%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET766+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 : n023.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 15:26:21 EDT 2023 % Result : Theorem 10.62s 2.20s % Output : Proof 13.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.10 % Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0. % 0.05/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.30 % Computer : n023.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Sat Aug 26 11:40:26 EDT 2023 % 0.10/0.30 % CPUTime : % 0.52/0.58 ________ _____ % 0.52/0.58 ___ __ \_________(_)________________________________ % 0.52/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.58 % 0.52/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.58 (2023-06-19) % 0.52/0.58 % 0.52/0.58 (c) Philipp Rümmer, 2009-2023 % 0.52/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.58 Amanda Stjerna. % 0.52/0.58 Free software under BSD-3-Clause. % 0.52/0.58 % 0.52/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.58 % 0.52/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.60 Running up to 7 provers in parallel. % 0.52/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.52/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.00/1.15 Prover 1: Preprocessing ... % 3.00/1.15 Prover 4: Preprocessing ... % 3.25/1.20 Prover 6: Preprocessing ... % 3.25/1.20 Prover 5: Preprocessing ... % 3.25/1.20 Prover 0: Preprocessing ... % 3.25/1.20 Prover 2: Preprocessing ... % 3.25/1.20 Prover 3: Preprocessing ... % 8.23/1.91 Prover 5: Proving ... % 8.23/1.92 Prover 6: Proving ... % 8.86/1.96 Prover 1: Constructing countermodel ... % 8.86/1.96 Prover 3: Constructing countermodel ... % 8.86/1.96 Prover 2: Proving ... % 10.62/2.19 Prover 3: proved (1586ms) % 10.62/2.20 % 10.62/2.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.62/2.20 % 10.62/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.62/2.21 Prover 2: stopped % 10.62/2.21 Prover 6: stopped % 10.62/2.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.62/2.21 Prover 5: stopped % 10.62/2.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.62/2.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.11/2.28 Prover 4: Constructing countermodel ... % 11.11/2.31 Prover 0: Proving ... % 11.11/2.31 Prover 0: stopped % 11.48/2.32 Prover 7: Preprocessing ... % 11.48/2.33 Prover 11: Preprocessing ... % 11.48/2.33 Prover 8: Preprocessing ... % 11.48/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.48/2.34 Prover 1: Found proof (size 27) % 11.48/2.34 Prover 1: proved (1732ms) % 11.48/2.35 Prover 4: stopped % 11.75/2.35 Prover 10: Preprocessing ... % 11.75/2.35 Prover 7: stopped % 11.75/2.37 Prover 13: Preprocessing ... % 11.75/2.38 Prover 10: stopped % 11.75/2.41 Prover 13: stopped % 11.75/2.42 Prover 11: stopped % 12.89/2.55 Prover 8: Warning: ignoring some quantifiers % 12.97/2.57 Prover 8: Constructing countermodel ... % 12.97/2.58 Prover 8: stopped % 12.97/2.58 % 12.97/2.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.97/2.58 % 12.97/2.59 % SZS output start Proof for theBenchmark % 12.97/2.60 Assumptions after simplification: % 12.97/2.60 --------------------------------- % 12.97/2.60 % 12.97/2.60 (equivalence) % 13.38/2.65 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equivalence(v1, v0) = % 13.38/2.65 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 13.38/2.65 [v6: int] : ( ~ (v6 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v6 & % 13.38/2.65 apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & % 13.38/2.65 member(v3, v0) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] % 13.38/2.65 : ? [v5: int] : ( ~ (v5 = 0) & apply(v1, v4, v3) = v5 & apply(v1, v3, v4) = % 13.38/2.65 0 & member(v4, v0) = 0 & member(v3, v0) = 0 & $i(v4) & $i(v3)) | ? [v3: % 13.38/2.65 $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v1, v3, v3) = v4 & member(v3, % 13.38/2.65 v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (equivalence(v1, % 13.38/2.65 v0) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: % 13.38/2.65 $i] : ! [v5: int] : (v5 = 0 | ~ (apply(v1, v2, v4) = v5) | ~ % 13.38/2.65 (apply(v1, v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: % 13.38/2.65 any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v1, v3, v4) % 13.38/2.65 = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6 % 13.38/2.65 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: % 13.38/2.65 $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v1, v2, v2) = v3) | ~ $i(v2) | % 13.38/2.65 ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v2: $i] : ! % 13.38/2.65 [v3: $i] : ( ~ (apply(v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: % 13.38/2.65 any] : ? [v5: any] : ? [v6: any] : (apply(v1, v3, v2) = v6 & % 13.38/2.65 member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) % 13.38/2.65 | v6 = 0))))) % 13.38/2.65 % 13.38/2.65 (equivalence_class) % 13.38/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.38/2.66 int] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, % 13.38/2.66 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 13.38/2.66 : ? [v7: any] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 = % 13.38/2.66 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.38/2.66 [v3: $i] : ! [v4: $i] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ % 13.38/2.66 (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.38/2.66 (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) % 13.38/2.66 % 13.38/2.66 (thIII02) % 13.38/2.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 13.38/2.66 = 0) & equivalence_class(v2, v0, v1) = v3 & equivalence(v1, v0) = 0 & % 13.38/2.66 member(v2, v3) = v4 & member(v2, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & % 13.38/2.66 $i(v0)) % 13.38/2.66 % 13.38/2.66 (function-axioms) % 13.38/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 13.38/2.67 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, % 13.38/2.67 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 13.38/2.67 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = % 13.38/2.67 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.38/2.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.38/2.67 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0: % 13.38/2.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.38/2.67 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) & % 13.38/2.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.38/2.67 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) % 13.38/2.67 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.38/2.67 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 13.38/2.67 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.38/2.67 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 13.38/2.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.38/2.67 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 13.38/2.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 13.38/2.67 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.38/2.67 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 13.38/2.67 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.38/2.67 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 13.38/2.67 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.38/2.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 13.38/2.67 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.38/2.67 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.38/2.67 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 13.38/2.67 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 13.38/2.67 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 13.38/2.67 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 13.38/2.67 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 13.38/2.67 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 13.38/2.67 (power_set(v2) = v0)) % 13.38/2.67 % 13.38/2.67 Further assumptions not needed in the proof: % 13.38/2.67 -------------------------------------------- % 13.38/2.68 difference, disjoint, empty_set, equal_set, intersection, partition, power_set, % 13.38/2.68 pre_order, product, singleton, subset, sum, union, unordered_pair % 13.38/2.68 % 13.38/2.68 Those formulas are unsatisfiable: % 13.38/2.68 --------------------------------- % 13.38/2.68 % 13.38/2.68 Begin of proof % 13.38/2.68 | % 13.38/2.68 | ALPHA: (equivalence) implies: % 13.38/2.68 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (equivalence(v1, v0) = 0) | ~ $i(v1) | % 13.38/2.68 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : % 13.38/2.68 | (v5 = 0 | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) % 13.38/2.68 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] % 13.38/2.68 | : ? [v8: any] : ? [v9: any] : (apply(v1, v3, v4) = v9 & % 13.38/2.68 | member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6 % 13.38/2.68 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & % 13.38/2.68 | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v1, v2, v2) = v3) | % 13.38/2.68 | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & % 13.38/2.68 | ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v1, v2, v3) = 0) | ~ $i(v3) % 13.38/2.68 | | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 13.38/2.68 | (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) = % 13.38/2.68 | v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))))) % 13.38/2.68 | % 13.38/2.68 | ALPHA: (equivalence_class) implies: % 13.38/2.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 13.38/2.69 | ! [v5: int] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ % 13.38/2.69 | (member(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 13.38/2.69 | | ? [v6: any] : ? [v7: any] : (apply(v0, v2, v3) = v7 & member(v3, % 13.38/2.69 | v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 13.38/2.69 | % 13.38/2.69 | ALPHA: (function-axioms) implies: % 13.38/2.69 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.38/2.69 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 13.38/2.69 | = v0)) % 13.38/2.69 | % 13.38/2.69 | DELTA: instantiating (thIII02) with fresh symbols all_20_0, all_20_1, % 13.38/2.69 | all_20_2, all_20_3, all_20_4 gives: % 13.38/2.69 | (4) ~ (all_20_0 = 0) & equivalence_class(all_20_2, all_20_4, all_20_3) = % 13.38/2.69 | all_20_1 & equivalence(all_20_3, all_20_4) = 0 & member(all_20_2, % 13.38/2.69 | all_20_1) = all_20_0 & member(all_20_2, all_20_4) = 0 & $i(all_20_1) % 13.38/2.69 | & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) % 13.38/2.69 | % 13.38/2.69 | ALPHA: (4) implies: % 13.38/2.69 | (5) ~ (all_20_0 = 0) % 13.38/2.69 | (6) $i(all_20_4) % 13.38/2.69 | (7) $i(all_20_3) % 13.38/2.69 | (8) $i(all_20_2) % 13.38/2.69 | (9) member(all_20_2, all_20_4) = 0 % 13.38/2.69 | (10) member(all_20_2, all_20_1) = all_20_0 % 13.38/2.69 | (11) equivalence(all_20_3, all_20_4) = 0 % 13.38/2.69 | (12) equivalence_class(all_20_2, all_20_4, all_20_3) = all_20_1 % 13.38/2.69 | % 13.38/2.69 | GROUND_INST: instantiating (1) with all_20_4, all_20_3, simplifying with (6), % 13.38/2.69 | (7), (11) gives: % 13.38/2.70 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.38/2.70 | (apply(all_20_3, v0, v2) = v3) | ~ (apply(all_20_3, v0, v1) = 0) | % 13.38/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 13.38/2.70 | [v6: any] : ? [v7: any] : (apply(all_20_3, v1, v2) = v7 & % 13.38/2.70 | member(v2, all_20_4) = v6 & member(v1, all_20_4) = v5 & member(v0, % 13.38/2.70 | all_20_4) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ % 13.38/2.70 | (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 13.38/2.70 | (apply(all_20_3, v0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 13.38/2.70 | = 0) & member(v0, all_20_4) = v2)) & ! [v0: $i] : ! [v1: $i] : % 13.38/2.70 | ( ~ (apply(all_20_3, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 13.38/2.70 | any] : ? [v3: any] : ? [v4: any] : (apply(all_20_3, v1, v0) = v4 % 13.38/2.70 | & member(v1, all_20_4) = v3 & member(v0, all_20_4) = v2 & ( ~ (v3 % 13.38/2.70 | = 0) | ~ (v2 = 0) | v4 = 0))) % 13.38/2.70 | % 13.38/2.70 | ALPHA: (13) implies: % 13.38/2.70 | (14) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_20_3, v0, v0) = % 13.38/2.70 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 13.38/2.70 | all_20_4) = v2)) % 13.38/2.70 | % 13.38/2.70 | GROUND_INST: instantiating (2) with all_20_3, all_20_4, all_20_2, all_20_2, % 13.38/2.70 | all_20_1, all_20_0, simplifying with (6), (7), (8), (10), (12) % 13.38/2.70 | gives: % 13.38/2.70 | (15) all_20_0 = 0 | ? [v0: any] : ? [v1: any] : (apply(all_20_3, % 13.38/2.70 | all_20_2, all_20_2) = v1 & member(all_20_2, all_20_4) = v0 & ( ~ % 13.38/2.70 | (v1 = 0) | ~ (v0 = 0))) % 13.38/2.70 | % 13.38/2.70 | BETA: splitting (15) gives: % 13.38/2.70 | % 13.38/2.70 | Case 1: % 13.38/2.70 | | % 13.38/2.70 | | (16) all_20_0 = 0 % 13.38/2.70 | | % 13.38/2.70 | | REDUCE: (5), (16) imply: % 13.38/2.70 | | (17) $false % 13.38/2.71 | | % 13.38/2.71 | | CLOSE: (17) is inconsistent. % 13.38/2.71 | | % 13.38/2.71 | Case 2: % 13.38/2.71 | | % 13.38/2.71 | | (18) ? [v0: any] : ? [v1: any] : (apply(all_20_3, all_20_2, all_20_2) = % 13.38/2.71 | | v1 & member(all_20_2, all_20_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 13.38/2.71 | | 0))) % 13.38/2.71 | | % 13.38/2.71 | | DELTA: instantiating (18) with fresh symbols all_32_0, all_32_1 gives: % 13.38/2.71 | | (19) apply(all_20_3, all_20_2, all_20_2) = all_32_0 & member(all_20_2, % 13.38/2.71 | | all_20_4) = all_32_1 & ( ~ (all_32_0 = 0) | ~ (all_32_1 = 0)) % 13.38/2.71 | | % 13.38/2.71 | | ALPHA: (19) implies: % 13.38/2.71 | | (20) member(all_20_2, all_20_4) = all_32_1 % 13.38/2.71 | | (21) apply(all_20_3, all_20_2, all_20_2) = all_32_0 % 13.38/2.71 | | (22) ~ (all_32_0 = 0) | ~ (all_32_1 = 0) % 13.38/2.71 | | % 13.38/2.71 | | GROUND_INST: instantiating (3) with 0, all_32_1, all_20_4, all_20_2, % 13.38/2.71 | | simplifying with (9), (20) gives: % 13.38/2.71 | | (23) all_32_1 = 0 % 13.38/2.71 | | % 13.38/2.71 | | BETA: splitting (22) gives: % 13.38/2.71 | | % 13.38/2.71 | | Case 1: % 13.38/2.71 | | | % 13.38/2.71 | | | (24) ~ (all_32_0 = 0) % 13.38/2.71 | | | % 13.38/2.71 | | | GROUND_INST: instantiating (14) with all_20_2, all_32_0, simplifying with % 13.38/2.71 | | | (8), (21) gives: % 13.38/2.71 | | | (25) all_32_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_20_2, % 13.38/2.71 | | | all_20_4) = v0) % 13.38/2.71 | | | % 13.38/2.71 | | | BETA: splitting (25) gives: % 13.38/2.71 | | | % 13.38/2.71 | | | Case 1: % 13.38/2.71 | | | | % 13.38/2.71 | | | | (26) all_32_0 = 0 % 13.38/2.71 | | | | % 13.38/2.71 | | | | REDUCE: (24), (26) imply: % 13.38/2.71 | | | | (27) $false % 13.38/2.71 | | | | % 13.38/2.71 | | | | CLOSE: (27) is inconsistent. % 13.38/2.71 | | | | % 13.38/2.71 | | | Case 2: % 13.38/2.71 | | | | % 13.38/2.71 | | | | (28) ? [v0: int] : ( ~ (v0 = 0) & member(all_20_2, all_20_4) = v0) % 13.38/2.71 | | | | % 13.38/2.71 | | | | DELTA: instantiating (28) with fresh symbol all_49_0 gives: % 13.38/2.71 | | | | (29) ~ (all_49_0 = 0) & member(all_20_2, all_20_4) = all_49_0 % 13.38/2.71 | | | | % 13.38/2.71 | | | | ALPHA: (29) implies: % 13.38/2.71 | | | | (30) ~ (all_49_0 = 0) % 13.38/2.71 | | | | (31) member(all_20_2, all_20_4) = all_49_0 % 13.38/2.71 | | | | % 13.38/2.71 | | | | GROUND_INST: instantiating (3) with 0, all_49_0, all_20_4, all_20_2, % 13.38/2.71 | | | | simplifying with (9), (31) gives: % 13.38/2.71 | | | | (32) all_49_0 = 0 % 13.38/2.71 | | | | % 13.38/2.71 | | | | REDUCE: (30), (32) imply: % 13.38/2.71 | | | | (33) $false % 13.38/2.71 | | | | % 13.38/2.71 | | | | CLOSE: (33) is inconsistent. % 13.38/2.71 | | | | % 13.38/2.71 | | | End of split % 13.38/2.71 | | | % 13.38/2.71 | | Case 2: % 13.38/2.71 | | | % 13.38/2.72 | | | (34) ~ (all_32_1 = 0) % 13.38/2.72 | | | % 13.38/2.72 | | | REDUCE: (23), (34) imply: % 13.38/2.72 | | | (35) $false % 13.38/2.72 | | | % 13.38/2.72 | | | CLOSE: (35) is inconsistent. % 13.38/2.72 | | | % 13.38/2.72 | | End of split % 13.38/2.72 | | % 13.38/2.72 | End of split % 13.38/2.72 | % 13.38/2.72 End of proof % 13.38/2.72 % SZS output end Proof for theBenchmark % 13.38/2.72 % 13.38/2.72 2134ms %------------------------------------------------------------------------------