%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET758+4 : TPTP v8.1.2. Bugfixed v2.2.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.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 15:26:19 EDT 2023 % Result : Theorem 10.82s 2.22s % Output : Proof 14.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET758+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n010.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 15:53:35 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.42/1.16 Prover 4: Preprocessing ... % 3.42/1.16 Prover 1: Preprocessing ... % 3.72/1.19 Prover 6: Preprocessing ... % 3.72/1.19 Prover 0: Preprocessing ... % 3.72/1.19 Prover 3: Preprocessing ... % 3.72/1.19 Prover 2: Preprocessing ... % 3.72/1.19 Prover 5: Preprocessing ... % 8.75/1.92 Prover 5: Proving ... % 9.20/1.94 Prover 2: Proving ... % 9.20/1.98 Prover 6: Proving ... % 9.20/2.02 Prover 1: Constructing countermodel ... % 9.20/2.04 Prover 3: Constructing countermodel ... % 10.82/2.22 Prover 3: proved (1594ms) % 10.82/2.22 % 10.82/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.82/2.22 % 10.82/2.22 Prover 2: stopped % 10.82/2.22 Prover 6: stopped % 10.82/2.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.82/2.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.82/2.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.82/2.23 Prover 5: stopped % 11.39/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.58/2.31 Prover 10: Preprocessing ... % 11.58/2.32 Prover 1: Found proof (size 45) % 11.97/2.35 Prover 7: Preprocessing ... % 11.97/2.35 Prover 1: proved (1713ms) % 11.97/2.35 Prover 11: Preprocessing ... % 12.14/2.36 Prover 8: Preprocessing ... % 12.14/2.36 Prover 10: stopped % 12.14/2.38 Prover 7: stopped % 12.98/2.47 Prover 11: stopped % 12.98/2.53 Prover 4: Constructing countermodel ... % 13.52/2.54 Prover 0: Proving ... % 13.52/2.54 Prover 0: stopped % 13.52/2.55 Prover 4: stopped % 13.69/2.61 Prover 8: Warning: ignoring some quantifiers % 13.69/2.62 Prover 8: Constructing countermodel ... % 13.69/2.63 Prover 8: stopped % 13.69/2.63 % 13.69/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.69/2.63 % 13.69/2.64 % SZS output start Proof for theBenchmark % 13.69/2.64 Assumptions after simplification: % 13.69/2.64 --------------------------------- % 13.69/2.64 % 13.69/2.64 (image3) % 13.69/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.69/2.67 int] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = v5) | % 13.69/2.67 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & % 13.69/2.67 member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v6, v3) = 0) | ~ % 13.69/2.67 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) & ! [v0: % 13.69/2.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.69/2.67 (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2) % 13.69/2.67 | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] : (apply(v0, v5, % 13.69/2.67 v3) = 0 & member(v5, v1) = 0 & $i(v5)))) % 13.69/2.67 % 13.69/2.67 (inverse_image3) % 13.69/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.69/2.67 int] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = % 13.69/2.68 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ % 13.69/2.68 (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v3, v6) = % 13.69/2.68 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) & % 13.69/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.69/2.68 (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~ % 13.69/2.68 $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] : % 13.69/2.68 (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5)))) % 13.69/2.68 % 13.69/2.68 (maps) % 13.69/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.69/2.68 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 13.69/2.68 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, % 13.69/2.68 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = % 13.69/2.68 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4) % 13.69/2.68 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( % 13.69/2.68 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 13.69/2.68 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( % 13.69/2.68 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) % 13.69/2.68 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 13.69/2.68 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 13.69/2.68 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) % 13.69/2.68 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~ % 13.69/2.68 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 & % 13.69/2.68 $i(v4))))) % 13.69/2.68 % 13.69/2.68 (subset) % 13.69/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 13.69/2.68 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 13.69/2.68 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 13.69/2.68 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 13.69/2.68 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 13.69/2.68 % 13.69/2.68 (thIIa08) % 13.69/2.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.69/2.69 $i] : ? [v6: int] : ( ~ (v6 = 0) & inverse_image3(v0, v3, v1) = v4 & % 13.69/2.69 image3(v0, v4, v2) = v5 & maps(v0, v1, v2) = 0 & subset(v5, v3) = v6 & % 13.69/2.69 subset(v3, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.69/2.69 % 13.69/2.69 (function-axioms) % 13.69/2.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.69/2.70 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 13.69/2.70 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 13.69/2.70 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.69/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.69/2.70 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 13.69/2.70 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.69/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.69/2.70 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 13.69/2.70 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.69/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.69/2.70 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 13.69/2.70 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.69/2.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 13.69/2.70 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 13.69/2.70 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 13.69/2.70 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.69/2.70 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 13.69/2.70 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.69/2.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.69/2.70 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 13.69/2.70 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.69/2.70 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 13.69/2.70 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.69/2.70 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 13.69/2.70 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.69/2.70 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 13.69/2.70 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.69/2.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 13.69/2.70 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 13.69/2.70 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.69/2.70 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 13.69/2.70 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.69/2.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 13.69/2.70 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 13.69/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.69/2.70 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 13.69/2.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.69/2.70 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 13.69/2.70 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.69/2.70 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 13.69/2.70 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.69/2.70 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 13.69/2.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.69/2.70 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 13.69/2.70 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.69/2.70 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 13.69/2.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.69/2.70 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 13.69/2.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 13.69/2.70 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.69/2.70 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 13.69/2.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.69/2.70 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 13.69/2.70 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.69/2.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 13.69/2.70 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.69/2.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.69/2.70 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 13.69/2.70 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 13.69/2.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 13.69/2.70 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 13.69/2.70 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 13.69/2.70 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 13.69/2.70 (power_set(v2) = v0)) % 13.69/2.70 % 13.69/2.70 Further assumptions not needed in the proof: % 13.69/2.70 -------------------------------------------- % 13.69/2.70 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 13.69/2.70 equal_maps, equal_set, identity, image2, increasing_function, injective, % 13.69/2.70 intersection, inverse_function, inverse_image2, inverse_predicate, isomorphism, % 13.69/2.70 one_to_one, power_set, product, singleton, sum, surjective, union, % 13.69/2.70 unordered_pair % 13.69/2.70 % 13.69/2.70 Those formulas are unsatisfiable: % 13.69/2.70 --------------------------------- % 13.69/2.70 % 13.69/2.70 Begin of proof % 13.69/2.70 | % 13.69/2.70 | ALPHA: (subset) implies: % 13.69/2.70 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 13.69/2.70 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 13.69/2.70 | member(v2, v1) = 0)) % 13.69/2.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 13.69/2.70 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 13.69/2.70 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 13.69/2.71 | % 13.69/2.71 | ALPHA: (maps) implies: % 13.69/2.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | % 13.69/2.71 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : ! % 13.69/2.71 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, % 13.69/2.71 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 13.69/2.71 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 13.69/2.71 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ % 13.69/2.71 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) % 13.69/2.71 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 13.69/2.71 | member(v4, v2) = 0 & $i(v4))))) % 13.69/2.71 | % 13.69/2.71 | ALPHA: (image3) implies: % 13.69/2.71 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 13.69/2.71 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | % 13.69/2.71 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] % 13.69/2.71 | : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0 & $i(v5)))) % 13.69/2.71 | % 13.69/2.71 | ALPHA: (inverse_image3) implies: % 13.69/2.71 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 13.69/2.71 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ % 13.69/2.71 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? % 13.69/2.71 | [v5: $i] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5)))) % 13.69/2.71 | % 13.69/2.71 | ALPHA: (function-axioms) implies: % 13.69/2.71 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.69/2.71 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 13.69/2.71 | = v0)) % 13.69/2.71 | % 13.69/2.71 | DELTA: instantiating (thIIa08) with fresh symbols all_32_0, all_32_1, % 13.69/2.71 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6 gives: % 13.69/2.71 | (7) ~ (all_32_0 = 0) & inverse_image3(all_32_6, all_32_3, all_32_5) = % 13.69/2.71 | all_32_2 & image3(all_32_6, all_32_2, all_32_4) = all_32_1 & % 13.69/2.71 | maps(all_32_6, all_32_5, all_32_4) = 0 & subset(all_32_1, all_32_3) = % 13.69/2.71 | all_32_0 & subset(all_32_3, all_32_4) = 0 & $i(all_32_1) & $i(all_32_2) % 13.69/2.71 | & $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) % 13.69/2.71 | % 13.69/2.71 | ALPHA: (7) implies: % 13.69/2.71 | (8) ~ (all_32_0 = 0) % 13.69/2.71 | (9) $i(all_32_6) % 13.69/2.71 | (10) $i(all_32_5) % 13.69/2.71 | (11) $i(all_32_4) % 13.69/2.71 | (12) $i(all_32_3) % 13.69/2.72 | (13) $i(all_32_2) % 13.69/2.72 | (14) $i(all_32_1) % 14.37/2.72 | (15) subset(all_32_3, all_32_4) = 0 % 14.37/2.72 | (16) subset(all_32_1, all_32_3) = all_32_0 % 14.37/2.72 | (17) maps(all_32_6, all_32_5, all_32_4) = 0 % 14.37/2.72 | (18) image3(all_32_6, all_32_2, all_32_4) = all_32_1 % 14.37/2.72 | (19) inverse_image3(all_32_6, all_32_3, all_32_5) = all_32_2 % 14.37/2.72 | % 14.37/2.72 | GROUND_INST: instantiating (1) with all_32_3, all_32_4, simplifying with (11), % 14.37/2.72 | (12), (15) gives: % 14.37/2.72 | (20) ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | member(v0, % 14.37/2.72 | all_32_4) = 0) % 14.37/2.72 | % 14.37/2.72 | GROUND_INST: instantiating (2) with all_32_1, all_32_3, all_32_0, simplifying % 14.37/2.72 | with (12), (14), (16) gives: % 14.37/2.72 | (21) all_32_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 14.37/2.72 | all_32_1) = 0 & member(v0, all_32_3) = v1 & $i(v0)) % 14.37/2.72 | % 14.37/2.72 | GROUND_INST: instantiating (3) with all_32_6, all_32_5, all_32_4, simplifying % 14.37/2.72 | with (9), (10), (11), (17) gives: % 14.37/2.72 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 14.37/2.72 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) | % 14.37/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 14.37/2.72 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_4) = v4 & % 14.37/2.72 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 14.37/2.72 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_5) = 0) | ~ % 14.37/2.72 | $i(v0) | ? [v1: $i] : (apply(all_32_6, v0, v1) = 0 & member(v1, % 14.37/2.72 | all_32_4) = 0 & $i(v1))) % 14.37/2.72 | % 14.37/2.72 | ALPHA: (22) implies: % 14.37/2.72 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 14.37/2.72 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) | % 14.37/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 14.37/2.72 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_4) = v4 & % 14.37/2.72 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 14.37/2.72 | 0)))) % 14.37/2.72 | % 14.37/2.72 | BETA: splitting (21) gives: % 14.37/2.72 | % 14.37/2.72 | Case 1: % 14.37/2.72 | | % 14.37/2.72 | | (24) all_32_0 = 0 % 14.37/2.72 | | % 14.37/2.72 | | REDUCE: (8), (24) imply: % 14.37/2.72 | | (25) $false % 14.37/2.73 | | % 14.37/2.73 | | CLOSE: (25) is inconsistent. % 14.37/2.73 | | % 14.37/2.73 | Case 2: % 14.37/2.73 | | % 14.37/2.73 | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) = 0 % 14.37/2.73 | | & member(v0, all_32_3) = v1 & $i(v0)) % 14.37/2.73 | | % 14.37/2.73 | | DELTA: instantiating (26) with fresh symbols all_44_0, all_44_1 gives: % 14.37/2.73 | | (27) ~ (all_44_0 = 0) & member(all_44_1, all_32_1) = 0 & % 14.37/2.73 | | member(all_44_1, all_32_3) = all_44_0 & $i(all_44_1) % 14.37/2.73 | | % 14.37/2.73 | | ALPHA: (27) implies: % 14.37/2.73 | | (28) ~ (all_44_0 = 0) % 14.37/2.73 | | (29) $i(all_44_1) % 14.37/2.73 | | (30) member(all_44_1, all_32_3) = all_44_0 % 14.37/2.73 | | (31) member(all_44_1, all_32_1) = 0 % 14.37/2.73 | | % 14.37/2.73 | | GROUND_INST: instantiating (4) with all_32_6, all_32_2, all_32_4, all_44_1, % 14.37/2.73 | | all_32_1, simplifying with (9), (11), (13), (18), (29), (31) % 14.37/2.73 | | gives: % 14.37/2.73 | | (32) member(all_44_1, all_32_4) = 0 & ? [v0: $i] : (apply(all_32_6, v0, % 14.37/2.73 | | all_44_1) = 0 & member(v0, all_32_2) = 0 & $i(v0)) % 14.37/2.73 | | % 14.37/2.73 | | ALPHA: (32) implies: % 14.37/2.73 | | (33) member(all_44_1, all_32_4) = 0 % 14.37/2.73 | | (34) ? [v0: $i] : (apply(all_32_6, v0, all_44_1) = 0 & member(v0, % 14.37/2.73 | | all_32_2) = 0 & $i(v0)) % 14.37/2.73 | | % 14.37/2.73 | | DELTA: instantiating (34) with fresh symbol all_52_0 gives: % 14.37/2.73 | | (35) apply(all_32_6, all_52_0, all_44_1) = 0 & member(all_52_0, all_32_2) % 14.37/2.73 | | = 0 & $i(all_52_0) % 14.37/2.73 | | % 14.37/2.73 | | ALPHA: (35) implies: % 14.37/2.73 | | (36) $i(all_52_0) % 14.37/2.73 | | (37) member(all_52_0, all_32_2) = 0 % 14.37/2.73 | | (38) apply(all_32_6, all_52_0, all_44_1) = 0 % 14.37/2.73 | | % 14.37/2.73 | | GROUND_INST: instantiating (5) with all_32_6, all_32_3, all_32_5, all_52_0, % 14.37/2.73 | | all_32_2, simplifying with (9), (10), (12), (19), (36), (37) % 14.37/2.73 | | gives: % 14.37/2.73 | | (39) member(all_52_0, all_32_5) = 0 & ? [v0: $i] : (apply(all_32_6, % 14.37/2.73 | | all_52_0, v0) = 0 & member(v0, all_32_3) = 0 & $i(v0)) % 14.37/2.73 | | % 14.37/2.73 | | ALPHA: (39) implies: % 14.37/2.73 | | (40) member(all_52_0, all_32_5) = 0 % 14.37/2.73 | | (41) ? [v0: $i] : (apply(all_32_6, all_52_0, v0) = 0 & member(v0, % 14.37/2.73 | | all_32_3) = 0 & $i(v0)) % 14.37/2.73 | | % 14.37/2.73 | | DELTA: instantiating (41) with fresh symbol all_60_0 gives: % 14.37/2.73 | | (42) apply(all_32_6, all_52_0, all_60_0) = 0 & member(all_60_0, all_32_3) % 14.37/2.73 | | = 0 & $i(all_60_0) % 14.37/2.73 | | % 14.37/2.73 | | ALPHA: (42) implies: % 14.37/2.73 | | (43) $i(all_60_0) % 14.37/2.73 | | (44) member(all_60_0, all_32_3) = 0 % 14.37/2.74 | | (45) apply(all_32_6, all_52_0, all_60_0) = 0 % 14.37/2.74 | | % 14.37/2.74 | | GROUND_INST: instantiating (20) with all_60_0, simplifying with (43), (44) % 14.37/2.74 | | gives: % 14.37/2.74 | | (46) member(all_60_0, all_32_4) = 0 % 14.37/2.74 | | % 14.37/2.74 | | GROUND_INST: instantiating (23) with all_52_0, all_60_0, all_44_1, % 14.37/2.74 | | simplifying with (29), (36), (38), (43), (45) gives: % 14.37/2.74 | | (47) all_60_0 = all_44_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 14.37/2.74 | | (member(all_60_0, all_32_4) = v1 & member(all_52_0, all_32_5) = v0 & % 14.37/2.74 | | member(all_44_1, all_32_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 14.37/2.74 | | (v0 = 0))) % 14.37/2.74 | | % 14.37/2.74 | | BETA: splitting (47) gives: % 14.37/2.74 | | % 14.37/2.74 | | Case 1: % 14.37/2.74 | | | % 14.37/2.74 | | | (48) all_60_0 = all_44_1 % 14.37/2.74 | | | % 14.37/2.74 | | | REDUCE: (44), (48) imply: % 14.37/2.74 | | | (49) member(all_44_1, all_32_3) = 0 % 14.37/2.74 | | | % 14.37/2.74 | | | GROUND_INST: instantiating (6) with all_44_0, 0, all_32_3, all_44_1, % 14.37/2.74 | | | simplifying with (30), (49) gives: % 14.37/2.74 | | | (50) all_44_0 = 0 % 14.37/2.74 | | | % 14.37/2.74 | | | REDUCE: (28), (50) imply: % 14.37/2.74 | | | (51) $false % 14.37/2.74 | | | % 14.37/2.74 | | | CLOSE: (51) is inconsistent. % 14.37/2.74 | | | % 14.37/2.74 | | Case 2: % 14.37/2.74 | | | % 14.49/2.74 | | | (52) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_60_0, % 14.49/2.74 | | | all_32_4) = v1 & member(all_52_0, all_32_5) = v0 & % 14.49/2.74 | | | member(all_44_1, all_32_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 14.49/2.74 | | | ~ (v0 = 0))) % 14.49/2.74 | | | % 14.49/2.74 | | | DELTA: instantiating (52) with fresh symbols all_74_0, all_74_1, all_74_2 % 14.49/2.74 | | | gives: % 14.49/2.74 | | | (53) member(all_60_0, all_32_4) = all_74_1 & member(all_52_0, all_32_5) % 14.49/2.74 | | | = all_74_2 & member(all_44_1, all_32_4) = all_74_0 & ( ~ (all_74_0 % 14.49/2.74 | | | = 0) | ~ (all_74_1 = 0) | ~ (all_74_2 = 0)) % 14.49/2.74 | | | % 14.49/2.74 | | | ALPHA: (53) implies: % 14.49/2.74 | | | (54) member(all_44_1, all_32_4) = all_74_0 % 14.49/2.74 | | | (55) member(all_52_0, all_32_5) = all_74_2 % 14.49/2.74 | | | (56) member(all_60_0, all_32_4) = all_74_1 % 14.49/2.74 | | | (57) ~ (all_74_0 = 0) | ~ (all_74_1 = 0) | ~ (all_74_2 = 0) % 14.49/2.74 | | | % 14.49/2.74 | | | GROUND_INST: instantiating (6) with 0, all_74_0, all_32_4, all_44_1, % 14.49/2.74 | | | simplifying with (33), (54) gives: % 14.49/2.74 | | | (58) all_74_0 = 0 % 14.49/2.74 | | | % 14.49/2.74 | | | GROUND_INST: instantiating (6) with 0, all_74_2, all_32_5, all_52_0, % 14.49/2.74 | | | simplifying with (40), (55) gives: % 14.49/2.74 | | | (59) all_74_2 = 0 % 14.49/2.74 | | | % 14.49/2.74 | | | GROUND_INST: instantiating (6) with 0, all_74_1, all_32_4, all_60_0, % 14.49/2.74 | | | simplifying with (46), (56) gives: % 14.49/2.74 | | | (60) all_74_1 = 0 % 14.49/2.74 | | | % 14.49/2.74 | | | BETA: splitting (57) gives: % 14.49/2.74 | | | % 14.49/2.74 | | | Case 1: % 14.49/2.74 | | | | % 14.49/2.74 | | | | (61) ~ (all_74_0 = 0) % 14.49/2.74 | | | | % 14.49/2.74 | | | | REDUCE: (58), (61) imply: % 14.49/2.74 | | | | (62) $false % 14.49/2.74 | | | | % 14.49/2.74 | | | | CLOSE: (62) is inconsistent. % 14.49/2.74 | | | | % 14.49/2.74 | | | Case 2: % 14.49/2.74 | | | | % 14.49/2.74 | | | | (63) ~ (all_74_1 = 0) | ~ (all_74_2 = 0) % 14.49/2.74 | | | | % 14.49/2.74 | | | | BETA: splitting (63) gives: % 14.49/2.74 | | | | % 14.49/2.74 | | | | Case 1: % 14.49/2.74 | | | | | % 14.49/2.74 | | | | | (64) ~ (all_74_1 = 0) % 14.49/2.74 | | | | | % 14.49/2.74 | | | | | REDUCE: (60), (64) imply: % 14.49/2.74 | | | | | (65) $false % 14.49/2.74 | | | | | % 14.49/2.74 | | | | | CLOSE: (65) is inconsistent. % 14.49/2.74 | | | | | % 14.49/2.74 | | | | Case 2: % 14.49/2.74 | | | | | % 14.49/2.74 | | | | | (66) ~ (all_74_2 = 0) % 14.49/2.74 | | | | | % 14.49/2.74 | | | | | REDUCE: (59), (66) imply: % 14.49/2.74 | | | | | (67) $false % 14.49/2.74 | | | | | % 14.49/2.74 | | | | | CLOSE: (67) is inconsistent. % 14.49/2.74 | | | | | % 14.49/2.75 | | | | End of split % 14.49/2.75 | | | | % 14.49/2.75 | | | End of split % 14.49/2.75 | | | % 14.49/2.75 | | End of split % 14.49/2.75 | | % 14.49/2.75 | End of split % 14.49/2.75 | % 14.49/2.75 End of proof % 14.49/2.75 % SZS output end Proof for theBenchmark % 14.49/2.75 % 14.49/2.75 2146ms %------------------------------------------------------------------------------