generated By:  CVUL
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, red black $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $16:NeList black red $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, red $14:NeList, black) → True = pairedList(black)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $16:NeList black red $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, red $14:NeList, red) → True = pairedList(red)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black $16:NeList black red $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, red $14:NeList, black $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black red $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, red $14:NeList, red $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.8.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, black $8:NeList, $15) → pairedList($15) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
True = shuffle(nil, red, $14) → True = pairedList(black $14)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(red $15:NeList)) /\ (True = even($15:NeList)) /\ True = shuffle(nil, red $15:NeList, $14) → True = pairedList(black $14)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
True = shuffle(nil, black, $14) → True = pairedList(red $14)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(black $15:NeList)) /\ (True = even($15:NeList)) /\ True = shuffle(nil, black $15:NeList, $14) → True = pairedList(red $14)
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
True = shuffle(black, nil, $14) → True = pairedList(red $14)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
(True = alter(black $15:NeList red)) /\ (True = even($15:NeList)) /\ True = shuffle(black $15:NeList, nil, $14) → True = pairedList(red $14)
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, black black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, red red) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, black black $15:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, red red $15:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, black black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, red red) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle($12:NeList, nil, red $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.2.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red)) /\ (True = even(black $17:NeList)) /\ True = shuffle(red $17:NeList, red, $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red $18:NeList)) /\ (True = even(black $17:NeList $18:NeList)) /\ True = shuffle(red $17:NeList, red $18:NeList, $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(black, black $14:NeList, $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black $18:NeList red black $14:NeList)) /\ (True = even(black $18:NeList $14:NeList)) /\ True = shuffle(black $18:NeList, black $14:NeList, $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red black $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(red $13:NeList, $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(red $13:NeList red black $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle($13:NeList, black $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
True = shuffle(red, nil, $14) → True = pairedList(black $14)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
(True = alter(red $15:NeList black)) /\ (True = even($15:NeList)) /\ True = shuffle(red $15:NeList, nil, $14) → True = pairedList(black $14)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black $13:NeList black red $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle($13:NeList, red $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black red $16:NeList)) /\ (True = even($13:NeList $16:NeList)) /\ True = shuffle(black $13:NeList, $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, black black) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, red red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, black black $15:NeList) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, red red $15:NeList) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, black black) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, red red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.1.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, nil, black $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black $16:NeList black red $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle($16:NeList, red $14:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black red $14:NeList)) /\ (True = even($16:NeList $14:NeList)) /\ True = shuffle(black $16:NeList, $14:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.2.1.6.2.1.3.1.15.1.3.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, red $7:NeList, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.4.1.6.1.1.4.1.15.1.4.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList)) /\ (True = even($7:NeList)) /\ True = shuffle(nil, black $7:NeList, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.5.1.6.1.1.4.1.16.1.4.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ red $14
$8 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red)) /\ (True = even($7:NeList)) /\ True = shuffle(black $7:NeList, nil, $14) → pairedList(red $14) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle($12:NeList, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle($12:NeList, nil, black $15:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle($12:NeList, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, red $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black red red)) /\ (True = even(red black)) /\ True = shuffle(red, nil, red $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black black $17:NeList red)) /\ (True = even(black $17:NeList black)) /\ True = shuffle(black $17:NeList, nil, red $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black red $17:NeList red)) /\ (True = even(red $17:NeList black)) /\ True = shuffle(red $17:NeList, nil, red $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $17:NeList red)) /\ (True = even(black $17:NeList)) /\ True = shuffle(red $17:NeList, red, black) → True = pairedList(black black)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $17:NeList red)) /\ (True = even(black $17:NeList)) /\ True = shuffle(red $17:NeList, red, red) → True = pairedList(black red)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ black $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, black $18) → false
Goal:
(True = alter(red $17:NeList red)) /\ (True = even(black $17:NeList)) /\ True = shuffle(red $17:NeList, red, black $18) → True = pairedList(black black $18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $18) → pairedList($18) ⇒ True
Goal:
(True = alter(red $17:NeList red)) /\ (True = even(black $17:NeList)) /\ True = shuffle(red $17:NeList, red, red $18) → True = pairedList(black red $18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.4.1.1
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red $18:NeList)) /\ (True = even(black $17:NeList $18:NeList)) /\ True = shuffle(red $17:NeList, red $18:NeList, $16) → (True = alter(black red $17:NeList red $18:NeList)) /\ True = even(red $17:NeList $18:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.4.1.2
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
(True = alter(red $17:NeList red $18:NeList)) /\ (True = alter(black red $17:NeList red $18:NeList)) /\ (True = even(black $17:NeList $18:NeList)) /\ (True = even(red $17:NeList $18:NeList)) /\ True = shuffle(red $17:NeList, red $18:NeList, $16) → True = pairedList(black $16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(black, black $14:NeList, black) → True = pairedList(red black)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(black, black $14:NeList, red) → True = pairedList(red red)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $18) → pairedList($18) ⇒ True
Goal:
(True = alter(black $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(black, black $14:NeList, black $18) → True = pairedList(red black $18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ red $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, red $18) → false
Goal:
(True = alter(black $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(black, black $14:NeList, red $18) → True = pairedList(red red $18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black $18:NeList red black $14:NeList)) /\ (True = even(black $18:NeList $14:NeList)) /\ True = shuffle(black $18:NeList, black $14:NeList, $16) → True = even($18:NeList black $14:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.2
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black $18:NeList red black $14:NeList)) /\ (True = even(black $18:NeList $14:NeList)) /\ (True = even($18:NeList black $14:NeList)) /\ True = shuffle(black $18:NeList, black $14:NeList, $16) → True = pairedList(red $16)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red black black)) /\ (True = even($13:NeList black)) /\ True = shuffle(red $13:NeList, black, $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red black red)) /\ (True = even($13:NeList red)) /\ True = shuffle(red $13:NeList, red, $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red black black $18:NeList)) /\ (True = even($13:NeList black $18:NeList)) /\ True = shuffle(red $13:NeList, black $18:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red black red $18:NeList)) /\ (True = even($13:NeList red $18:NeList)) /\ True = shuffle(red $13:NeList, red $18:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(red black red black $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(black, black $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(red red red black $16:NeList)) /\ (True = even(red $16:NeList)) /\ True = shuffle(red, black $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(red black $18:NeList red black $16:NeList)) /\ (True = even(black $18:NeList $16:NeList)) /\ True = shuffle(black $18:NeList, black $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(red red $18:NeList red black $16:NeList)) /\ (True = even(red $18:NeList $16:NeList)) /\ True = shuffle(red $18:NeList, black $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.7.1.6.2.1.3.1.16.1.3.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.NeList
$13.NeList
$14.NeList
$8.Card
$9.Card
Executable Hypotheses:
$10 ⇒ $13
$13 ⇒ black $14
$8 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black)) /\ (True = even($7:NeList)) /\ True = shuffle(red $7:NeList, nil, $14) → pairedList(black $14) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black black black red $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(black, red $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black red black red $16:NeList)) /\ (True = even(red $16:NeList)) /\ True = shuffle(red, red $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black black $18:NeList black red $16:NeList)) /\ (True = even(black $18:NeList $16:NeList)) /\ True = shuffle(black $18:NeList, red $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black red $18:NeList black red $16:NeList)) /\ (True = even(red $18:NeList $16:NeList)) /\ True = shuffle(red $18:NeList, red $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black red black)) /\ (True = even($13:NeList black)) /\ True = shuffle(black $13:NeList, black, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black red red)) /\ (True = even($13:NeList red)) /\ True = shuffle(black $13:NeList, red, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black red black $18:NeList)) /\ (True = even($13:NeList black $18:NeList)) /\ True = shuffle(black $13:NeList, black $18:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black red red $18:NeList)) /\ (True = even($13:NeList red $18:NeList)) /\ True = shuffle(black $13:NeList, red $18:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, nil, red $15:NeList) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle($12:NeList, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, black $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red red black)) /\ (True = even(black red)) /\ True = shuffle(red, nil, black $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red black $17:NeList black)) /\ (True = even(black black $17:NeList)) /\ True = shuffle(black $17:NeList, nil, black $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red red $17:NeList black)) /\ (True = even(black red $17:NeList)) /\ True = shuffle(red $17:NeList, nil, black $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black black black red $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(black, red $14:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black red black red $14:NeList)) /\ (True = even(red $14:NeList)) /\ True = shuffle(red, red $14:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black black $18:NeList black red $14:NeList)) /\ (True = even(black $18:NeList $14:NeList)) /\ True = shuffle(black $18:NeList, red $14:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(black red $18:NeList black red $14:NeList)) /\ (True = even(red $18:NeList $14:NeList)) /\ True = shuffle(red $18:NeList, red $14:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black red black)) /\ (True = even($16:NeList black)) /\ True = shuffle(black $16:NeList, black, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black red red)) /\ (True = even($16:NeList red)) /\ True = shuffle(black $16:NeList, red, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black red black $18:NeList)) /\ (True = even($16:NeList black $18:NeList)) /\ True = shuffle(black $16:NeList, black $18:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black red red $18:NeList)) /\ (True = even($16:NeList red $18:NeList)) /\ True = shuffle(black $16:NeList, red $18:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red red)) /\ (True = even(red black)) /\ True = shuffle(red, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $15:NeList red)) /\ (True = even(black $15:NeList black)) /\ True = shuffle(black $15:NeList, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $15:NeList red)) /\ (True = even(red $15:NeList black)) /\ True = shuffle(red $15:NeList, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, black $15:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red red)) /\ (True = even(red black)) /\ True = shuffle(red, nil, black $15:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $16:NeList red)) /\ (True = even(black $16:NeList black)) /\ True = shuffle(black $16:NeList, nil, black $15:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $16:NeList red)) /\ (True = even(red $16:NeList black)) /\ True = shuffle(red $16:NeList, nil, black $15:NeList) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red red)) /\ (True = even(red black)) /\ True = shuffle(red, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $15:NeList red)) /\ (True = even(black $15:NeList black)) /\ True = shuffle(black $15:NeList, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $15:NeList red)) /\ (True = even(red $15:NeList black)) /\ True = shuffle(red $15:NeList, nil, black) → false
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.3.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(red $17:NeList red)) /\ (True = even($17:NeList)) /\ True = shuffle($17:NeList, nil, $16) → True = pairedList($16)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ black $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, black $18) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $18) → pairedList($18) ⇒ True
Goal:
(True = alter(red $17:NeList red)) /\ (True = even(black $17:NeList)) /\ True = shuffle(red $17:NeList, red, red $18) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.4.1.2.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $16) → pairedList(black $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $18) → pairedList($18) ⇒ True
Goal:
(True = alter(black $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(black, black $14:NeList, black $18) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ red $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, red $18) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black red red black $14:NeList)) /\ (True = even(black red $14:NeList)) /\ True = shuffle(black red, black $14:NeList, $16) → True = even(red black $14:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black black $19:NeList red black $14:NeList)) /\ (True = even(black black $19:NeList $14:NeList)) /\ True = shuffle(black black $19:NeList, black $14:NeList, $16) → True = even(black $19:NeList black $14:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
(True = alter(black red $19:NeList red black $14:NeList)) /\ (True = even(black red $19:NeList $14:NeList)) /\ True = shuffle(black red $19:NeList, black $14:NeList, $16) → True = even(red $19:NeList black $14:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.2.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red)) /\ (True = even(black $13:NeList)) /\ True = shuffle(red $13:NeList, red, $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red $18:NeList)) /\ (True = even(black $13:NeList $18:NeList)) /\ True = shuffle(red $13:NeList, red $18:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(black, black $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $18:NeList red black $16:NeList)) /\ (True = even(black $18:NeList $16:NeList)) /\ True = shuffle(black $18:NeList, black $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(red, red $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $18:NeList black red $16:NeList)) /\ (True = even(black $18:NeList $16:NeList)) /\ True = shuffle(red $18:NeList, red $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black)) /\ (True = even($13:NeList black)) /\ True = shuffle(black $13:NeList, black, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black $18:NeList)) /\ (True = even($13:NeList black $18:NeList)) /\ True = shuffle(black $13:NeList, black $18:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red black)) /\ (True = even(black red)) /\ True = shuffle(red, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $15:NeList black)) /\ (True = even(black black $15:NeList)) /\ True = shuffle(black $15:NeList, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $15:NeList black)) /\ (True = even(black red $15:NeList)) /\ True = shuffle(red $15:NeList, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, red $15:NeList) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red black)) /\ (True = even(black red)) /\ True = shuffle(red, nil, red $15:NeList) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $16:NeList black)) /\ (True = even(black black $16:NeList)) /\ True = shuffle(black $16:NeList, nil, red $15:NeList) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $16:NeList black)) /\ (True = even(black red $16:NeList)) /\ True = shuffle(red $16:NeList, nil, red $15:NeList) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red black)) /\ (True = even(black red)) /\ True = shuffle(red, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $15:NeList black)) /\ (True = even(black black $15:NeList)) /\ True = shuffle(black $15:NeList, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $15:NeList black)) /\ (True = even(black red $15:NeList)) /\ True = shuffle(red $15:NeList, nil, red) → false
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
(True = alter(black $17:NeList black)) /\ (True = even($17:NeList)) /\ True = shuffle($17:NeList, nil, $16) → True = pairedList($16)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(red, red $14:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $18:NeList black red $14:NeList)) /\ (True = even(black $18:NeList $14:NeList)) /\ True = shuffle(red $18:NeList, red $14:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black)) /\ (True = even($16:NeList black)) /\ True = shuffle(black $16:NeList, black, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black $18:NeList)) /\ (True = even($16:NeList black $18:NeList)) /\ True = shuffle(black $16:NeList, black $18:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.2.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.5.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.1.1.16.1.1.6.1.1.4.1.1
Generated By:  CS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ black
$15 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $12:NeList red)) /\ (True = even($12:NeList black)) /\ True = shuffle(black $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.3.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $16) → pairedList(red $16) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $13:NeList red)) /\ (True = even(black $13:NeList)) /\ True = shuffle(red $13:NeList, red, black) → True = pairedList(black black)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $13:NeList red)) /\ (True = even(black $13:NeList)) /\ True = shuffle(red $13:NeList, red, red) → True = pairedList(black red)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, black $18) → false
Goal:
(True = alter(red $13:NeList red)) /\ (True = even(black $13:NeList)) /\ True = shuffle(red $13:NeList, red, black $18) → True = pairedList(black black $18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $18) → pairedList($18) ⇒ True
Goal:
(True = alter(red $13:NeList red)) /\ (True = even(black $13:NeList)) /\ True = shuffle(red $13:NeList, red, red $18) → True = pairedList(black red $18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.4.1.1
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red $18:NeList)) /\ (True = even(black $13:NeList $18:NeList)) /\ True = shuffle(red $13:NeList, red $18:NeList, $17) → (True = alter(black red $13:NeList red $18:NeList)) /\ True = even(red $13:NeList $18:NeList)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.4.1.2
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $13:NeList red $18:NeList)) /\ (True = alter(black red $13:NeList red $18:NeList)) /\ (True = even(black $13:NeList $18:NeList)) /\ (True = even(red $13:NeList $18:NeList)) /\ True = shuffle(red $13:NeList, red $18:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(black, black $16:NeList, black) → True = pairedList(red black)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(black, black $16:NeList, red) → True = pairedList(red red)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $18) → pairedList($18) ⇒ True
Goal:
(True = alter(black $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(black, black $16:NeList, black $18) → True = pairedList(red black $18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, red $18) → false
Goal:
(True = alter(black $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(black, black $16:NeList, red $18) → True = pairedList(red red $18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $18:NeList red black $16:NeList)) /\ (True = even(black $18:NeList $16:NeList)) /\ True = shuffle(black $18:NeList, black $16:NeList, $17) → True = even($18:NeList black $16:NeList)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.2
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $18:NeList red black $16:NeList)) /\ (True = even(black $18:NeList $16:NeList)) /\ (True = even($18:NeList black $16:NeList)) /\ True = shuffle(black $18:NeList, black $16:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(red, red $16:NeList, black) → True = pairedList(black black)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(red, red $16:NeList, red) → True = pairedList(black red)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, black $18) → false
Goal:
(True = alter(red $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(red, red $16:NeList, black $18) → True = pairedList(black black $18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $18) → pairedList($18) ⇒ True
Goal:
(True = alter(red $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(red, red $16:NeList, red $18) → True = pairedList(black red $18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.4.1.1
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $18:NeList black red $16:NeList)) /\ (True = even(black $18:NeList $16:NeList)) /\ True = shuffle(red $18:NeList, red $16:NeList, $17) → True = even($18:NeList red $16:NeList)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.4.1.2
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $18:NeList black red $16:NeList)) /\ (True = even(black $18:NeList $16:NeList)) /\ (True = even($18:NeList red $16:NeList)) /\ True = shuffle(red $18:NeList, red $16:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $13:NeList black)) /\ (True = even($13:NeList black)) /\ True = shuffle(black $13:NeList, black, black) → True = pairedList(red black)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $13:NeList black)) /\ (True = even($13:NeList black)) /\ True = shuffle(black $13:NeList, black, red) → True = pairedList(red red)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $18) → pairedList($18) ⇒ True
Goal:
(True = alter(black $13:NeList black)) /\ (True = even($13:NeList black)) /\ True = shuffle(black $13:NeList, black, black $18) → True = pairedList(red black $18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, red $18) → false
Goal:
(True = alter(black $13:NeList black)) /\ (True = even($13:NeList black)) /\ True = shuffle(black $13:NeList, black, red $18) → True = pairedList(red red $18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black $18:NeList)) /\ (True = even($13:NeList black $18:NeList)) /\ True = shuffle(black $13:NeList, black $18:NeList, $17) → (True = alter(red black $13:NeList black $18:NeList)) /\ True = even(black $13:NeList $18:NeList)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.2
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black $18:NeList)) /\ (True = alter(red black $13:NeList black $18:NeList)) /\ (True = even(black $13:NeList $18:NeList)) /\ (True = even($13:NeList black $18:NeList)) /\ True = shuffle(black $13:NeList, black $18:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.2.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.4.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.5.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.2.1.16.1.1.6.2.1.3.1.1
Generated By:  CS
Skolem Ops:
$14.Card
$15.Card
$16.NeList
Executable Hypotheses:
$14 ⇒ red
$15 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $12:NeList black)) /\ (True = even(black $12:NeList)) /\ True = shuffle(red $12:NeList, nil, $16) → pairedList($16) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(red, red $14:NeList, black) → True = pairedList(black black)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(red, red $14:NeList, red) → True = pairedList(black red)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, black $18) → false
Goal:
(True = alter(red $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(red, red $14:NeList, black $18) → True = pairedList(black black $18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $18) → pairedList($18) ⇒ True
Goal:
(True = alter(red $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(red, red $14:NeList, red $18) → True = pairedList(black red $18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.4.1.1
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $18:NeList black red $14:NeList)) /\ (True = even(black $18:NeList $14:NeList)) /\ True = shuffle(red $18:NeList, red $14:NeList, $17) → True = even($18:NeList red $14:NeList)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.4.1.2
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
(True = alter(red $18:NeList black red $14:NeList)) /\ (True = even(black $18:NeList $14:NeList)) /\ (True = even($18:NeList red $14:NeList)) /\ True = shuffle(red $18:NeList, red $14:NeList, $17) → True = pairedList(black $17)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $16:NeList black)) /\ (True = even($16:NeList black)) /\ True = shuffle(black $16:NeList, black, black) → True = pairedList(red black)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $16:NeList black)) /\ (True = even($16:NeList black)) /\ True = shuffle(black $16:NeList, black, red) → True = pairedList(red red)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $18) → pairedList($18) ⇒ True
Goal:
(True = alter(black $16:NeList black)) /\ (True = even($16:NeList black)) /\ True = shuffle(black $16:NeList, black, black $18) → True = pairedList(red black $18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, red $18) → false
Goal:
(True = alter(black $16:NeList black)) /\ (True = even($16:NeList black)) /\ True = shuffle(black $16:NeList, black, red $18) → True = pairedList(red red $18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black $18:NeList)) /\ (True = even($16:NeList black $18:NeList)) /\ True = shuffle(black $16:NeList, black $18:NeList, $17) → (True = alter(red black $16:NeList black $18:NeList)) /\ True = even(black $16:NeList $18:NeList)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.2
Generated By:  CUT
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black $18:NeList)) /\ (True = alter(red black $16:NeList black $18:NeList)) /\ (True = even(black $16:NeList $18:NeList)) /\ (True = even($16:NeList black $18:NeList)) /\ True = shuffle(black $16:NeList, black $18:NeList, $17) → True = pairedList(red $17)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, black $18) → false
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $18) → pairedList($18) ⇒ True
Goal:
(True = alter(red $13:NeList red)) /\ (True = even(black $13:NeList)) /\ True = shuffle(red $13:NeList, red, red $18) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.4.1.2.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $18) → pairedList($18) ⇒ True
Goal:
(True = alter(black $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(black, black $16:NeList, black $18) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, red $18) → false
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black red red black $16:NeList)) /\ (True = even(black red $16:NeList)) /\ True = shuffle(black red, black $16:NeList, $17) → True = even(red black $16:NeList)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black black $19:NeList red black $16:NeList)) /\ (True = even(black black $19:NeList $16:NeList)) /\ True = shuffle(black black $19:NeList, black $16:NeList, $17) → True = even(black $19:NeList black $16:NeList)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black red $19:NeList red black $16:NeList)) /\ (True = even(black red $19:NeList $16:NeList)) /\ True = shuffle(black red $19:NeList, black $16:NeList, $17) → True = even(red $19:NeList black $16:NeList)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.2.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, black $18) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $18) → pairedList($18) ⇒ True
Goal:
(True = alter(red $16:NeList)) /\ (True = even(black $16:NeList)) /\ True = shuffle(red, red $16:NeList, red $18) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.4.1.2.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $18) → pairedList($18) ⇒ True
Goal:
(True = alter(black $13:NeList black)) /\ (True = even($13:NeList black)) /\ True = shuffle(black $13:NeList, black, black $18) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red $18
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, red $18) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $13:NeList black $18:NeList)) /\ (True = even($13:NeList black $18:NeList)) /\ True = shuffle(black $13:NeList, black $18:NeList, $17) → True = even(black $13:NeList $18:NeList)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.2.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ black $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, black $18) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $18) → pairedList($18) ⇒ True
Goal:
(True = alter(red $14:NeList)) /\ (True = even(black $14:NeList)) /\ True = shuffle(red, red $14:NeList, red $18) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.4.1.2.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, $17) → pairedList(black $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $18) → pairedList($18) ⇒ True
Goal:
(True = alter(black $16:NeList black)) /\ (True = even($16:NeList black)) /\ True = shuffle(black $16:NeList, black, black $18) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ red $18
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, red $18) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black $16:NeList black $18:NeList)) /\ (True = even($16:NeList black $18:NeList)) /\ True = shuffle(black $16:NeList, black $18:NeList, $17) → True = even(black $16:NeList $18:NeList)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.2.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red black $21:NeList red)) /\ (True = even(black black $21:NeList)) /\ True = shuffle(black $21:NeList, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red red $21:NeList red)) /\ (True = even(black red $21:NeList)) /\ True = shuffle(red $21:NeList, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1
Generated By:  RST
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20:NeList) → True = pairedList($20:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1
Generated By:  RST
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20:NeList) → True = pairedList($20:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(black, black, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(black, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black black $21:NeList)) /\ (True = even(black black $21:NeList)) /\ True = shuffle(black, black $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black red $21:NeList)) /\ (True = even(black red $21:NeList)) /\ True = shuffle(black, red $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.3.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ True = even($19:NeList black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ True = even($19:NeList black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black red black $18:NeList)) /\ (True = even(red black $18:NeList)) /\ True = shuffle(black red, black $18:NeList, $17) → True = even(black red $18:NeList)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black black $19:NeList black $18:NeList)) /\ (True = even(black $19:NeList black $18:NeList)) /\ True = shuffle(black black $19:NeList, black $18:NeList, $17) → True = even(black black $19:NeList $18:NeList)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black red $19:NeList black $18:NeList)) /\ (True = even(red $19:NeList black $18:NeList)) /\ True = shuffle(black red $19:NeList, black $18:NeList, $17) → True = even(black red $19:NeList $18:NeList)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.1
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.10
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.11
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ True = even($19:NeList black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.12
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.13
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.14
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.16
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.2
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.3
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ True = even($19:NeList black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.4
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.5
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.6
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.7
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.8
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.9
Generated By:  NS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black red black $18:NeList)) /\ (True = even(red black $18:NeList)) /\ True = shuffle(black red, black $18:NeList, $17) → True = even(black red $18:NeList)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black black $19:NeList black $18:NeList)) /\ (True = even(black $19:NeList black $18:NeList)) /\ True = shuffle(black black $19:NeList, black $18:NeList, $17) → True = even(black black $19:NeList $18:NeList)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
(True = alter(black red $19:NeList black $18:NeList)) /\ (True = even(red $19:NeList black $18:NeList)) /\ True = shuffle(black red $19:NeList, black $18:NeList, $17) → True = even(black red $19:NeList $18:NeList)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
True = shuffle(black, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $21:NeList red)) /\ (True = even($21:NeList)) /\ True = shuffle(black $21:NeList, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $21:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $21:Card $21:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired($21:Card, $22:Card)) /\ True = shuffle(red $19:NeList, nil, $21:Card $22:Card) → True = pairedList(nil)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $21:Card $21:Card $22:NeList) → False = True
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $21:Card $21:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6
Generated By:  NI
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired($21, $22)) /\ True = shuffle(red $19:NeList, nil, $21 $22 $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired($21:Card, $22:Card)) /\ True = shuffle(red $19:NeList, nil, $21:Card $22:Card) → True = pairedList(nil)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $21:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $21:Card $21:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired($21:Card, $22:Card)) /\ True = shuffle(nil, black $19:NeList, $21:Card $22:Card) → True = pairedList(nil)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $21:Card $21:Card $22:NeList) → False = True
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $21:Card $21:Card) → False = True
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6
Generated By:  NI
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired($21, $22)) /\ True = shuffle(nil, black $19:NeList, $21 $22 $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired($21:Card, $22:Card)) /\ True = shuffle(nil, black $19:NeList, $21:Card $22:Card) → True = pairedList(nil)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
True = shuffle(black, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $21:NeList)) /\ (True = even($21:NeList)) /\ True = shuffle(black, red $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red $19:NeList, nil, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, red, $20)) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle($19:NeList, red, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black, $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, black $19:NeList, $20)) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(black, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(black, black)) /\ True = shuffle(nil, black $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ True = even($19:NeList black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.3.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ True = even(black $19:NeList) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(red, $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(nil, red $19:NeList, $20)) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = paired(red, red) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(False = paired(red, red)) /\ (True = True) /\ (True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red, $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired(red, red)) /\ True = shuffle(nil, red $19:NeList, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.10.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.11.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.12.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.13.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.14.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.16.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.2.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.3.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ True = even($19:NeList black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.4.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle(black $19:NeList, nil, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.5.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.6.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = True) /\ (False = shuffle($19:NeList, black, $20)) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = paired(black, black) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.7.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.8.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(False = paired(black, black)) /\ (True = True) /\ (True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.9.1
Generated By:  LSB
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired(black, black)) /\ True = shuffle($19:NeList, black, $20) → True = pairedList($18)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.3.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, $17) → pairedList(red $17) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.15.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $16
$16 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $21:Card $21:Card) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $21:Card $21:Card $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $21:Card $21:Card) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.1
Generated By:  CVUL
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, black red $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2
Generated By:  CVUL
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, red black $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $21:Card $21:Card) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $21:Card $21:Card $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $21:Card $21:Card) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1
Generated By:  CVUL
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, black red $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.2
Generated By:  CVUL
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, red black $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.16.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$16.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $16
$16 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red black $21:NeList red)) /\ (True = even(black black $21:NeList)) /\ True = shuffle(black $21:NeList, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red red $21:NeList red)) /\ (True = even(black red $21:NeList)) /\ True = shuffle(red $21:NeList, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.16.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.15.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(black, black, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(black, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black black $21:NeList)) /\ (True = even(black black $21:NeList)) /\ True = shuffle(black, black $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black red $21:NeList)) /\ (True = even(black red $21:NeList)) /\ True = shuffle(black, red $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1
Generated By:  RST
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $20:NeList) → True = pairedList($20:NeList)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(red, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(red, red, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red black $21:NeList)) /\ (True = even(black black $21:NeList)) /\ True = shuffle(red, black $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red red $21:NeList)) /\ (True = even(black red $21:NeList)) /\ True = shuffle(red, red $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black red black)) /\ (True = even(red black)) /\ True = shuffle(red, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black black $21:NeList black)) /\ (True = even(black $21:NeList black)) /\ True = shuffle(black $21:NeList, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black red $21:NeList black)) /\ (True = even(red $21:NeList black)) /\ True = shuffle(red $21:NeList, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1
Generated By:  RST
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $20:NeList) → True = pairedList($20:NeList)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.15.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(red, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(red, red, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red black $21:NeList)) /\ (True = even(black black $21:NeList)) /\ True = shuffle(red, black $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red red $21:NeList)) /\ (True = even(black red $21:NeList)) /\ True = shuffle(red, red $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.1
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.2
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black red black)) /\ (True = even(red black)) /\ True = shuffle(red, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.3
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black black $21:NeList black)) /\ (True = even(black $21:NeList black)) /\ True = shuffle(black $21:NeList, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.4
Generated By:  CAS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black red $21:NeList black)) /\ (True = even(red $21:NeList black)) /\ True = shuffle(red $21:NeList, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.16.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, black black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, red red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, black black $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, red red $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, black black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, red red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, nil, black $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, black black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, red red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, black black $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, red red $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, black black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, red red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, $19:NeList, red $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
True = shuffle(black, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $21:NeList red)) /\ (True = even($21:NeList)) /\ True = shuffle(black $21:NeList, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
True = shuffle(black, red, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $21:NeList)) /\ (True = even($21:NeList)) /\ True = shuffle(black, red $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $21:Card) → False = True
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $21:Card $21:Card) → False = True
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired($21:Card, $22:Card)) /\ True = shuffle(nil, red $19:NeList, $21:Card $22:Card) → True = pairedList(nil)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $21:Card $21:Card $22:NeList) → False = True
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $21:Card $21:Card) → False = True
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6
Generated By:  NI
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired($21, $22)) /\ True = shuffle(nil, red $19:NeList, $21 $22 $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ (True = paired($21:Card, $22:Card)) /\ True = shuffle(nil, red $19:NeList, $21:Card $22:Card) → True = pairedList(nil)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
True = shuffle(red, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $21:NeList)) /\ (True = even($21:NeList)) /\ True = shuffle(red, black $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
True = shuffle(red, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $21:NeList black)) /\ (True = even($21:NeList)) /\ True = shuffle(red $21:NeList, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.1
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $21:Card) → False = True
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $21:Card $21:Card) → False = True
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.3
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired($21:Card, $22:Card)) /\ True = shuffle(black $19:NeList, nil, $21:Card $22:Card) → True = pairedList(nil)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $21:Card $21:Card $22:NeList) → False = True
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $21:Card $21:Card) → False = True
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6
Generated By:  NI
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired($21, $22)) /\ True = shuffle(black $19:NeList, nil, $21 $22 $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.7
Generated By:  NI
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ (True = paired($21:Card, $22:Card)) /\ True = shuffle(black $19:NeList, nil, $21:Card $22:Card) → True = pairedList(nil)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
True = shuffle(red, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
(True = alter(black $21:NeList)) /\ (True = even($21:NeList)) /\ True = shuffle(red, black $21:NeList, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.1.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.2.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
True = shuffle(red, black, $20) → True = pairedList($20)
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.3.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.4.1
Generated By:  EPS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
(True = alter(red $21:NeList black)) /\ (True = even($21:NeList)) /\ True = shuffle(red $21:NeList, black, $20) → True = pairedList($20)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, nil, red $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle($19:NeList, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, black $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, nil, black $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red black $24:NeList red)) /\ (True = even(black black $24:NeList)) /\ True = shuffle(black $24:NeList, nil, black $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red red $24:NeList red)) /\ (True = even(black red $24:NeList)) /\ True = shuffle(red $24:NeList, nil, black $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, $19:NeList, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, $19:NeList, black $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, $19:NeList, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, red $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, red $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black $24:NeList)) /\ (True = even(black black $24:NeList)) /\ True = shuffle(nil, black $24:NeList, red $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red $24:NeList)) /\ (True = even(black red $24:NeList)) /\ True = shuffle(nil, red $24:NeList, red $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.3.1.2.1.4.1.15.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, red $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.2.1.4.1.8.1.3.1.4.1.1.1.3.1.16.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $7:NeList red $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(black $7:NeList, $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $21:Card $21:Card) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $21:Card $21:Card $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $21:Card $21:Card) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.1
Generated By:  CVUL
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, black red $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2
Generated By:  CVUL
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, red black $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.16.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.15.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ black
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $21:Card $21:Card) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $21:Card $21:Card $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $21:Card $21:Card) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1
Generated By:  CVUL
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, black red $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.2
Generated By:  CVUL
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, red black $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.7.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.1.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.3.1.2.1.4.1.16.1.3.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ black $17
$17 ⇒ red $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle(red $7:NeList, $8:NeList, red $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.2.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.2.1.4.1.7.1.3.1.4.1.1.1.3.1.15.1.4.1.1
Generated By:  CS
Skolem Ops:
$10.Card
$11.NeList
$15.NeList
$17.NeList
$18.NeList
$20.NeList
$9.Card
Executable Hypotheses:
$10 ⇒ red
$11 ⇒ $15
$15 ⇒ red $17
$17 ⇒ black $18
$18 ⇒ $20
$9 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $7:NeList black $8:NeList)) /\ (True = even($7:NeList $8:NeList)) /\ True = shuffle($7:NeList, black $8:NeList, black $20) → pairedList($20) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $22:NeList red)) /\ (True = even(black black $22:NeList)) /\ True = shuffle(black $22:NeList, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $22:NeList red)) /\ (True = even(black red $22:NeList)) /\ True = shuffle(red $22:NeList, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, red $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, nil, red $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $23:NeList red)) /\ (True = even(black black $23:NeList)) /\ True = shuffle(black $23:NeList, nil, red $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $23:NeList red)) /\ (True = even(black red $23:NeList)) /\ True = shuffle(red $23:NeList, nil, red $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black red)) /\ (True = even(black black)) /\ True = shuffle(black, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red red)) /\ (True = even(black red)) /\ True = shuffle(red, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $22:NeList red)) /\ (True = even(black black $22:NeList)) /\ True = shuffle(black $22:NeList, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $22:NeList red)) /\ (True = even(black red $22:NeList)) /\ True = shuffle(red $22:NeList, nil, red) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $24:NeList red)) /\ (True = even($24:NeList)) /\ True = shuffle($24:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $22:NeList)) /\ (True = even(black black $22:NeList)) /\ True = shuffle(nil, black $22:NeList, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $22:NeList)) /\ (True = even(black red $22:NeList)) /\ True = shuffle(nil, red $22:NeList, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, black $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, black $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $23:NeList)) /\ (True = even(black black $23:NeList)) /\ True = shuffle(nil, black $23:NeList, black $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $23:NeList)) /\ (True = even(black red $23:NeList)) /\ True = shuffle(nil, red $23:NeList, black $22:NeList) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $22:NeList)) /\ (True = even(black black $22:NeList)) /\ True = shuffle(nil, black $22:NeList, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $22:NeList)) /\ (True = even(black red $22:NeList)) /\ True = shuffle(nil, red $22:NeList, black) → false
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $24:NeList)) /\ (True = even($24:NeList)) /\ True = shuffle(nil, $24:NeList, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, black black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, red red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, black black $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, red red $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, black black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, red red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, $19:NeList, black $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, black black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, red red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, black black $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, red red $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, black black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.2
Generated By:  GND
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, red red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, nil, red $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.2.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.4.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.5.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black red)) /\ (True = even(black)) /\ True = shuffle(black, nil, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red red)) /\ (True = even(red)) /\ True = shuffle(red, nil, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black $25:NeList red)) /\ (True = even(black $25:NeList)) /\ True = shuffle(black $25:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red $25:NeList red)) /\ (True = even(red $25:NeList)) /\ True = shuffle(red $25:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.2.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.5.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black)) /\ True = shuffle(nil, black, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(red)) /\ True = shuffle(nil, red, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red black $25:NeList)) /\ (True = even(black $25:NeList)) /\ True = shuffle(nil, black $25:NeList, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red red $25:NeList)) /\ (True = even(red $25:NeList)) /\ True = shuffle(nil, red $25:NeList, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, $19:NeList, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, $19:NeList, red $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, $19:NeList, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, black $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, black $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red black $24:NeList)) /\ (True = even(black black $24:NeList)) /\ True = shuffle(nil, black $24:NeList, black $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red red $24:NeList)) /\ (True = even(black red $24:NeList)) /\ True = shuffle(nil, red $24:NeList, black $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, nil, black $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle($19:NeList, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, red $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red black)) /\ (True = even(red black)) /\ True = shuffle(red, nil, red $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black $24:NeList black)) /\ (True = even(black $24:NeList black)) /\ True = shuffle(black $24:NeList, nil, red $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red $24:NeList black)) /\ (True = even(red $24:NeList black)) /\ True = shuffle(red $24:NeList, nil, red $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $25:NeList red)) /\ (True = even(black $25:NeList)) /\ True = shuffle(red $25:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $25:NeList)) /\ (True = even(black $25:NeList)) /\ True = shuffle(nil, black $25:NeList, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $22:NeList)) /\ (True = even(black black $22:NeList)) /\ True = shuffle(nil, black $22:NeList, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $22:NeList)) /\ (True = even(black red $22:NeList)) /\ True = shuffle(nil, red $22:NeList, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, red $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, red $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $23:NeList)) /\ (True = even(black black $23:NeList)) /\ True = shuffle(nil, black $23:NeList, red $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $23:NeList)) /\ (True = even(black red $23:NeList)) /\ True = shuffle(nil, red $23:NeList, red $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black)) /\ (True = even(black black)) /\ True = shuffle(nil, black, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red)) /\ (True = even(black red)) /\ True = shuffle(nil, red, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red black $22:NeList)) /\ (True = even(black black $22:NeList)) /\ True = shuffle(nil, black $22:NeList, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(red red $22:NeList)) /\ (True = even(black red $22:NeList)) /\ True = shuffle(nil, red $22:NeList, red) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $24:NeList)) /\ (True = even($24:NeList)) /\ True = shuffle(nil, $24:NeList, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red black)) /\ (True = even(red black)) /\ True = shuffle(red, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $22:NeList black)) /\ (True = even(black $22:NeList black)) /\ True = shuffle(black $22:NeList, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $22:NeList black)) /\ (True = even(red $22:NeList black)) /\ True = shuffle(red $22:NeList, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, black $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red black)) /\ (True = even(red black)) /\ True = shuffle(red, nil, black $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $23:NeList black)) /\ (True = even(black $23:NeList black)) /\ True = shuffle(black $23:NeList, nil, black $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $23:NeList black)) /\ (True = even(red $23:NeList black)) /\ True = shuffle(red $23:NeList, nil, black $22:NeList) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1.1
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black black)) /\ (True = even(black black)) /\ True = shuffle(black, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1.2
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red black)) /\ (True = even(red black)) /\ True = shuffle(red, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1.3
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black black $22:NeList black)) /\ (True = even(black $22:NeList black)) /\ True = shuffle(black $22:NeList, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1.4
Generated By:  CAS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
(True = alter(black red $22:NeList black)) /\ (True = even(red $22:NeList black)) /\ True = shuffle(red $22:NeList, nil, black) → false
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $24:NeList black)) /\ (True = even($24:NeList)) /\ True = shuffle($24:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.6.1.6.1.1.3.7.1.3.4.1.2.1.4.1.16.1.1.6.2.1.3.1.4.1.1
Generated By:  CS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList red)) /\ (True = even(black $19:NeList)) /\ True = shuffle(red $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.6.1.6.1.1.3.7.1.4.4.1.1.1.3.1.15.1.1.6.1.1.4.1.3.1.1
Generated By:  CS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, black $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.2.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.4.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.5.1.2.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black)) /\ (True = even(black)) /\ True = shuffle(nil, black, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red)) /\ (True = even(red)) /\ True = shuffle(nil, red, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black $25:NeList)) /\ (True = even(black $25:NeList)) /\ True = shuffle(nil, black $25:NeList, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red $25:NeList)) /\ (True = even(red $25:NeList)) /\ True = shuffle(nil, red $25:NeList, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.2.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.4.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1.1.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1.2.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1.3.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.5.1.1.1.4.1
Generated By:  EPS
Skolem Ops:
None
Executable Hypotheses:
None
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red black black)) /\ (True = even(black)) /\ True = shuffle(black, nil, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red red black)) /\ (True = even(red)) /\ True = shuffle(red, nil, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red black $25:NeList black)) /\ (True = even(black $25:NeList)) /\ True = shuffle(black $25:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red red $25:NeList black)) /\ (True = even(red $25:NeList)) /\ True = shuffle(red $25:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(red $25:NeList)) /\ (True = even(black $25:NeList)) /\ True = shuffle(nil, red $25:NeList, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.1.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $25:NeList black)) /\ (True = even(black $25:NeList)) /\ True = shuffle(black $25:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.3.1.2.1.4.1.15.1.1.6.2.1.3.1.4.1.1
Generated By:  CS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ red
$22 ⇒ black
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(red $19:NeList)) /\ (True = even(black $19:NeList)) /\ True = shuffle(nil, red $19:NeList, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1
Generated By:  CUT
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $25:NeList black)) /\ (True = even(black $25:NeList)) /\ True = shuffle(black $25:NeList, nil, $23) → True = even($25:NeList black)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.2
Generated By:  CUT
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black $25:NeList black)) /\ (True = even(black $25:NeList)) /\ (True = even($25:NeList black)) /\ True = shuffle(black $25:NeList, nil, $23) → True = pairedList($23)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1.1
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1.2
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red black)) /\ (True = even(black red)) /\ True = shuffle(black red, nil, $23) → True = even(red black)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1.3
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black black $26:NeList black)) /\ (True = even(black black $26:NeList)) /\ True = shuffle(black black $26:NeList, nil, $23) → True = even(black $26:NeList black)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1.4
Generated By:  CAS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
(True = alter(black red $26:NeList black)) /\ (True = even(black red $26:NeList)) /\ True = shuffle(black red $26:NeList, nil, $23) → True = even(red $26:NeList black)
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.2.1
Generated By:  CS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1.2.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1.3.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true
Goal Id:  0.8.8.1.6.1.1.3.1.8.1.4.1.4.1.1.1.3.1.16.1.1.6.1.1.4.1.3.1.1.4.1
Generated By:  EPS
Skolem Ops:
$21.Card
$22.Card
$23.NeList
Executable Hypotheses:
$21 ⇒ black
$22 ⇒ red
Non-Executable Hypotheses:
(True = alter(H1:List H0:Card H2:List H0:Card H3:List)) /\ True = even(H2:List) → false
(True = alter(black $19:NeList black)) /\ (True = even($19:NeList black)) /\ True = shuffle(black $19:NeList, nil, $23) → pairedList($23) ⇒ True
Goal:
true

Proof Tree