%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------