TSTP Solution File: SET693+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET693+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 : n004.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 15:26:01 EDT 2023
% Result : Theorem 8.77s 1.90s
% Output : Proof 12.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 15:33:52 EDT 2023
% 0.12/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 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 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 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
% 2.05/1.00 Prover 1: Preprocessing ...
% 2.05/1.00 Prover 4: Preprocessing ...
% 2.67/1.04 Prover 5: Preprocessing ...
% 2.67/1.04 Prover 6: Preprocessing ...
% 2.67/1.04 Prover 2: Preprocessing ...
% 2.67/1.04 Prover 0: Preprocessing ...
% 2.67/1.04 Prover 3: Preprocessing ...
% 4.19/1.42 Prover 5: Proving ...
% 4.19/1.43 Prover 1: Constructing countermodel ...
% 5.04/1.44 Prover 4: Constructing countermodel ...
% 5.04/1.45 Prover 6: Proving ...
% 5.04/1.46 Prover 2: Proving ...
% 5.04/1.47 Prover 3: Constructing countermodel ...
% 5.04/1.49 Prover 0: Proving ...
% 6.82/1.62 Prover 3: gave up
% 7.03/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.03/1.65 Prover 7: Preprocessing ...
% 7.03/1.66 Prover 1: gave up
% 7.03/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.03/1.71 Prover 8: Preprocessing ...
% 7.03/1.71 Prover 7: Warning: ignoring some quantifiers
% 7.75/1.73 Prover 7: Constructing countermodel ...
% 8.24/1.81 Prover 7: gave up
% 8.24/1.83 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.24/1.85 Prover 8: Warning: ignoring some quantifiers
% 8.73/1.87 Prover 9: Preprocessing ...
% 8.77/1.87 Prover 8: Constructing countermodel ...
% 8.77/1.89 Prover 6: proved (1257ms)
% 8.77/1.90
% 8.77/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.77/1.90
% 8.77/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.77/1.90 Prover 5: stopped
% 8.77/1.90 Prover 0: stopped
% 8.77/1.90 Prover 2: stopped
% 8.77/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.77/1.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.02/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.02/1.92 Prover 16: Preprocessing ...
% 9.02/1.93 Prover 10: Preprocessing ...
% 9.02/1.96 Prover 13: Preprocessing ...
% 9.02/1.96 Prover 11: Preprocessing ...
% 9.29/2.03 Prover 10: Warning: ignoring some quantifiers
% 9.29/2.04 Prover 16: Warning: ignoring some quantifiers
% 9.29/2.06 Prover 10: Constructing countermodel ...
% 9.29/2.07 Prover 16: Constructing countermodel ...
% 9.29/2.11 Prover 13: Warning: ignoring some quantifiers
% 10.38/2.12 Prover 9: Constructing countermodel ...
% 10.38/2.13 Prover 9: stopped
% 10.38/2.13 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 10.38/2.13 Prover 13: Constructing countermodel ...
% 10.38/2.14 Prover 19: Preprocessing ...
% 10.38/2.15 Prover 11: Constructing countermodel ...
% 10.38/2.15 Prover 10: gave up
% 10.85/2.19 Prover 8: gave up
% 10.85/2.25 Prover 19: Warning: ignoring some quantifiers
% 11.36/2.27 Prover 19: Constructing countermodel ...
% 11.47/2.30 Prover 4: Found proof (size 119)
% 11.47/2.30 Prover 4: proved (1667ms)
% 11.47/2.30 Prover 11: stopped
% 11.47/2.30 Prover 19: stopped
% 11.47/2.30 Prover 13: stopped
% 11.47/2.31 Prover 16: stopped
% 11.47/2.31
% 11.47/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.47/2.31
% 11.70/2.32 % SZS output start Proof for theBenchmark
% 11.70/2.33 Assumptions after simplification:
% 11.70/2.33 ---------------------------------
% 11.70/2.33
% 11.70/2.33 (equal_set)
% 11.79/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 11.79/2.36 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 11.79/2.36 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 11.79/2.36 $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | ~ $i(v1) |
% 11.79/2.36 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 &
% 11.79/2.36 subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] :
% 11.79/2.36 ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 11.79/2.36 | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) =
% 11.79/2.36 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.79/2.36 (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v0) = 0 &
% 11.79/2.36 subset(v0, v1) = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) =
% 11.79/2.36 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0,
% 11.79/2.36 v1) = v3 & subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i]
% 11.79/2.36 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 11.79/2.36 any] : ? [v3: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = v2 & ( ~
% 11.79/2.36 (v2 = 0) | v3 = 0)))
% 11.79/2.36
% 11.79/2.36 (subset)
% 11.79/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.79/2.36 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 11.79/2.36 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 11.79/2.36 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 11.79/2.36 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 11.79/2.36 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.79/2.36 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 11.79/2.36 ~ $i(v0) | member(v2, v1) = 0)
% 11.79/2.36
% 11.79/2.36 (thI20)
% 11.79/2.37 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 11.79/2.37 (union(v0, v1) = v2 & equal_set(v0, v2) = v3 & subset(v1, v0) = v4 & $i(v2) &
% 11.79/2.37 $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 11.79/2.37
% 11.79/2.37 (union)
% 11.79/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 11.79/2.37 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 11.79/2.37 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 11.79/2.37 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 11.79/2.37 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 11.79/2.37 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 11.79/2.37 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 11.79/2.37
% 11.79/2.37 (function-axioms)
% 11.79/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.37 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 11.79/2.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.37 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 11.79/2.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 11.79/2.37 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.79/2.37 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 11.79/2.37 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.79/2.37 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 11.79/2.37 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.79/2.37 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 11.79/2.37 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.79/2.38 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.38 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 11.79/2.38 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 11.79/2.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 11.79/2.38 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 11.79/2.38 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 11.79/2.38 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 11.79/2.38 (power_set(v2) = v0))
% 11.79/2.38
% 11.79/2.38 Further assumptions not needed in the proof:
% 11.79/2.38 --------------------------------------------
% 11.79/2.38 difference, empty_set, intersection, power_set, product, singleton, sum,
% 11.79/2.38 unordered_pair
% 11.79/2.38
% 11.79/2.38 Those formulas are unsatisfiable:
% 11.79/2.38 ---------------------------------
% 11.79/2.38
% 11.79/2.38 Begin of proof
% 11.79/2.38 |
% 11.79/2.38 | ALPHA: (subset) implies:
% 11.79/2.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 11.79/2.38 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 11.79/2.38 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 11.79/2.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.79/2.38 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~
% 11.79/2.38 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) =
% 11.79/2.38 | v4))
% 11.79/2.38 |
% 11.79/2.38 | ALPHA: (equal_set) implies:
% 11.79/2.38 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 11.79/2.38 | $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, v1) = v3 &
% 11.79/2.38 | subset(v1, v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 11.79/2.38 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) |
% 11.79/2.38 | ~ $i(v0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 11.79/2.38 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) |
% 11.79/2.38 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0,
% 11.79/2.38 | v1) = v3 & subset(v1, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 =
% 11.79/2.38 | 0))))
% 11.79/2.38 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) |
% 11.79/2.38 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0,
% 11.79/2.38 | v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 =
% 11.79/2.38 | 0))))
% 11.79/2.38 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 11.79/2.38 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 11.79/2.38 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 11.79/2.38 | 0))))
% 11.79/2.38 |
% 11.79/2.38 | ALPHA: (union) implies:
% 11.79/2.39 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 11.79/2.39 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 11.79/2.39 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 11.79/2.39 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 11.79/2.39 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 11.79/2.39 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 11.79/2.39 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 11.79/2.39 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 11.79/2.39 | v5))
% 11.79/2.39 |
% 11.79/2.39 | ALPHA: (function-axioms) implies:
% 11.79/2.39 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.79/2.39 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 11.79/2.39 | v2) = v0))
% 11.79/2.39 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.79/2.39 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 11.79/2.39 | v2) = v0))
% 11.79/2.39 |
% 11.79/2.39 | DELTA: instantiating (thI20) with fresh symbols all_15_0, all_15_1, all_15_2,
% 11.79/2.39 | all_15_3, all_15_4 gives:
% 11.79/2.39 | (12) union(all_15_4, all_15_3) = all_15_2 & equal_set(all_15_4, all_15_2) =
% 11.79/2.39 | all_15_1 & subset(all_15_3, all_15_4) = all_15_0 & $i(all_15_2) &
% 11.79/2.39 | $i(all_15_3) & $i(all_15_4) & ((all_15_0 = 0 & ~ (all_15_1 = 0)) |
% 11.79/2.39 | (all_15_1 = 0 & ~ (all_15_0 = 0)))
% 11.79/2.39 |
% 11.79/2.39 | ALPHA: (12) implies:
% 11.79/2.39 | (13) $i(all_15_4)
% 11.79/2.39 | (14) $i(all_15_3)
% 11.79/2.39 | (15) $i(all_15_2)
% 11.79/2.39 | (16) subset(all_15_3, all_15_4) = all_15_0
% 11.79/2.39 | (17) equal_set(all_15_4, all_15_2) = all_15_1
% 11.79/2.39 | (18) union(all_15_4, all_15_3) = all_15_2
% 11.79/2.39 | (19) (all_15_0 = 0 & ~ (all_15_1 = 0)) | (all_15_1 = 0 & ~ (all_15_0 =
% 11.79/2.39 | 0))
% 11.79/2.39 |
% 11.79/2.39 | GROUND_INST: instantiating (1) with all_15_3, all_15_4, all_15_0, simplifying
% 11.79/2.39 | with (13), (14), (16) gives:
% 11.79/2.39 | (20) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 11.79/2.39 | all_15_3) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 11.79/2.39 |
% 11.79/2.39 | GROUND_INST: instantiating (6) with all_15_4, all_15_3, all_15_0, simplifying
% 11.79/2.39 | with (13), (14), (16) gives:
% 11.79/2.39 | (21) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_3) = v0 &
% 11.79/2.39 | subset(all_15_4, all_15_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_0
% 11.79/2.39 | = 0)))
% 11.79/2.39 |
% 11.79/2.39 | GROUND_INST: instantiating (5) with all_15_3, all_15_4, all_15_0, simplifying
% 11.79/2.39 | with (13), (14), (16) gives:
% 11.79/2.39 | (22) ? [v0: any] : ? [v1: any] : (equal_set(all_15_3, all_15_4) = v0 &
% 11.79/2.39 | subset(all_15_4, all_15_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_0
% 11.79/2.39 | = 0)))
% 11.79/2.39 |
% 11.79/2.39 | GROUND_INST: instantiating (7) with all_15_4, all_15_2, all_15_1, simplifying
% 11.79/2.39 | with (13), (15), (17) gives:
% 11.79/2.40 | (23) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_2,
% 11.79/2.40 | all_15_4) = v1 & subset(all_15_4, all_15_2) = v0 & ( ~ (v1 = 0) |
% 11.79/2.40 | ~ (v0 = 0)))
% 11.79/2.40 |
% 11.79/2.40 | DELTA: instantiating (22) with fresh symbols all_22_0, all_22_1 gives:
% 11.79/2.40 | (24) equal_set(all_15_3, all_15_4) = all_22_1 & subset(all_15_4, all_15_3)
% 11.79/2.40 | = all_22_0 & ( ~ (all_22_1 = 0) | (all_22_0 = 0 & all_15_0 = 0))
% 11.79/2.40 |
% 11.79/2.40 | ALPHA: (24) implies:
% 11.79/2.40 | (25) subset(all_15_4, all_15_3) = all_22_0
% 11.79/2.40 |
% 11.79/2.40 | DELTA: instantiating (21) with fresh symbols all_24_0, all_24_1 gives:
% 11.79/2.40 | (26) equal_set(all_15_4, all_15_3) = all_24_1 & subset(all_15_4, all_15_3)
% 11.79/2.40 | = all_24_0 & ( ~ (all_24_1 = 0) | (all_24_0 = 0 & all_15_0 = 0))
% 11.79/2.40 |
% 11.79/2.40 | ALPHA: (26) implies:
% 11.79/2.40 | (27) subset(all_15_4, all_15_3) = all_24_0
% 11.79/2.40 |
% 11.79/2.40 | GROUND_INST: instantiating (11) with all_22_0, all_24_0, all_15_3, all_15_4,
% 11.79/2.40 | simplifying with (25), (27) gives:
% 11.79/2.40 | (28) all_24_0 = all_22_0
% 11.79/2.40 |
% 11.79/2.40 | GROUND_INST: instantiating (6) with all_15_3, all_15_4, all_22_0, simplifying
% 11.79/2.40 | with (13), (14), (25) gives:
% 11.79/2.40 | (29) ? [v0: any] : ? [v1: any] : (equal_set(all_15_3, all_15_4) = v0 &
% 11.79/2.40 | subset(all_15_3, all_15_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_22_0
% 11.79/2.40 | = 0)))
% 11.79/2.40 |
% 11.79/2.40 | GROUND_INST: instantiating (5) with all_15_4, all_15_3, all_22_0, simplifying
% 11.79/2.40 | with (13), (14), (25) gives:
% 11.79/2.40 | (30) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_3) = v0 &
% 11.79/2.40 | subset(all_15_3, all_15_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_22_0
% 11.79/2.40 | = 0)))
% 11.79/2.40 |
% 11.79/2.40 | DELTA: instantiating (30) with fresh symbols all_35_0, all_35_1 gives:
% 11.79/2.40 | (31) equal_set(all_15_4, all_15_3) = all_35_1 & subset(all_15_3, all_15_4)
% 11.79/2.40 | = all_35_0 & ( ~ (all_35_1 = 0) | (all_35_0 = 0 & all_22_0 = 0))
% 11.79/2.40 |
% 11.79/2.40 | ALPHA: (31) implies:
% 11.79/2.40 | (32) subset(all_15_3, all_15_4) = all_35_0
% 11.79/2.40 |
% 11.79/2.40 | DELTA: instantiating (29) with fresh symbols all_37_0, all_37_1 gives:
% 11.79/2.40 | (33) equal_set(all_15_3, all_15_4) = all_37_1 & subset(all_15_3, all_15_4)
% 11.79/2.40 | = all_37_0 & ( ~ (all_37_1 = 0) | (all_37_0 = 0 & all_22_0 = 0))
% 11.79/2.40 |
% 11.79/2.40 | ALPHA: (33) implies:
% 11.79/2.40 | (34) subset(all_15_3, all_15_4) = all_37_0
% 11.79/2.40 |
% 11.79/2.40 | GROUND_INST: instantiating (11) with all_15_0, all_37_0, all_15_4, all_15_3,
% 11.79/2.40 | simplifying with (16), (34) gives:
% 11.79/2.40 | (35) all_37_0 = all_15_0
% 11.79/2.40 |
% 11.79/2.40 | GROUND_INST: instantiating (11) with all_35_0, all_37_0, all_15_4, all_15_3,
% 11.79/2.40 | simplifying with (32), (34) gives:
% 11.79/2.40 | (36) all_37_0 = all_35_0
% 11.79/2.40 |
% 11.79/2.40 | COMBINE_EQS: (35), (36) imply:
% 11.79/2.40 | (37) all_35_0 = all_15_0
% 11.79/2.40 |
% 11.79/2.40 | BETA: splitting (19) gives:
% 11.79/2.40 |
% 11.79/2.40 | Case 1:
% 11.79/2.40 | |
% 11.79/2.40 | | (38) all_15_0 = 0 & ~ (all_15_1 = 0)
% 11.79/2.40 | |
% 11.79/2.40 | | ALPHA: (38) implies:
% 11.79/2.40 | | (39) all_15_0 = 0
% 11.79/2.40 | | (40) ~ (all_15_1 = 0)
% 11.79/2.40 | |
% 11.79/2.40 | | REDUCE: (16), (39) imply:
% 11.79/2.40 | | (41) subset(all_15_3, all_15_4) = 0
% 11.79/2.40 | |
% 11.79/2.40 | | BETA: splitting (23) gives:
% 11.79/2.40 | |
% 11.79/2.40 | | Case 1:
% 11.79/2.40 | | |
% 11.79/2.40 | | | (42) all_15_1 = 0
% 11.79/2.40 | | |
% 11.79/2.40 | | | REDUCE: (40), (42) imply:
% 11.79/2.40 | | | (43) $false
% 11.79/2.40 | | |
% 11.79/2.40 | | | CLOSE: (43) is inconsistent.
% 11.79/2.40 | | |
% 11.79/2.40 | | Case 2:
% 11.79/2.40 | | |
% 11.79/2.41 | | | (44) ? [v0: any] : ? [v1: any] : (subset(all_15_2, all_15_4) = v1 &
% 11.79/2.41 | | | subset(all_15_4, all_15_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.79/2.41 | | |
% 11.79/2.41 | | | DELTA: instantiating (44) with fresh symbols all_54_0, all_54_1 gives:
% 11.79/2.41 | | | (45) subset(all_15_2, all_15_4) = all_54_0 & subset(all_15_4, all_15_2)
% 11.79/2.41 | | | = all_54_1 & ( ~ (all_54_0 = 0) | ~ (all_54_1 = 0))
% 11.79/2.41 | | |
% 11.79/2.41 | | | ALPHA: (45) implies:
% 11.79/2.41 | | | (46) subset(all_15_4, all_15_2) = all_54_1
% 11.79/2.41 | | | (47) subset(all_15_2, all_15_4) = all_54_0
% 11.79/2.41 | | | (48) ~ (all_54_0 = 0) | ~ (all_54_1 = 0)
% 11.79/2.41 | | |
% 11.79/2.41 | | | GROUND_INST: instantiating (1) with all_15_4, all_15_2, all_54_1,
% 11.79/2.41 | | | simplifying with (13), (15), (46) gives:
% 11.79/2.41 | | | (49) all_54_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.79/2.41 | | | member(v0, all_15_2) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 11.79/2.41 | | |
% 11.79/2.41 | | | GROUND_INST: instantiating (1) with all_15_2, all_15_4, all_54_0,
% 11.79/2.41 | | | simplifying with (13), (15), (47) gives:
% 11.79/2.41 | | | (50) all_54_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.79/2.41 | | | member(v0, all_15_2) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 11.79/2.41 | | |
% 11.79/2.41 | | | BETA: splitting (48) gives:
% 11.79/2.41 | | |
% 11.79/2.41 | | | Case 1:
% 11.79/2.41 | | | |
% 11.79/2.41 | | | | (51) ~ (all_54_0 = 0)
% 11.79/2.41 | | | |
% 11.79/2.41 | | | | BETA: splitting (50) gives:
% 11.79/2.41 | | | |
% 11.79/2.41 | | | | Case 1:
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | (52) all_54_0 = 0
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | REDUCE: (51), (52) imply:
% 11.79/2.41 | | | | | (53) $false
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | CLOSE: (53) is inconsistent.
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | Case 2:
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | (54) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 11.79/2.41 | | | | | all_15_2) = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | DELTA: instantiating (54) with fresh symbols all_125_0, all_125_1
% 11.79/2.41 | | | | | gives:
% 11.79/2.41 | | | | | (55) ~ (all_125_0 = 0) & member(all_125_1, all_15_2) = 0 &
% 11.79/2.41 | | | | | member(all_125_1, all_15_4) = all_125_0 & $i(all_125_1)
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | ALPHA: (55) implies:
% 11.79/2.41 | | | | | (56) ~ (all_125_0 = 0)
% 11.79/2.41 | | | | | (57) $i(all_125_1)
% 11.79/2.41 | | | | | (58) member(all_125_1, all_15_4) = all_125_0
% 11.79/2.41 | | | | | (59) member(all_125_1, all_15_2) = 0
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | GROUND_INST: instantiating (2) with all_15_3, all_15_4, all_125_1,
% 11.79/2.41 | | | | | all_125_0, simplifying with (13), (14), (41), (57), (58)
% 11.79/2.41 | | | | | gives:
% 11.79/2.41 | | | | | (60) all_125_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 11.79/2.41 | | | | | member(all_125_1, all_15_3) = v0)
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | GROUND_INST: instantiating (8) with all_125_1, all_15_4, all_15_3,
% 11.79/2.41 | | | | | all_15_2, simplifying with (13), (14), (18), (57), (59)
% 11.79/2.41 | | | | | gives:
% 11.79/2.41 | | | | | (61) ? [v0: any] : ? [v1: any] : (member(all_125_1, all_15_3) =
% 11.79/2.41 | | | | | v1 & member(all_125_1, all_15_4) = v0 & (v1 = 0 | v0 = 0))
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | DELTA: instantiating (61) with fresh symbols all_142_0, all_142_1
% 11.79/2.41 | | | | | gives:
% 11.79/2.41 | | | | | (62) member(all_125_1, all_15_3) = all_142_0 & member(all_125_1,
% 11.79/2.41 | | | | | all_15_4) = all_142_1 & (all_142_0 = 0 | all_142_1 = 0)
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | ALPHA: (62) implies:
% 11.79/2.41 | | | | | (63) member(all_125_1, all_15_4) = all_142_1
% 11.79/2.41 | | | | | (64) member(all_125_1, all_15_3) = all_142_0
% 11.79/2.41 | | | | | (65) all_142_0 = 0 | all_142_1 = 0
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | BETA: splitting (60) gives:
% 11.79/2.41 | | | | |
% 11.79/2.41 | | | | | Case 1:
% 11.79/2.41 | | | | | |
% 11.79/2.41 | | | | | | (66) all_125_0 = 0
% 11.79/2.41 | | | | | |
% 11.79/2.41 | | | | | | REDUCE: (56), (66) imply:
% 11.79/2.41 | | | | | | (67) $false
% 12.22/2.41 | | | | | |
% 12.22/2.41 | | | | | | CLOSE: (67) is inconsistent.
% 12.22/2.41 | | | | | |
% 12.22/2.41 | | | | | Case 2:
% 12.22/2.41 | | | | | |
% 12.22/2.42 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & member(all_125_1, all_15_3) =
% 12.22/2.42 | | | | | | v0)
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | DELTA: instantiating (68) with fresh symbol all_148_0 gives:
% 12.22/2.42 | | | | | | (69) ~ (all_148_0 = 0) & member(all_125_1, all_15_3) = all_148_0
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | ALPHA: (69) implies:
% 12.22/2.42 | | | | | | (70) ~ (all_148_0 = 0)
% 12.22/2.42 | | | | | | (71) member(all_125_1, all_15_3) = all_148_0
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | GROUND_INST: instantiating (10) with all_125_0, all_142_1, all_15_4,
% 12.22/2.42 | | | | | | all_125_1, simplifying with (58), (63) gives:
% 12.22/2.42 | | | | | | (72) all_142_1 = all_125_0
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | GROUND_INST: instantiating (10) with all_142_0, all_148_0, all_15_3,
% 12.22/2.42 | | | | | | all_125_1, simplifying with (64), (71) gives:
% 12.22/2.42 | | | | | | (73) all_148_0 = all_142_0
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | REDUCE: (70), (73) imply:
% 12.22/2.42 | | | | | | (74) ~ (all_142_0 = 0)
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | BETA: splitting (65) gives:
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | Case 1:
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | | (75) all_142_0 = 0
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | | REDUCE: (74), (75) imply:
% 12.22/2.42 | | | | | | | (76) $false
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | | CLOSE: (76) is inconsistent.
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | Case 2:
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | | (77) all_142_1 = 0
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | | COMBINE_EQS: (72), (77) imply:
% 12.22/2.42 | | | | | | | (78) all_125_0 = 0
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | | SIMP: (78) implies:
% 12.22/2.42 | | | | | | | (79) all_125_0 = 0
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | | REDUCE: (56), (79) imply:
% 12.22/2.42 | | | | | | | (80) $false
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | | CLOSE: (80) is inconsistent.
% 12.22/2.42 | | | | | | |
% 12.22/2.42 | | | | | | End of split
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | End of split
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | End of split
% 12.22/2.42 | | | |
% 12.22/2.42 | | | Case 2:
% 12.22/2.42 | | | |
% 12.22/2.42 | | | | (81) ~ (all_54_1 = 0)
% 12.22/2.42 | | | |
% 12.22/2.42 | | | | BETA: splitting (49) gives:
% 12.22/2.42 | | | |
% 12.22/2.42 | | | | Case 1:
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | (82) all_54_1 = 0
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | REDUCE: (81), (82) imply:
% 12.22/2.42 | | | | | (83) $false
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | CLOSE: (83) is inconsistent.
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | Case 2:
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | (84) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 12.22/2.42 | | | | | all_15_2) = v1 & member(v0, all_15_4) = 0 & $i(v0))
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | DELTA: instantiating (84) with fresh symbols all_125_0, all_125_1
% 12.22/2.42 | | | | | gives:
% 12.22/2.42 | | | | | (85) ~ (all_125_0 = 0) & member(all_125_1, all_15_2) = all_125_0 &
% 12.22/2.42 | | | | | member(all_125_1, all_15_4) = 0 & $i(all_125_1)
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | ALPHA: (85) implies:
% 12.22/2.42 | | | | | (86) ~ (all_125_0 = 0)
% 12.22/2.42 | | | | | (87) $i(all_125_1)
% 12.22/2.42 | | | | | (88) member(all_125_1, all_15_4) = 0
% 12.22/2.42 | | | | | (89) member(all_125_1, all_15_2) = all_125_0
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | GROUND_INST: instantiating (9) with all_125_1, all_15_4, all_15_3,
% 12.22/2.42 | | | | | all_15_2, all_125_0, simplifying with (13), (14), (18),
% 12.22/2.42 | | | | | (87), (89) gives:
% 12.22/2.42 | | | | | (90) all_125_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.22/2.42 | | | | | ~ (v0 = 0) & member(all_125_1, all_15_3) = v1 &
% 12.22/2.42 | | | | | member(all_125_1, all_15_4) = v0)
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | BETA: splitting (90) gives:
% 12.22/2.42 | | | | |
% 12.22/2.42 | | | | | Case 1:
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | (91) all_125_0 = 0
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | REDUCE: (86), (91) imply:
% 12.22/2.42 | | | | | | (92) $false
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | CLOSE: (92) is inconsistent.
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | Case 2:
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | (93) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 12.22/2.42 | | | | | | member(all_125_1, all_15_3) = v1 & member(all_125_1,
% 12.22/2.42 | | | | | | all_15_4) = v0)
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | DELTA: instantiating (93) with fresh symbols all_143_0, all_143_1
% 12.22/2.42 | | | | | | gives:
% 12.22/2.42 | | | | | | (94) ~ (all_143_0 = 0) & ~ (all_143_1 = 0) & member(all_125_1,
% 12.22/2.42 | | | | | | all_15_3) = all_143_0 & member(all_125_1, all_15_4) =
% 12.22/2.42 | | | | | | all_143_1
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | ALPHA: (94) implies:
% 12.22/2.42 | | | | | | (95) ~ (all_143_1 = 0)
% 12.22/2.42 | | | | | | (96) member(all_125_1, all_15_4) = all_143_1
% 12.22/2.42 | | | | | |
% 12.22/2.42 | | | | | | GROUND_INST: instantiating (10) with 0, all_143_1, all_15_4,
% 12.22/2.43 | | | | | | all_125_1, simplifying with (88), (96) gives:
% 12.22/2.43 | | | | | | (97) all_143_1 = 0
% 12.22/2.43 | | | | | |
% 12.22/2.43 | | | | | | REDUCE: (95), (97) imply:
% 12.22/2.43 | | | | | | (98) $false
% 12.22/2.43 | | | | | |
% 12.22/2.43 | | | | | | CLOSE: (98) is inconsistent.
% 12.22/2.43 | | | | | |
% 12.22/2.43 | | | | | End of split
% 12.22/2.43 | | | | |
% 12.22/2.43 | | | | End of split
% 12.22/2.43 | | | |
% 12.22/2.43 | | | End of split
% 12.22/2.43 | | |
% 12.22/2.43 | | End of split
% 12.22/2.43 | |
% 12.22/2.43 | Case 2:
% 12.22/2.43 | |
% 12.22/2.43 | | (99) all_15_1 = 0 & ~ (all_15_0 = 0)
% 12.22/2.43 | |
% 12.22/2.43 | | ALPHA: (99) implies:
% 12.22/2.43 | | (100) all_15_1 = 0
% 12.22/2.43 | | (101) ~ (all_15_0 = 0)
% 12.22/2.43 | |
% 12.22/2.43 | | REDUCE: (17), (100) imply:
% 12.22/2.43 | | (102) equal_set(all_15_4, all_15_2) = 0
% 12.22/2.43 | |
% 12.22/2.43 | | BETA: splitting (20) gives:
% 12.22/2.43 | |
% 12.22/2.43 | | Case 1:
% 12.22/2.43 | | |
% 12.22/2.43 | | | (103) all_15_0 = 0
% 12.22/2.43 | | |
% 12.22/2.43 | | | REDUCE: (101), (103) imply:
% 12.22/2.43 | | | (104) $false
% 12.22/2.43 | | |
% 12.22/2.43 | | | CLOSE: (104) is inconsistent.
% 12.22/2.43 | | |
% 12.22/2.43 | | Case 2:
% 12.22/2.43 | | |
% 12.22/2.43 | | | (105) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_3)
% 12.22/2.43 | | | = 0 & member(v0, all_15_4) = v1 & $i(v0))
% 12.22/2.43 | | |
% 12.22/2.43 | | | DELTA: instantiating (105) with fresh symbols all_57_0, all_57_1 gives:
% 12.22/2.43 | | | (106) ~ (all_57_0 = 0) & member(all_57_1, all_15_3) = 0 &
% 12.22/2.43 | | | member(all_57_1, all_15_4) = all_57_0 & $i(all_57_1)
% 12.22/2.43 | | |
% 12.22/2.43 | | | ALPHA: (106) implies:
% 12.22/2.43 | | | (107) ~ (all_57_0 = 0)
% 12.22/2.43 | | | (108) $i(all_57_1)
% 12.22/2.43 | | | (109) member(all_57_1, all_15_4) = all_57_0
% 12.22/2.43 | | | (110) member(all_57_1, all_15_3) = 0
% 12.22/2.43 | | |
% 12.22/2.43 | | | GROUND_INST: instantiating (4) with all_15_4, all_15_2, simplifying with
% 12.22/2.43 | | | (13), (15), (102) gives:
% 12.22/2.43 | | | (111) subset(all_15_2, all_15_4) = 0 & subset(all_15_4, all_15_2) = 0
% 12.22/2.43 | | |
% 12.22/2.43 | | | ALPHA: (111) implies:
% 12.22/2.43 | | | (112) subset(all_15_4, all_15_2) = 0
% 12.22/2.43 | | | (113) subset(all_15_2, all_15_4) = 0
% 12.22/2.43 | | |
% 12.22/2.43 | | | GROUND_INST: instantiating (2) with all_15_2, all_15_4, all_57_1,
% 12.22/2.43 | | | all_57_0, simplifying with (13), (15), (108), (109), (113)
% 12.22/2.43 | | | gives:
% 12.22/2.43 | | | (114) all_57_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_57_1,
% 12.22/2.43 | | | all_15_2) = v0)
% 12.22/2.43 | | |
% 12.22/2.43 | | | GROUND_INST: instantiating (3) with all_15_2, all_15_4, simplifying with
% 12.22/2.43 | | | (13), (15), (113) gives:
% 12.22/2.43 | | | (115) ? [v0: any] : ? [v1: any] : (equal_set(all_15_2, all_15_4) = v1
% 12.22/2.43 | | | & subset(all_15_4, all_15_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 12.22/2.43 | | |
% 12.22/2.43 | | | GROUND_INST: instantiating (5) with all_15_2, all_15_4, 0, simplifying
% 12.22/2.43 | | | with (13), (15), (113) gives:
% 12.22/2.43 | | | (116) ? [v0: any] : ? [v1: any] : (equal_set(all_15_2, all_15_4) = v0
% 12.22/2.43 | | | & subset(all_15_4, all_15_2) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 12.22/2.43 | | |
% 12.22/2.43 | | | DELTA: instantiating (115) with fresh symbols all_83_0, all_83_1 gives:
% 12.22/2.43 | | | (117) equal_set(all_15_2, all_15_4) = all_83_0 & subset(all_15_4,
% 12.22/2.43 | | | all_15_2) = all_83_1 & ( ~ (all_83_1 = 0) | all_83_0 = 0)
% 12.22/2.43 | | |
% 12.22/2.43 | | | ALPHA: (117) implies:
% 12.22/2.43 | | | (118) subset(all_15_4, all_15_2) = all_83_1
% 12.22/2.43 | | | (119) ~ (all_83_1 = 0) | all_83_0 = 0
% 12.22/2.43 | | |
% 12.22/2.43 | | | DELTA: instantiating (116) with fresh symbols all_87_0, all_87_1 gives:
% 12.22/2.43 | | | (120) equal_set(all_15_2, all_15_4) = all_87_1 & subset(all_15_4,
% 12.22/2.43 | | | all_15_2) = all_87_0 & ( ~ (all_87_1 = 0) | all_87_0 = 0)
% 12.22/2.43 | | |
% 12.22/2.43 | | | ALPHA: (120) implies:
% 12.22/2.43 | | | (121) subset(all_15_4, all_15_2) = all_87_0
% 12.22/2.43 | | |
% 12.22/2.43 | | | BETA: splitting (114) gives:
% 12.22/2.43 | | |
% 12.22/2.43 | | | Case 1:
% 12.22/2.43 | | | |
% 12.22/2.43 | | | | (122) all_57_0 = 0
% 12.22/2.43 | | | |
% 12.22/2.43 | | | | REDUCE: (107), (122) imply:
% 12.22/2.43 | | | | (123) $false
% 12.22/2.43 | | | |
% 12.22/2.43 | | | | CLOSE: (123) is inconsistent.
% 12.22/2.43 | | | |
% 12.22/2.43 | | | Case 2:
% 12.22/2.43 | | | |
% 12.22/2.44 | | | | (124) ? [v0: int] : ( ~ (v0 = 0) & member(all_57_1, all_15_2) = v0)
% 12.22/2.44 | | | |
% 12.22/2.44 | | | | DELTA: instantiating (124) with fresh symbol all_95_0 gives:
% 12.22/2.44 | | | | (125) ~ (all_95_0 = 0) & member(all_57_1, all_15_2) = all_95_0
% 12.22/2.44 | | | |
% 12.22/2.44 | | | | ALPHA: (125) implies:
% 12.22/2.44 | | | | (126) ~ (all_95_0 = 0)
% 12.22/2.44 | | | | (127) member(all_57_1, all_15_2) = all_95_0
% 12.22/2.44 | | | |
% 12.22/2.44 | | | | GROUND_INST: instantiating (11) with 0, all_87_0, all_15_2, all_15_4,
% 12.22/2.44 | | | | simplifying with (112), (121) gives:
% 12.22/2.44 | | | | (128) all_87_0 = 0
% 12.22/2.44 | | | |
% 12.22/2.44 | | | | GROUND_INST: instantiating (11) with all_83_1, all_87_0, all_15_2,
% 12.22/2.44 | | | | all_15_4, simplifying with (118), (121) gives:
% 12.22/2.44 | | | | (129) all_87_0 = all_83_1
% 12.22/2.44 | | | |
% 12.22/2.44 | | | | COMBINE_EQS: (128), (129) imply:
% 12.22/2.44 | | | | (130) all_83_1 = 0
% 12.22/2.44 | | | |
% 12.22/2.44 | | | | BETA: splitting (119) gives:
% 12.22/2.44 | | | |
% 12.22/2.44 | | | | Case 1:
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | | (131) ~ (all_83_1 = 0)
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | | REDUCE: (130), (131) imply:
% 12.22/2.44 | | | | | (132) $false
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | | CLOSE: (132) is inconsistent.
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | Case 2:
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | | GROUND_INST: instantiating (9) with all_57_1, all_15_4, all_15_3,
% 12.22/2.44 | | | | | all_15_2, all_95_0, simplifying with (13), (14), (18),
% 12.22/2.44 | | | | | (108), (127) gives:
% 12.22/2.44 | | | | | (133) all_95_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.22/2.44 | | | | | ~ (v0 = 0) & member(all_57_1, all_15_3) = v1 &
% 12.22/2.44 | | | | | member(all_57_1, all_15_4) = v0)
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | | BETA: splitting (133) gives:
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | | Case 1:
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | (134) all_95_0 = 0
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | REDUCE: (126), (134) imply:
% 12.22/2.44 | | | | | | (135) $false
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | CLOSE: (135) is inconsistent.
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | Case 2:
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | (136) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 12.22/2.44 | | | | | | member(all_57_1, all_15_3) = v1 & member(all_57_1,
% 12.22/2.44 | | | | | | all_15_4) = v0)
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | DELTA: instantiating (136) with fresh symbols all_116_0, all_116_1
% 12.22/2.44 | | | | | | gives:
% 12.22/2.44 | | | | | | (137) ~ (all_116_0 = 0) & ~ (all_116_1 = 0) & member(all_57_1,
% 12.22/2.44 | | | | | | all_15_3) = all_116_0 & member(all_57_1, all_15_4) =
% 12.22/2.44 | | | | | | all_116_1
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | ALPHA: (137) implies:
% 12.22/2.44 | | | | | | (138) ~ (all_116_0 = 0)
% 12.22/2.44 | | | | | | (139) member(all_57_1, all_15_3) = all_116_0
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | GROUND_INST: instantiating (10) with 0, all_116_0, all_15_3,
% 12.22/2.44 | | | | | | all_57_1, simplifying with (110), (139) gives:
% 12.22/2.44 | | | | | | (140) all_116_0 = 0
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | REDUCE: (138), (140) imply:
% 12.22/2.44 | | | | | | (141) $false
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | | CLOSE: (141) is inconsistent.
% 12.22/2.44 | | | | | |
% 12.22/2.44 | | | | | End of split
% 12.22/2.44 | | | | |
% 12.22/2.44 | | | | End of split
% 12.22/2.44 | | | |
% 12.22/2.44 | | | End of split
% 12.22/2.44 | | |
% 12.22/2.44 | | End of split
% 12.22/2.44 | |
% 12.22/2.44 | End of split
% 12.22/2.44 |
% 12.22/2.44 End of proof
% 12.22/2.44 % SZS output end Proof for theBenchmark
% 12.22/2.44
% 12.22/2.44 1826ms
%------------------------------------------------------------------------------