TSTP Solution File: SET156+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET156+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:24:04 EDT 2023
% Result : Theorem 8.18s 1.87s
% Output : Proof 11.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET156+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:13:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.09/1.05 Prover 4: Preprocessing ...
% 2.09/1.07 Prover 1: Preprocessing ...
% 2.83/1.11 Prover 2: Preprocessing ...
% 2.83/1.11 Prover 0: Preprocessing ...
% 2.83/1.11 Prover 5: Preprocessing ...
% 2.83/1.11 Prover 6: Preprocessing ...
% 2.92/1.12 Prover 3: Preprocessing ...
% 4.85/1.51 Prover 5: Proving ...
% 5.44/1.52 Prover 1: Constructing countermodel ...
% 5.44/1.52 Prover 6: Proving ...
% 5.87/1.54 Prover 3: Constructing countermodel ...
% 5.95/1.55 Prover 0: Proving ...
% 5.95/1.55 Prover 2: Proving ...
% 5.95/1.56 Prover 4: Constructing countermodel ...
% 8.18/1.86 Prover 3: proved (1226ms)
% 8.18/1.87
% 8.18/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.18/1.87
% 8.18/1.87 Prover 5: stopped
% 8.18/1.87 Prover 6: stopped
% 8.18/1.87 Prover 2: stopped
% 8.18/1.89 Prover 0: stopped
% 8.18/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.18/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.18/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.18/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.18/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.62/1.93 Prover 10: Preprocessing ...
% 8.62/1.93 Prover 11: Preprocessing ...
% 8.62/1.93 Prover 7: Preprocessing ...
% 8.62/1.94 Prover 13: Preprocessing ...
% 8.62/1.94 Prover 8: Preprocessing ...
% 9.05/2.01 Prover 7: Warning: ignoring some quantifiers
% 9.05/2.01 Prover 10: Warning: ignoring some quantifiers
% 9.05/2.02 Prover 7: Constructing countermodel ...
% 9.05/2.02 Prover 10: Constructing countermodel ...
% 9.05/2.05 Prover 8: Warning: ignoring some quantifiers
% 9.05/2.05 Prover 8: Constructing countermodel ...
% 9.05/2.07 Prover 13: Warning: ignoring some quantifiers
% 9.05/2.08 Prover 11: Constructing countermodel ...
% 9.05/2.12 Prover 13: Constructing countermodel ...
% 9.05/2.12 Prover 10: gave up
% 9.05/2.13 Prover 7: gave up
% 9.05/2.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.05/2.14 Prover 1: Found proof (size 123)
% 9.05/2.14 Prover 1: proved (1507ms)
% 9.05/2.14 Prover 11: stopped
% 9.05/2.15 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.05/2.15 Prover 4: stopped
% 9.05/2.15 Prover 16: Preprocessing ...
% 9.05/2.15 Prover 8: stopped
% 9.05/2.15 Prover 13: stopped
% 10.23/2.16 Prover 19: Preprocessing ...
% 10.23/2.16 Prover 16: stopped
% 10.76/2.24 Prover 19: Warning: ignoring some quantifiers
% 10.77/2.25 Prover 19: Constructing countermodel ...
% 10.77/2.25 Prover 19: stopped
% 10.77/2.25
% 10.77/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.77/2.25
% 10.77/2.27 % SZS output start Proof for theBenchmark
% 10.77/2.27 Assumptions after simplification:
% 10.77/2.27 ---------------------------------
% 10.77/2.27
% 10.77/2.27 (difference)
% 10.77/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 10.77/2.30 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 10.77/2.30 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 &
% 10.77/2.30 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 10.77/2.30 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0,
% 10.77/2.30 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 10.77/2.30 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 10.77/2.30
% 10.77/2.30 (equal_set)
% 11.07/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 11.07/2.30 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 11.07/2.30 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 11.07/2.30 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 11.07/2.30 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 11.07/2.30
% 11.07/2.30 (intersection)
% 11.07/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 11.07/2.30 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 11.07/2.30 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 &
% 11.07/2.30 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 11.07/2.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~
% 11.07/2.30 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) =
% 11.07/2.30 0 & member(v0, v1) = 0))
% 11.07/2.30
% 11.07/2.30 (subset)
% 11.07/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 11.07/2.31 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 11.07/2.31 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 11.07/2.31 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 11.07/2.31 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 11.07/2.31
% 11.07/2.31 (thI25)
% 11.07/2.31 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 11.07/2.31 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 11.07/2.31 difference(v2, v3) = v4 & difference(v2, v1) = v6 & difference(v2, v0) = v5
% 11.07/2.31 & union(v5, v6) = v7 & intersection(v0, v1) = v3 & equal_set(v4, v7) = v8 &
% 11.07/2.31 subset(v1, v2) = 0 & subset(v0, v2) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4)
% 11.07/2.31 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.07/2.31
% 11.07/2.31 (union)
% 11.07/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 11.07/2.31 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 11.07/2.31 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 11.07/2.31 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 11.07/2.31 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 11.07/2.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 11.07/2.31 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 11.07/2.31
% 11.07/2.31 (function-axioms)
% 11.07/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.07/2.31 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 11.07/2.31 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.07/2.31 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 11.07/2.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 11.07/2.31 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.07/2.31 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 11.07/2.31 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.07/2.31 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 11.07/2.31 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.07/2.31 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 11.07/2.31 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.07/2.31 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.07/2.31 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 11.07/2.31 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 11.07/2.31 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 11.07/2.31 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 11.07/2.31 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 11.07/2.31 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 11.07/2.31 (power_set(v2) = v0))
% 11.07/2.31
% 11.07/2.31 Further assumptions not needed in the proof:
% 11.07/2.31 --------------------------------------------
% 11.07/2.31 empty_set, power_set, product, singleton, sum, unordered_pair
% 11.07/2.31
% 11.07/2.31 Those formulas are unsatisfiable:
% 11.07/2.31 ---------------------------------
% 11.07/2.31
% 11.07/2.31 Begin of proof
% 11.07/2.31 |
% 11.07/2.32 | ALPHA: (subset) implies:
% 11.07/2.32 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 11.07/2.32 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 11.07/2.32 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 11.07/2.32 |
% 11.07/2.32 | ALPHA: (equal_set) implies:
% 11.07/2.32 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 11.07/2.32 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 11.07/2.32 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 11.07/2.32 | 0))))
% 11.07/2.32 |
% 11.07/2.32 | ALPHA: (intersection) implies:
% 11.07/2.32 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.07/2.32 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) |
% 11.07/2.32 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 11.07/2.32 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 11.07/2.32 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) |
% 11.07/2.32 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 11.07/2.32 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 11.07/2.32 | 0))))
% 11.07/2.32 |
% 11.07/2.32 | ALPHA: (union) implies:
% 11.07/2.32 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 11.07/2.32 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 11.07/2.32 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 11.07/2.32 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 11.07/2.32 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 11.07/2.32 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 11.07/2.32 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 11.07/2.32 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 11.07/2.32 | v5))
% 11.07/2.32 |
% 11.07/2.32 | ALPHA: (difference) implies:
% 11.07/2.32 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.07/2.32 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~
% 11.07/2.32 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0
% 11.07/2.32 | & member(v0, v1) = v4))
% 11.07/2.32 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 11.07/2.32 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~
% 11.07/2.32 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 11.07/2.32 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 11.07/2.32 |
% 11.07/2.32 | ALPHA: (function-axioms) implies:
% 11.07/2.32 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.07/2.32 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 11.07/2.32 | = v0))
% 11.07/2.32 |
% 11.07/2.33 | DELTA: instantiating (thI25) with fresh symbols all_15_0, all_15_1, all_15_2,
% 11.07/2.33 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7, all_15_8 gives:
% 11.07/2.33 | (10) ~ (all_15_0 = 0) & difference(all_15_6, all_15_5) = all_15_4 &
% 11.07/2.33 | difference(all_15_6, all_15_7) = all_15_2 & difference(all_15_6,
% 11.07/2.33 | all_15_8) = all_15_3 & union(all_15_3, all_15_2) = all_15_1 &
% 11.07/2.33 | intersection(all_15_8, all_15_7) = all_15_5 & equal_set(all_15_4,
% 11.07/2.33 | all_15_1) = all_15_0 & subset(all_15_7, all_15_6) = 0 &
% 11.07/2.33 | subset(all_15_8, all_15_6) = 0 & $i(all_15_1) & $i(all_15_2) &
% 11.07/2.33 | $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) &
% 11.07/2.33 | $i(all_15_7) & $i(all_15_8)
% 11.07/2.33 |
% 11.07/2.33 | ALPHA: (10) implies:
% 11.07/2.33 | (11) ~ (all_15_0 = 0)
% 11.07/2.33 | (12) $i(all_15_8)
% 11.07/2.33 | (13) $i(all_15_7)
% 11.07/2.33 | (14) $i(all_15_6)
% 11.07/2.33 | (15) $i(all_15_5)
% 11.07/2.33 | (16) $i(all_15_4)
% 11.07/2.33 | (17) $i(all_15_3)
% 11.07/2.33 | (18) $i(all_15_2)
% 11.07/2.33 | (19) $i(all_15_1)
% 11.07/2.33 | (20) equal_set(all_15_4, all_15_1) = all_15_0
% 11.07/2.33 | (21) intersection(all_15_8, all_15_7) = all_15_5
% 11.07/2.33 | (22) union(all_15_3, all_15_2) = all_15_1
% 11.07/2.33 | (23) difference(all_15_6, all_15_8) = all_15_3
% 11.07/2.33 | (24) difference(all_15_6, all_15_7) = all_15_2
% 11.07/2.33 | (25) difference(all_15_6, all_15_5) = all_15_4
% 11.07/2.33 |
% 11.07/2.33 | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_15_0, simplifying
% 11.07/2.33 | with (16), (19), (20) gives:
% 11.07/2.33 | (26) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 11.07/2.33 | all_15_4) = v1 & subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) |
% 11.07/2.33 | ~ (v0 = 0)))
% 11.07/2.33 |
% 11.07/2.33 | BETA: splitting (26) gives:
% 11.07/2.33 |
% 11.07/2.33 | Case 1:
% 11.07/2.33 | |
% 11.07/2.33 | | (27) all_15_0 = 0
% 11.07/2.33 | |
% 11.07/2.33 | | REDUCE: (11), (27) imply:
% 11.07/2.33 | | (28) $false
% 11.07/2.33 | |
% 11.07/2.33 | | CLOSE: (28) is inconsistent.
% 11.07/2.33 | |
% 11.07/2.33 | Case 2:
% 11.07/2.33 | |
% 11.07/2.33 | | (29) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v1 &
% 11.07/2.33 | | subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.07/2.33 | |
% 11.07/2.33 | | DELTA: instantiating (29) with fresh symbols all_27_0, all_27_1 gives:
% 11.07/2.33 | | (30) subset(all_15_1, all_15_4) = all_27_0 & subset(all_15_4, all_15_1) =
% 11.07/2.33 | | all_27_1 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0))
% 11.07/2.33 | |
% 11.07/2.33 | | ALPHA: (30) implies:
% 11.07/2.33 | | (31) subset(all_15_4, all_15_1) = all_27_1
% 11.07/2.33 | | (32) subset(all_15_1, all_15_4) = all_27_0
% 11.07/2.33 | | (33) ~ (all_27_0 = 0) | ~ (all_27_1 = 0)
% 11.07/2.33 | |
% 11.07/2.33 | | GROUND_INST: instantiating (1) with all_15_4, all_15_1, all_27_1,
% 11.07/2.33 | | simplifying with (16), (19), (31) gives:
% 11.07/2.33 | | (34) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.07/2.33 | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 11.07/2.33 | |
% 11.07/2.34 | | GROUND_INST: instantiating (1) with all_15_1, all_15_4, all_27_0,
% 11.07/2.34 | | simplifying with (16), (19), (32) gives:
% 11.07/2.34 | | (35) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.07/2.34 | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 11.07/2.34 | |
% 11.07/2.34 | | BETA: splitting (33) gives:
% 11.07/2.34 | |
% 11.07/2.34 | | Case 1:
% 11.07/2.34 | | |
% 11.07/2.34 | | | (36) ~ (all_27_0 = 0)
% 11.07/2.34 | | |
% 11.07/2.34 | | | BETA: splitting (35) gives:
% 11.07/2.34 | | |
% 11.07/2.34 | | | Case 1:
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | (37) all_27_0 = 0
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | REDUCE: (36), (37) imply:
% 11.07/2.34 | | | | (38) $false
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | CLOSE: (38) is inconsistent.
% 11.07/2.34 | | | |
% 11.07/2.34 | | | Case 2:
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | (39) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 11.07/2.34 | | | | = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | DELTA: instantiating (39) with fresh symbols all_40_0, all_40_1 gives:
% 11.07/2.34 | | | | (40) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = 0 &
% 11.07/2.34 | | | | member(all_40_1, all_15_4) = all_40_0 & $i(all_40_1)
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | ALPHA: (40) implies:
% 11.07/2.34 | | | | (41) ~ (all_40_0 = 0)
% 11.07/2.34 | | | | (42) $i(all_40_1)
% 11.07/2.34 | | | | (43) member(all_40_1, all_15_4) = all_40_0
% 11.07/2.34 | | | | (44) member(all_40_1, all_15_1) = 0
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | GROUND_INST: instantiating (8) with all_40_1, all_15_5, all_15_6,
% 11.07/2.34 | | | | all_15_4, all_40_0, simplifying with (14), (15), (25),
% 11.07/2.34 | | | | (42), (43) gives:
% 11.07/2.34 | | | | (45) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1,
% 11.07/2.34 | | | | all_15_5) = v1 & member(all_40_1, all_15_6) = v0 & ( ~ (v0 =
% 11.07/2.34 | | | | 0) | v1 = 0))
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_3, all_15_2,
% 11.07/2.34 | | | | all_15_1, simplifying with (17), (18), (22), (42), (44)
% 11.07/2.34 | | | | gives:
% 11.07/2.34 | | | | (46) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_2) = v1 &
% 11.07/2.34 | | | | member(all_40_1, all_15_3) = v0 & (v1 = 0 | v0 = 0))
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | DELTA: instantiating (46) with fresh symbols all_47_0, all_47_1 gives:
% 11.07/2.34 | | | | (47) member(all_40_1, all_15_2) = all_47_0 & member(all_40_1,
% 11.07/2.34 | | | | all_15_3) = all_47_1 & (all_47_0 = 0 | all_47_1 = 0)
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | ALPHA: (47) implies:
% 11.07/2.34 | | | | (48) member(all_40_1, all_15_3) = all_47_1
% 11.07/2.34 | | | | (49) member(all_40_1, all_15_2) = all_47_0
% 11.07/2.34 | | | | (50) all_47_0 = 0 | all_47_1 = 0
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | BETA: splitting (45) gives:
% 11.07/2.34 | | | |
% 11.07/2.34 | | | | Case 1:
% 11.07/2.34 | | | | |
% 11.07/2.34 | | | | | (51) all_40_0 = 0
% 11.07/2.34 | | | | |
% 11.07/2.34 | | | | | REDUCE: (41), (51) imply:
% 11.07/2.34 | | | | | (52) $false
% 11.07/2.34 | | | | |
% 11.07/2.34 | | | | | CLOSE: (52) is inconsistent.
% 11.07/2.34 | | | | |
% 11.07/2.34 | | | | Case 2:
% 11.07/2.34 | | | | |
% 11.07/2.34 | | | | | (53) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_5) = v1
% 11.07/2.34 | | | | | & member(all_40_1, all_15_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 11.07/2.34 | | | | |
% 11.07/2.34 | | | | | DELTA: instantiating (53) with fresh symbols all_53_0, all_53_1 gives:
% 11.07/2.34 | | | | | (54) member(all_40_1, all_15_5) = all_53_0 & member(all_40_1,
% 11.07/2.34 | | | | | all_15_6) = all_53_1 & ( ~ (all_53_1 = 0) | all_53_0 = 0)
% 11.07/2.34 | | | | |
% 11.07/2.34 | | | | | ALPHA: (54) implies:
% 11.07/2.34 | | | | | (55) member(all_40_1, all_15_6) = all_53_1
% 11.07/2.34 | | | | | (56) member(all_40_1, all_15_5) = all_53_0
% 11.07/2.34 | | | | | (57) ~ (all_53_1 = 0) | all_53_0 = 0
% 11.07/2.34 | | | | |
% 11.07/2.34 | | | | | GROUND_INST: instantiating (8) with all_40_1, all_15_7, all_15_6,
% 11.07/2.34 | | | | | all_15_2, all_47_0, simplifying with (13), (14), (24),
% 11.07/2.34 | | | | | (42), (49) gives:
% 11.07/2.35 | | | | | (58) all_47_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1,
% 11.07/2.35 | | | | | all_15_6) = v0 & member(all_40_1, all_15_7) = v1 & ( ~ (v0
% 11.07/2.35 | | | | | = 0) | v1 = 0))
% 11.07/2.35 | | | | |
% 11.07/2.35 | | | | | BETA: splitting (50) gives:
% 11.07/2.35 | | | | |
% 11.07/2.35 | | | | | Case 1:
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | (59) all_47_0 = 0
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | REDUCE: (49), (59) imply:
% 11.07/2.35 | | | | | | (60) member(all_40_1, all_15_2) = 0
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_7, all_15_6,
% 11.07/2.35 | | | | | | all_15_2, simplifying with (13), (14), (24), (42), (60)
% 11.07/2.35 | | | | | | gives:
% 11.07/2.35 | | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_6) = 0
% 11.07/2.35 | | | | | | & member(all_40_1, all_15_7) = v0)
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | DELTA: instantiating (61) with fresh symbol all_77_0 gives:
% 11.07/2.35 | | | | | | (62) ~ (all_77_0 = 0) & member(all_40_1, all_15_6) = 0 &
% 11.07/2.35 | | | | | | member(all_40_1, all_15_7) = all_77_0
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | ALPHA: (62) implies:
% 11.07/2.35 | | | | | | (63) ~ (all_77_0 = 0)
% 11.07/2.35 | | | | | | (64) member(all_40_1, all_15_7) = all_77_0
% 11.07/2.35 | | | | | | (65) member(all_40_1, all_15_6) = 0
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | GROUND_INST: instantiating (9) with all_53_1, 0, all_15_6, all_40_1,
% 11.07/2.35 | | | | | | simplifying with (55), (65) gives:
% 11.07/2.35 | | | | | | (66) all_53_1 = 0
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | BETA: splitting (57) gives:
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | Case 1:
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | (67) ~ (all_53_1 = 0)
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | REDUCE: (66), (67) imply:
% 11.07/2.35 | | | | | | | (68) $false
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | CLOSE: (68) is inconsistent.
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | Case 2:
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | (69) all_53_0 = 0
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | REDUCE: (56), (69) imply:
% 11.07/2.35 | | | | | | | (70) member(all_40_1, all_15_5) = 0
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | GROUND_INST: instantiating (3) with all_40_1, all_15_8, all_15_7,
% 11.07/2.35 | | | | | | | all_15_5, simplifying with (12), (13), (21), (42),
% 11.07/2.35 | | | | | | | (70) gives:
% 11.07/2.35 | | | | | | | (71) member(all_40_1, all_15_7) = 0 & member(all_40_1,
% 11.07/2.35 | | | | | | | all_15_8) = 0
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | ALPHA: (71) implies:
% 11.07/2.35 | | | | | | | (72) member(all_40_1, all_15_7) = 0
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | GROUND_INST: instantiating (9) with all_77_0, 0, all_15_7,
% 11.07/2.35 | | | | | | | all_40_1, simplifying with (64), (72) gives:
% 11.07/2.35 | | | | | | | (73) all_77_0 = 0
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | REDUCE: (63), (73) imply:
% 11.07/2.35 | | | | | | | (74) $false
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | CLOSE: (74) is inconsistent.
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | End of split
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | Case 2:
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | (75) all_47_1 = 0
% 11.07/2.35 | | | | | | (76) ~ (all_47_0 = 0)
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | REDUCE: (48), (75) imply:
% 11.07/2.35 | | | | | | (77) member(all_40_1, all_15_3) = 0
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | BETA: splitting (58) gives:
% 11.07/2.35 | | | | | |
% 11.07/2.35 | | | | | | Case 1:
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | (78) all_47_0 = 0
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | REDUCE: (76), (78) imply:
% 11.07/2.35 | | | | | | | (79) $false
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | CLOSE: (79) is inconsistent.
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | Case 2:
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | (80) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_6)
% 11.07/2.35 | | | | | | | = v0 & member(all_40_1, all_15_7) = v1 & ( ~ (v0 = 0) |
% 11.07/2.35 | | | | | | | v1 = 0))
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | DELTA: instantiating (80) with fresh symbols all_76_0, all_76_1
% 11.07/2.35 | | | | | | | gives:
% 11.07/2.35 | | | | | | | (81) member(all_40_1, all_15_6) = all_76_1 & member(all_40_1,
% 11.07/2.35 | | | | | | | all_15_7) = all_76_0 & ( ~ (all_76_1 = 0) | all_76_0 =
% 11.07/2.35 | | | | | | | 0)
% 11.07/2.35 | | | | | | |
% 11.07/2.35 | | | | | | | ALPHA: (81) implies:
% 11.07/2.35 | | | | | | | (82) member(all_40_1, all_15_6) = all_76_1
% 11.07/2.36 | | | | | | |
% 11.07/2.36 | | | | | | | GROUND_INST: instantiating (9) with all_53_1, all_76_1, all_15_6,
% 11.07/2.36 | | | | | | | all_40_1, simplifying with (55), (82) gives:
% 11.07/2.36 | | | | | | | (83) all_76_1 = all_53_1
% 11.07/2.36 | | | | | | |
% 11.07/2.36 | | | | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_8, all_15_6,
% 11.07/2.36 | | | | | | | all_15_3, simplifying with (12), (14), (23), (42),
% 11.35/2.36 | | | | | | | (77) gives:
% 11.35/2.36 | | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_6) =
% 11.35/2.36 | | | | | | | 0 & member(all_40_1, all_15_8) = v0)
% 11.35/2.36 | | | | | | |
% 11.35/2.36 | | | | | | | DELTA: instantiating (84) with fresh symbol all_87_0 gives:
% 11.35/2.36 | | | | | | | (85) ~ (all_87_0 = 0) & member(all_40_1, all_15_6) = 0 &
% 11.35/2.36 | | | | | | | member(all_40_1, all_15_8) = all_87_0
% 11.35/2.36 | | | | | | |
% 11.35/2.36 | | | | | | | ALPHA: (85) implies:
% 11.35/2.36 | | | | | | | (86) ~ (all_87_0 = 0)
% 11.35/2.36 | | | | | | | (87) member(all_40_1, all_15_8) = all_87_0
% 11.35/2.36 | | | | | | | (88) member(all_40_1, all_15_6) = 0
% 11.35/2.36 | | | | | | |
% 11.35/2.36 | | | | | | | GROUND_INST: instantiating (9) with all_53_1, 0, all_15_6,
% 11.35/2.36 | | | | | | | all_40_1, simplifying with (55), (88) gives:
% 11.35/2.36 | | | | | | | (89) all_53_1 = 0
% 11.35/2.36 | | | | | | |
% 11.35/2.36 | | | | | | | BETA: splitting (57) gives:
% 11.35/2.36 | | | | | | |
% 11.35/2.36 | | | | | | | Case 1:
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | (90) ~ (all_53_1 = 0)
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | REDUCE: (89), (90) imply:
% 11.35/2.36 | | | | | | | | (91) $false
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | CLOSE: (91) is inconsistent.
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | Case 2:
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | (92) all_53_0 = 0
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | REDUCE: (56), (92) imply:
% 11.35/2.36 | | | | | | | | (93) member(all_40_1, all_15_5) = 0
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | GROUND_INST: instantiating (3) with all_40_1, all_15_8,
% 11.35/2.36 | | | | | | | | all_15_7, all_15_5, simplifying with (12), (13),
% 11.35/2.36 | | | | | | | | (21), (42), (93) gives:
% 11.35/2.36 | | | | | | | | (94) member(all_40_1, all_15_7) = 0 & member(all_40_1,
% 11.35/2.36 | | | | | | | | all_15_8) = 0
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | ALPHA: (94) implies:
% 11.35/2.36 | | | | | | | | (95) member(all_40_1, all_15_8) = 0
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | GROUND_INST: instantiating (9) with all_87_0, 0, all_15_8,
% 11.35/2.36 | | | | | | | | all_40_1, simplifying with (87), (95) gives:
% 11.35/2.36 | | | | | | | | (96) all_87_0 = 0
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | REDUCE: (86), (96) imply:
% 11.35/2.36 | | | | | | | | (97) $false
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | | CLOSE: (97) is inconsistent.
% 11.35/2.36 | | | | | | | |
% 11.35/2.36 | | | | | | | End of split
% 11.35/2.36 | | | | | | |
% 11.35/2.36 | | | | | | End of split
% 11.35/2.36 | | | | | |
% 11.35/2.36 | | | | | End of split
% 11.35/2.36 | | | | |
% 11.35/2.36 | | | | End of split
% 11.35/2.36 | | | |
% 11.35/2.36 | | | End of split
% 11.35/2.36 | | |
% 11.35/2.36 | | Case 2:
% 11.35/2.36 | | |
% 11.35/2.36 | | | (98) ~ (all_27_1 = 0)
% 11.35/2.36 | | |
% 11.35/2.36 | | | BETA: splitting (34) gives:
% 11.35/2.36 | | |
% 11.35/2.36 | | | Case 1:
% 11.35/2.36 | | | |
% 11.35/2.36 | | | | (99) all_27_1 = 0
% 11.35/2.36 | | | |
% 11.35/2.36 | | | | REDUCE: (98), (99) imply:
% 11.35/2.36 | | | | (100) $false
% 11.35/2.36 | | | |
% 11.35/2.36 | | | | CLOSE: (100) is inconsistent.
% 11.35/2.36 | | | |
% 11.35/2.36 | | | Case 2:
% 11.35/2.36 | | | |
% 11.35/2.36 | | | | (101) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 11.35/2.36 | | | | all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 11.35/2.36 | | | |
% 11.35/2.36 | | | | DELTA: instantiating (101) with fresh symbols all_62_0, all_62_1 gives:
% 11.35/2.36 | | | | (102) ~ (all_62_0 = 0) & member(all_62_1, all_15_1) = all_62_0 &
% 11.35/2.36 | | | | member(all_62_1, all_15_4) = 0 & $i(all_62_1)
% 11.35/2.36 | | | |
% 11.35/2.36 | | | | ALPHA: (102) implies:
% 11.35/2.36 | | | | (103) ~ (all_62_0 = 0)
% 11.35/2.36 | | | | (104) $i(all_62_1)
% 11.35/2.36 | | | | (105) member(all_62_1, all_15_4) = 0
% 11.35/2.36 | | | | (106) member(all_62_1, all_15_1) = all_62_0
% 11.35/2.36 | | | |
% 11.35/2.36 | | | | GROUND_INST: instantiating (7) with all_62_1, all_15_5, all_15_6,
% 11.35/2.36 | | | | all_15_4, simplifying with (14), (15), (25), (104), (105)
% 11.35/2.36 | | | | gives:
% 11.35/2.36 | | | | (107) ? [v0: int] : ( ~ (v0 = 0) & member(all_62_1, all_15_5) = v0 &
% 11.35/2.37 | | | | member(all_62_1, all_15_6) = 0)
% 11.35/2.37 | | | |
% 11.35/2.37 | | | | GROUND_INST: instantiating (6) with all_62_1, all_15_3, all_15_2,
% 11.35/2.37 | | | | all_15_1, all_62_0, simplifying with (17), (18), (22),
% 11.35/2.37 | | | | (104), (106) gives:
% 11.35/2.37 | | | | (108) all_62_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 11.35/2.37 | | | | (v0 = 0) & member(all_62_1, all_15_2) = v1 & member(all_62_1,
% 11.35/2.37 | | | | all_15_3) = v0)
% 11.35/2.37 | | | |
% 11.35/2.37 | | | | DELTA: instantiating (107) with fresh symbol all_69_0 gives:
% 11.35/2.37 | | | | (109) ~ (all_69_0 = 0) & member(all_62_1, all_15_5) = all_69_0 &
% 11.35/2.37 | | | | member(all_62_1, all_15_6) = 0
% 11.35/2.37 | | | |
% 11.35/2.37 | | | | ALPHA: (109) implies:
% 11.35/2.37 | | | | (110) ~ (all_69_0 = 0)
% 11.35/2.37 | | | | (111) member(all_62_1, all_15_6) = 0
% 11.35/2.37 | | | | (112) member(all_62_1, all_15_5) = all_69_0
% 11.35/2.37 | | | |
% 11.35/2.37 | | | | BETA: splitting (108) gives:
% 11.35/2.37 | | | |
% 11.35/2.37 | | | | Case 1:
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | (113) all_62_0 = 0
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | REDUCE: (103), (113) imply:
% 11.35/2.37 | | | | | (114) $false
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | CLOSE: (114) is inconsistent.
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | Case 2:
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | (115) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 11.35/2.37 | | | | | member(all_62_1, all_15_2) = v1 & member(all_62_1,
% 11.35/2.37 | | | | | all_15_3) = v0)
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | DELTA: instantiating (115) with fresh symbols all_75_0, all_75_1
% 11.35/2.37 | | | | | gives:
% 11.35/2.37 | | | | | (116) ~ (all_75_0 = 0) & ~ (all_75_1 = 0) & member(all_62_1,
% 11.35/2.37 | | | | | all_15_2) = all_75_0 & member(all_62_1, all_15_3) =
% 11.35/2.37 | | | | | all_75_1
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | ALPHA: (116) implies:
% 11.35/2.37 | | | | | (117) ~ (all_75_1 = 0)
% 11.35/2.37 | | | | | (118) ~ (all_75_0 = 0)
% 11.35/2.37 | | | | | (119) member(all_62_1, all_15_3) = all_75_1
% 11.35/2.37 | | | | | (120) member(all_62_1, all_15_2) = all_75_0
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | GROUND_INST: instantiating (4) with all_62_1, all_15_8, all_15_7,
% 11.35/2.37 | | | | | all_15_5, all_69_0, simplifying with (12), (13), (21),
% 11.35/2.37 | | | | | (104), (112) gives:
% 11.35/2.37 | | | | | (121) all_69_0 = 0 | ? [v0: any] : ? [v1: any] :
% 11.35/2.37 | | | | | (member(all_62_1, all_15_7) = v1 & member(all_62_1, all_15_8)
% 11.35/2.37 | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | GROUND_INST: instantiating (8) with all_62_1, all_15_8, all_15_6,
% 11.35/2.37 | | | | | all_15_3, all_75_1, simplifying with (12), (14), (23),
% 11.35/2.37 | | | | | (104), (119) gives:
% 11.35/2.37 | | | | | (122) all_75_1 = 0 | ? [v0: any] : ? [v1: any] :
% 11.35/2.37 | | | | | (member(all_62_1, all_15_6) = v0 & member(all_62_1, all_15_8)
% 11.35/2.37 | | | | | = v1 & ( ~ (v0 = 0) | v1 = 0))
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | GROUND_INST: instantiating (8) with all_62_1, all_15_7, all_15_6,
% 11.35/2.37 | | | | | all_15_2, all_75_0, simplifying with (13), (14), (24),
% 11.35/2.37 | | | | | (104), (120) gives:
% 11.35/2.37 | | | | | (123) all_75_0 = 0 | ? [v0: any] : ? [v1: any] :
% 11.35/2.37 | | | | | (member(all_62_1, all_15_6) = v0 & member(all_62_1, all_15_7)
% 11.35/2.37 | | | | | = v1 & ( ~ (v0 = 0) | v1 = 0))
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | BETA: splitting (123) gives:
% 11.35/2.37 | | | | |
% 11.35/2.37 | | | | | Case 1:
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | | (124) all_75_0 = 0
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | | REDUCE: (118), (124) imply:
% 11.35/2.37 | | | | | | (125) $false
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | | CLOSE: (125) is inconsistent.
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | Case 2:
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | | (126) ? [v0: any] : ? [v1: any] : (member(all_62_1, all_15_6) =
% 11.35/2.37 | | | | | | v0 & member(all_62_1, all_15_7) = v1 & ( ~ (v0 = 0) | v1
% 11.35/2.37 | | | | | | = 0))
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | | DELTA: instantiating (126) with fresh symbols all_88_0, all_88_1
% 11.35/2.37 | | | | | | gives:
% 11.35/2.37 | | | | | | (127) member(all_62_1, all_15_6) = all_88_1 & member(all_62_1,
% 11.35/2.37 | | | | | | all_15_7) = all_88_0 & ( ~ (all_88_1 = 0) | all_88_0 = 0)
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | | ALPHA: (127) implies:
% 11.35/2.37 | | | | | | (128) member(all_62_1, all_15_7) = all_88_0
% 11.35/2.37 | | | | | | (129) member(all_62_1, all_15_6) = all_88_1
% 11.35/2.37 | | | | | | (130) ~ (all_88_1 = 0) | all_88_0 = 0
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | | BETA: splitting (122) gives:
% 11.35/2.37 | | | | | |
% 11.35/2.37 | | | | | | Case 1:
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | | (131) all_75_1 = 0
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | | REDUCE: (117), (131) imply:
% 11.35/2.37 | | | | | | | (132) $false
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | | CLOSE: (132) is inconsistent.
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | Case 2:
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | | (133) ? [v0: any] : ? [v1: any] : (member(all_62_1, all_15_6)
% 11.35/2.37 | | | | | | | = v0 & member(all_62_1, all_15_8) = v1 & ( ~ (v0 = 0) |
% 11.35/2.37 | | | | | | | v1 = 0))
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | | DELTA: instantiating (133) with fresh symbols all_94_0, all_94_1
% 11.35/2.37 | | | | | | | gives:
% 11.35/2.37 | | | | | | | (134) member(all_62_1, all_15_6) = all_94_1 & member(all_62_1,
% 11.35/2.37 | | | | | | | all_15_8) = all_94_0 & ( ~ (all_94_1 = 0) | all_94_0 =
% 11.35/2.37 | | | | | | | 0)
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | | ALPHA: (134) implies:
% 11.35/2.37 | | | | | | | (135) member(all_62_1, all_15_8) = all_94_0
% 11.35/2.37 | | | | | | | (136) member(all_62_1, all_15_6) = all_94_1
% 11.35/2.37 | | | | | | | (137) ~ (all_94_1 = 0) | all_94_0 = 0
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | | BETA: splitting (121) gives:
% 11.35/2.37 | | | | | | |
% 11.35/2.37 | | | | | | | Case 1:
% 11.35/2.37 | | | | | | | |
% 11.35/2.37 | | | | | | | | (138) all_69_0 = 0
% 11.35/2.37 | | | | | | | |
% 11.35/2.37 | | | | | | | | REDUCE: (110), (138) imply:
% 11.35/2.38 | | | | | | | | (139) $false
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | CLOSE: (139) is inconsistent.
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | Case 2:
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | (140) ? [v0: any] : ? [v1: any] : (member(all_62_1,
% 11.35/2.38 | | | | | | | | all_15_7) = v1 & member(all_62_1, all_15_8) = v0 &
% 11.35/2.38 | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | DELTA: instantiating (140) with fresh symbols all_99_0, all_99_1
% 11.35/2.38 | | | | | | | | gives:
% 11.35/2.38 | | | | | | | | (141) member(all_62_1, all_15_7) = all_99_0 &
% 11.35/2.38 | | | | | | | | member(all_62_1, all_15_8) = all_99_1 & ( ~ (all_99_0 =
% 11.35/2.38 | | | | | | | | 0) | ~ (all_99_1 = 0))
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | ALPHA: (141) implies:
% 11.35/2.38 | | | | | | | | (142) member(all_62_1, all_15_8) = all_99_1
% 11.35/2.38 | | | | | | | | (143) member(all_62_1, all_15_7) = all_99_0
% 11.35/2.38 | | | | | | | | (144) ~ (all_99_0 = 0) | ~ (all_99_1 = 0)
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | GROUND_INST: instantiating (9) with all_94_0, all_99_1,
% 11.35/2.38 | | | | | | | | all_15_8, all_62_1, simplifying with (135), (142)
% 11.35/2.38 | | | | | | | | gives:
% 11.35/2.38 | | | | | | | | (145) all_99_1 = all_94_0
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | GROUND_INST: instantiating (9) with all_88_0, all_99_0,
% 11.35/2.38 | | | | | | | | all_15_7, all_62_1, simplifying with (128), (143)
% 11.35/2.38 | | | | | | | | gives:
% 11.35/2.38 | | | | | | | | (146) all_99_0 = all_88_0
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_94_1, all_15_6,
% 11.35/2.38 | | | | | | | | all_62_1, simplifying with (111), (136) gives:
% 11.35/2.38 | | | | | | | | (147) all_94_1 = 0
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | GROUND_INST: instantiating (9) with all_88_1, all_94_1,
% 11.35/2.38 | | | | | | | | all_15_6, all_62_1, simplifying with (129), (136)
% 11.35/2.38 | | | | | | | | gives:
% 11.35/2.38 | | | | | | | | (148) all_94_1 = all_88_1
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | COMBINE_EQS: (147), (148) imply:
% 11.35/2.38 | | | | | | | | (149) all_88_1 = 0
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | BETA: splitting (137) gives:
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | | Case 1:
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | | (150) ~ (all_94_1 = 0)
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | | REDUCE: (147), (150) imply:
% 11.35/2.38 | | | | | | | | | (151) $false
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | | CLOSE: (151) is inconsistent.
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | Case 2:
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | | (152) all_94_0 = 0
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | | COMBINE_EQS: (145), (152) imply:
% 11.35/2.38 | | | | | | | | | (153) all_99_1 = 0
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | | BETA: splitting (130) gives:
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | | Case 1:
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | (154) ~ (all_88_1 = 0)
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | REDUCE: (149), (154) imply:
% 11.35/2.38 | | | | | | | | | | (155) $false
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | CLOSE: (155) is inconsistent.
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | Case 2:
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | (156) all_88_0 = 0
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | COMBINE_EQS: (146), (156) imply:
% 11.35/2.38 | | | | | | | | | | (157) all_99_0 = 0
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | BETA: splitting (144) gives:
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | Case 1:
% 11.35/2.38 | | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | | (158) ~ (all_99_0 = 0)
% 11.35/2.38 | | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | | REDUCE: (157), (158) imply:
% 11.35/2.38 | | | | | | | | | | | (159) $false
% 11.35/2.38 | | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 11.35/2.38 | | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | Case 2:
% 11.35/2.38 | | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | | (160) ~ (all_99_1 = 0)
% 11.35/2.38 | | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | | REDUCE: (153), (160) imply:
% 11.35/2.38 | | | | | | | | | | | (161) $false
% 11.35/2.38 | | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 11.35/2.38 | | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | | End of split
% 11.35/2.38 | | | | | | | | | |
% 11.35/2.38 | | | | | | | | | End of split
% 11.35/2.38 | | | | | | | | |
% 11.35/2.38 | | | | | | | | End of split
% 11.35/2.38 | | | | | | | |
% 11.35/2.38 | | | | | | | End of split
% 11.35/2.38 | | | | | | |
% 11.35/2.38 | | | | | | End of split
% 11.35/2.38 | | | | | |
% 11.35/2.38 | | | | | End of split
% 11.35/2.38 | | | | |
% 11.35/2.38 | | | | End of split
% 11.35/2.38 | | | |
% 11.35/2.38 | | | End of split
% 11.35/2.38 | | |
% 11.35/2.38 | | End of split
% 11.35/2.38 | |
% 11.35/2.38 | End of split
% 11.35/2.38 |
% 11.35/2.38 End of proof
% 11.35/2.38 % SZS output end Proof for theBenchmark
% 11.35/2.38
% 11.35/2.38 1771ms
%------------------------------------------------------------------------------