%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET731+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 : n012.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 15:26:12 EDT 2023 % Result : Theorem 12.49s 2.51s % Output : Proof 15.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET731+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n012.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 14:06:10 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.61/1.25 Prover 1: Preprocessing ... % 3.61/1.26 Prover 4: Preprocessing ... % 3.61/1.30 Prover 2: Preprocessing ... % 3.61/1.30 Prover 5: Preprocessing ... % 3.61/1.30 Prover 3: Preprocessing ... % 3.61/1.30 Prover 6: Preprocessing ... % 3.61/1.31 Prover 0: Preprocessing ... % 9.21/2.12 Prover 5: Proving ... % 9.21/2.17 Prover 2: Proving ... % 9.94/2.25 Prover 6: Proving ... % 9.94/2.26 Prover 3: Constructing countermodel ... % 9.94/2.29 Prover 1: Constructing countermodel ... % 12.49/2.51 Prover 3: proved (1880ms) % 12.49/2.51 % 12.49/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.49/2.51 % 12.49/2.53 Prover 2: stopped % 12.49/2.54 Prover 5: stopped % 12.49/2.55 Prover 6: stopped % 12.49/2.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.49/2.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.49/2.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.49/2.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.49/2.58 Prover 7: Preprocessing ... % 13.18/2.64 Prover 8: Preprocessing ... % 13.18/2.64 Prover 10: Preprocessing ... % 13.18/2.67 Prover 11: Preprocessing ... % 13.82/2.72 Prover 1: Found proof (size 44) % 13.82/2.72 Prover 1: proved (2092ms) % 13.82/2.77 Prover 10: Warning: ignoring some quantifiers % 14.57/2.80 Prover 0: Proving ... % 14.57/2.80 Prover 0: stopped % 14.57/2.80 Prover 7: Warning: ignoring some quantifiers % 14.57/2.83 Prover 10: Constructing countermodel ... % 14.57/2.84 Prover 7: Constructing countermodel ... % 14.57/2.87 Prover 10: stopped % 14.57/2.88 Prover 7: stopped % 14.57/2.88 Prover 11: stopped % 14.57/2.91 Prover 8: Warning: ignoring some quantifiers % 14.57/2.93 Prover 8: Constructing countermodel ... % 14.57/2.93 Prover 8: stopped % 14.57/2.94 Prover 4: Constructing countermodel ... % 15.48/2.96 Prover 4: stopped % 15.48/2.96 % 15.48/2.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.48/2.96 % 15.48/2.97 % SZS output start Proof for theBenchmark % 15.48/2.98 Assumptions after simplification: % 15.48/2.98 --------------------------------- % 15.48/2.98 % 15.48/2.98 (image2) % 15.48/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.48/3.01 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 15.48/3.01 $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) = 0) | ~ $i(v5) | % 15.48/3.01 ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : ! % 15.48/3.01 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, v1) = v3) | ~ % 15.48/3.01 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 15.48/3.01 (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4))) % 15.48/3.01 % 15.48/3.01 (maps) % 15.48/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.48/3.02 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 15.48/3.02 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, % 15.48/3.02 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = % 15.48/3.02 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4) % 15.48/3.02 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( % 15.48/3.02 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 15.48/3.02 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( % 15.48/3.02 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) % 15.48/3.02 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 15.48/3.02 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 15.48/3.02 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) % 15.48/3.02 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~ % 15.48/3.02 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 & % 15.48/3.02 $i(v4))))) % 15.48/3.02 % 15.48/3.02 (surjective) % 15.48/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.48/3.03 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 15.48/3.03 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4) % 15.48/3.03 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = % 15.48/3.03 v6)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, % 15.48/3.03 v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ % 15.48/3.03 (member(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v4, v3) = 0 & % 15.48/3.03 member(v4, v1) = 0 & $i(v4)))) % 15.48/3.03 % 15.48/3.03 (thII22) % 15.48/3.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.48/3.03 int] : ( ~ (v5 = 0) & image2(v0, v2) = v4 & surjective(v1, v2, v4) = v5 & % 15.48/3.03 maps(v0, v2, v3) = 0 & subset(v4, v3) = 0 & $i(v4) & $i(v3) & $i(v2) & % 15.48/3.03 $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: $i] : ! [v8: any] : ( ~ (apply(v0, % 15.48/3.03 v6, v7) = v8) | ~ $i(v7) | ~ $i(v6) | ? [v9: any] : ? [v10: any] : % 15.48/3.03 ? [v11: any] : (apply(v1, v6, v7) = v11 & member(v7, v4) = v10 & % 15.48/3.03 member(v6, v2) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | (( ~ (v11 = 0) | v8 % 15.48/3.03 = 0) & ( ~ (v8 = 0) | v11 = 0)))))) % 15.48/3.03 % 15.48/3.03 (function-axioms) % 15.48/3.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.48/3.04 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 15.48/3.04 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 15.48/3.04 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.48/3.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.48/3.04 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 15.48/3.04 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.48/3.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.48/3.04 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 15.48/3.04 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.48/3.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.48/3.04 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 15.48/3.04 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.48/3.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 15.48/3.04 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 15.48/3.04 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 15.48/3.04 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.48/3.04 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 15.48/3.04 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.48/3.04 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.48/3.04 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 15.48/3.04 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.48/3.04 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 15.48/3.04 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.48/3.04 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 15.48/3.04 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.48/3.04 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 15.48/3.04 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.48/3.04 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 15.48/3.04 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 15.48/3.04 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.48/3.04 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 15.48/3.04 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.48/3.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.48/3.04 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 15.48/3.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.48/3.04 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 15.48/3.04 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.48/3.04 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 15.48/3.04 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.48/3.04 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 15.48/3.04 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.48/3.04 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 15.48/3.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.48/3.04 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 15.48/3.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.48/3.04 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 15.48/3.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.48/3.04 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 15.48/3.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 15.48/3.04 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.48/3.04 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 15.48/3.04 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.48/3.04 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 15.48/3.04 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.48/3.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 15.48/3.04 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.48/3.04 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.48/3.04 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 15.48/3.04 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 15.48/3.04 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 15.48/3.04 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.48/3.04 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 15.48/3.04 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 15.48/3.04 (power_set(v2) = v0)) % 15.48/3.04 % 15.48/3.04 Further assumptions not needed in the proof: % 15.48/3.04 -------------------------------------------- % 15.48/3.04 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 15.48/3.04 equal_maps, equal_set, identity, image3, increasing_function, injective, % 15.48/3.04 intersection, inverse_function, inverse_image2, inverse_image3, % 15.48/3.04 inverse_predicate, isomorphism, one_to_one, power_set, product, singleton, % 15.48/3.04 subset, sum, union, unordered_pair % 15.48/3.04 % 15.48/3.04 Those formulas are unsatisfiable: % 15.48/3.04 --------------------------------- % 15.48/3.04 % 15.48/3.04 Begin of proof % 15.48/3.04 | % 15.48/3.04 | ALPHA: (maps) implies: % 15.95/3.05 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | % 15.95/3.05 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : ! % 15.95/3.05 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, % 15.95/3.05 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 15.95/3.05 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 15.95/3.05 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ % 15.95/3.05 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) % 15.95/3.05 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 15.95/3.05 | member(v4, v2) = 0 & $i(v4))))) % 15.95/3.05 | % 15.95/3.05 | ALPHA: (surjective) implies: % 15.95/3.05 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.95/3.05 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 15.95/3.05 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ % 15.95/3.05 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) % 15.95/3.05 | & member(v5, v1) = v6)))) % 15.95/3.05 | % 15.95/3.05 | ALPHA: (image2) implies: % 15.95/3.05 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, % 15.95/3.05 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 15.95/3.05 | $i(v0) | ? [v4: $i] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & % 15.95/3.05 | $i(v4))) % 15.95/3.05 | % 15.95/3.05 | ALPHA: (function-axioms) implies: % 15.95/3.05 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.95/3.05 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 15.95/3.05 | = v0)) % 15.95/3.05 | % 15.95/3.05 | DELTA: instantiating (thII22) with fresh symbols all_32_0, all_32_1, all_32_2, % 15.95/3.05 | all_32_3, all_32_4, all_32_5 gives: % 15.95/3.06 | (5) ~ (all_32_0 = 0) & image2(all_32_5, all_32_3) = all_32_1 & % 15.95/3.06 | surjective(all_32_4, all_32_3, all_32_1) = all_32_0 & maps(all_32_5, % 15.95/3.06 | all_32_3, all_32_2) = 0 & subset(all_32_1, all_32_2) = 0 & % 15.95/3.06 | $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & % 15.95/3.06 | $i(all_32_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 15.95/3.06 | (apply(all_32_5, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] % 15.95/3.06 | : ? [v4: any] : ? [v5: any] : (apply(all_32_4, v0, v1) = v5 & % 15.95/3.06 | member(v1, all_32_1) = v4 & member(v0, all_32_3) = v3 & ( ~ (v4 = % 15.95/3.06 | 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 % 15.95/3.06 | = 0))))) % 15.95/3.06 | % 15.95/3.06 | ALPHA: (5) implies: % 15.95/3.06 | (6) ~ (all_32_0 = 0) % 15.95/3.06 | (7) $i(all_32_5) % 15.95/3.06 | (8) $i(all_32_4) % 15.95/3.06 | (9) $i(all_32_3) % 15.95/3.06 | (10) $i(all_32_2) % 15.95/3.06 | (11) $i(all_32_1) % 15.95/3.06 | (12) maps(all_32_5, all_32_3, all_32_2) = 0 % 15.95/3.06 | (13) surjective(all_32_4, all_32_3, all_32_1) = all_32_0 % 15.95/3.06 | (14) image2(all_32_5, all_32_3) = all_32_1 % 15.95/3.06 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_32_5, v0, % 15.95/3.06 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 15.95/3.06 | : ? [v5: any] : (apply(all_32_4, v0, v1) = v5 & member(v1, % 15.95/3.06 | all_32_1) = v4 & member(v0, all_32_3) = v3 & ( ~ (v4 = 0) | ~ % 15.95/3.06 | (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) % 15.95/3.06 | % 15.95/3.06 | GROUND_INST: instantiating (1) with all_32_5, all_32_3, all_32_2, simplifying % 15.95/3.06 | with (7), (9), (10), (12) gives: % 15.95/3.06 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 15.95/3.06 | (apply(all_32_5, v0, v2) = 0) | ~ (apply(all_32_5, v0, v1) = 0) | % 15.95/3.06 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 15.95/3.06 | [v5: any] : (member(v2, all_32_2) = v5 & member(v1, all_32_2) = v4 & % 15.95/3.06 | member(v0, all_32_3) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 15.95/3.06 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ % 15.95/3.06 | $i(v0) | ? [v1: $i] : (apply(all_32_5, v0, v1) = 0 & member(v1, % 15.95/3.06 | all_32_2) = 0 & $i(v1))) % 15.95/3.06 | % 15.95/3.06 | ALPHA: (16) implies: % 15.95/3.06 | (17) ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | ? [v1: $i] % 15.95/3.06 | : (apply(all_32_5, v0, v1) = 0 & member(v1, all_32_2) = 0 & $i(v1))) % 15.95/3.06 | % 15.95/3.06 | GROUND_INST: instantiating (2) with all_32_4, all_32_3, all_32_1, all_32_0, % 15.95/3.06 | simplifying with (8), (9), (11), (13) gives: % 15.95/3.06 | (18) all_32_0 = 0 | ? [v0: $i] : (member(v0, all_32_1) = 0 & $i(v0) & ! % 15.95/3.06 | [v1: $i] : ( ~ (apply(all_32_4, v1, v0) = 0) | ~ $i(v1) | ? [v2: % 15.95/3.06 | int] : ( ~ (v2 = 0) & member(v1, all_32_3) = v2))) % 15.95/3.06 | % 15.95/3.06 | BETA: splitting (18) gives: % 15.95/3.06 | % 15.95/3.07 | Case 1: % 15.95/3.07 | | % 15.95/3.07 | | (19) all_32_0 = 0 % 15.95/3.07 | | % 15.95/3.07 | | REDUCE: (6), (19) imply: % 15.95/3.07 | | (20) $false % 15.95/3.07 | | % 15.95/3.07 | | CLOSE: (20) is inconsistent. % 15.95/3.07 | | % 15.95/3.07 | Case 2: % 15.95/3.07 | | % 15.95/3.07 | | (21) ? [v0: $i] : (member(v0, all_32_1) = 0 & $i(v0) & ! [v1: $i] : ( ~ % 15.95/3.07 | | (apply(all_32_4, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ % 15.95/3.07 | | (v2 = 0) & member(v1, all_32_3) = v2))) % 15.95/3.07 | | % 15.95/3.07 | | DELTA: instantiating (21) with fresh symbol all_45_0 gives: % 15.95/3.07 | | (22) member(all_45_0, all_32_1) = 0 & $i(all_45_0) & ! [v0: $i] : ( ~ % 15.95/3.07 | | (apply(all_32_4, v0, all_45_0) = 0) | ~ $i(v0) | ? [v1: int] : ( % 15.95/3.07 | | ~ (v1 = 0) & member(v0, all_32_3) = v1)) % 15.95/3.07 | | % 15.95/3.07 | | ALPHA: (22) implies: % 15.95/3.07 | | (23) $i(all_45_0) % 15.95/3.07 | | (24) member(all_45_0, all_32_1) = 0 % 15.95/3.07 | | (25) ! [v0: $i] : ( ~ (apply(all_32_4, v0, all_45_0) = 0) | ~ $i(v0) | % 15.95/3.07 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_3) = v1)) % 15.95/3.07 | | % 15.95/3.07 | | GROUND_INST: instantiating (3) with all_32_5, all_32_3, all_45_0, all_32_1, % 15.95/3.07 | | simplifying with (7), (9), (14), (23), (24) gives: % 15.95/3.07 | | (26) ? [v0: $i] : (apply(all_32_5, v0, all_45_0) = 0 & member(v0, % 15.95/3.07 | | all_32_3) = 0 & $i(v0)) % 15.95/3.07 | | % 15.95/3.07 | | DELTA: instantiating (26) with fresh symbol all_54_0 gives: % 15.95/3.07 | | (27) apply(all_32_5, all_54_0, all_45_0) = 0 & member(all_54_0, all_32_3) % 15.95/3.07 | | = 0 & $i(all_54_0) % 15.95/3.07 | | % 15.95/3.07 | | ALPHA: (27) implies: % 15.95/3.07 | | (28) $i(all_54_0) % 15.95/3.07 | | (29) member(all_54_0, all_32_3) = 0 % 15.95/3.07 | | (30) apply(all_32_5, all_54_0, all_45_0) = 0 % 15.95/3.07 | | % 15.95/3.07 | | GROUND_INST: instantiating (17) with all_54_0, simplifying with (28), (29) % 15.95/3.07 | | gives: % 15.95/3.07 | | (31) ? [v0: $i] : (apply(all_32_5, all_54_0, v0) = 0 & member(v0, % 15.95/3.07 | | all_32_2) = 0 & $i(v0)) % 15.95/3.07 | | % 15.95/3.07 | | GROUND_INST: instantiating (15) with all_54_0, all_45_0, 0, simplifying with % 15.95/3.07 | | (23), (28), (30) gives: % 15.95/3.07 | | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4, % 15.95/3.07 | | all_54_0, all_45_0) = v2 & member(all_54_0, all_32_3) = v0 & % 15.95/3.07 | | member(all_45_0, all_32_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 % 15.95/3.07 | | = 0)) % 15.95/3.07 | | % 15.95/3.07 | | DELTA: instantiating (31) with fresh symbol all_61_0 gives: % 15.95/3.07 | | (33) apply(all_32_5, all_54_0, all_61_0) = 0 & member(all_61_0, all_32_2) % 15.95/3.07 | | = 0 & $i(all_61_0) % 15.95/3.07 | | % 15.95/3.07 | | ALPHA: (33) implies: % 15.95/3.07 | | (34) $i(all_61_0) % 15.95/3.08 | | (35) apply(all_32_5, all_54_0, all_61_0) = 0 % 15.95/3.08 | | % 15.95/3.08 | | DELTA: instantiating (32) with fresh symbols all_63_0, all_63_1, all_63_2 % 15.95/3.08 | | gives: % 15.95/3.08 | | (36) apply(all_32_4, all_54_0, all_45_0) = all_63_0 & member(all_54_0, % 15.95/3.08 | | all_32_3) = all_63_2 & member(all_45_0, all_32_1) = all_63_1 & ( ~ % 15.95/3.08 | | (all_63_1 = 0) | ~ (all_63_2 = 0) | all_63_0 = 0) % 15.95/3.08 | | % 15.95/3.08 | | ALPHA: (36) implies: % 15.95/3.08 | | (37) member(all_45_0, all_32_1) = all_63_1 % 15.95/3.08 | | (38) member(all_54_0, all_32_3) = all_63_2 % 15.95/3.08 | | (39) apply(all_32_4, all_54_0, all_45_0) = all_63_0 % 15.95/3.08 | | (40) ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | all_63_0 = 0 % 15.95/3.08 | | % 15.95/3.08 | | GROUND_INST: instantiating (4) with 0, all_63_1, all_32_1, all_45_0, % 15.95/3.08 | | simplifying with (24), (37) gives: % 15.95/3.08 | | (41) all_63_1 = 0 % 15.95/3.08 | | % 15.95/3.08 | | GROUND_INST: instantiating (4) with 0, all_63_2, all_32_3, all_54_0, % 15.95/3.08 | | simplifying with (29), (38) gives: % 15.95/3.08 | | (42) all_63_2 = 0 % 15.95/3.08 | | % 15.95/3.08 | | BETA: splitting (40) gives: % 15.95/3.08 | | % 15.95/3.08 | | Case 1: % 15.95/3.08 | | | % 15.95/3.08 | | | (43) ~ (all_63_1 = 0) % 15.95/3.08 | | | % 15.95/3.08 | | | REDUCE: (41), (43) imply: % 15.95/3.08 | | | (44) $false % 15.95/3.08 | | | % 15.95/3.08 | | | CLOSE: (44) is inconsistent. % 15.95/3.08 | | | % 15.95/3.08 | | Case 2: % 15.95/3.08 | | | % 15.95/3.08 | | | (45) ~ (all_63_2 = 0) | all_63_0 = 0 % 15.95/3.08 | | | % 15.95/3.08 | | | BETA: splitting (45) gives: % 15.95/3.08 | | | % 15.95/3.08 | | | Case 1: % 15.95/3.08 | | | | % 15.95/3.08 | | | | (46) ~ (all_63_2 = 0) % 15.95/3.08 | | | | % 15.95/3.08 | | | | REDUCE: (42), (46) imply: % 15.95/3.08 | | | | (47) $false % 15.95/3.08 | | | | % 15.95/3.08 | | | | CLOSE: (47) is inconsistent. % 15.95/3.08 | | | | % 15.95/3.08 | | | Case 2: % 15.95/3.08 | | | | % 15.95/3.08 | | | | (48) all_63_0 = 0 % 15.95/3.08 | | | | % 15.95/3.08 | | | | REDUCE: (39), (48) imply: % 15.95/3.08 | | | | (49) apply(all_32_4, all_54_0, all_45_0) = 0 % 15.95/3.08 | | | | % 15.95/3.08 | | | | GROUND_INST: instantiating (15) with all_54_0, all_61_0, 0, simplifying % 15.95/3.08 | | | | with (28), (34), (35) gives: % 15.95/3.08 | | | | (50) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4, % 15.95/3.08 | | | | all_54_0, all_61_0) = v2 & member(all_61_0, all_32_1) = v1 & % 15.95/3.08 | | | | member(all_54_0, all_32_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | % 15.95/3.08 | | | | v2 = 0)) % 15.95/3.08 | | | | % 15.95/3.08 | | | | GROUND_INST: instantiating (25) with all_54_0, simplifying with (28), % 15.95/3.08 | | | | (49) gives: % 15.95/3.08 | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & member(all_54_0, all_32_3) = v0) % 15.95/3.08 | | | | % 15.95/3.08 | | | | DELTA: instantiating (51) with fresh symbol all_82_0 gives: % 15.95/3.08 | | | | (52) ~ (all_82_0 = 0) & member(all_54_0, all_32_3) = all_82_0 % 15.95/3.08 | | | | % 15.95/3.08 | | | | ALPHA: (52) implies: % 15.95/3.08 | | | | (53) ~ (all_82_0 = 0) % 15.95/3.08 | | | | (54) member(all_54_0, all_32_3) = all_82_0 % 15.95/3.08 | | | | % 15.95/3.08 | | | | DELTA: instantiating (50) with fresh symbols all_84_0, all_84_1, % 15.95/3.08 | | | | all_84_2 gives: % 15.95/3.08 | | | | (55) apply(all_32_4, all_54_0, all_61_0) = all_84_0 & % 15.95/3.08 | | | | member(all_61_0, all_32_1) = all_84_1 & member(all_54_0, % 15.95/3.08 | | | | all_32_3) = all_84_2 & ( ~ (all_84_1 = 0) | ~ (all_84_2 = 0) % 15.95/3.08 | | | | | all_84_0 = 0) % 15.95/3.08 | | | | % 15.95/3.08 | | | | ALPHA: (55) implies: % 15.95/3.08 | | | | (56) member(all_54_0, all_32_3) = all_84_2 % 15.95/3.08 | | | | % 15.95/3.08 | | | | GROUND_INST: instantiating (4) with 0, all_84_2, all_32_3, all_54_0, % 15.95/3.08 | | | | simplifying with (29), (56) gives: % 15.95/3.08 | | | | (57) all_84_2 = 0 % 15.95/3.08 | | | | % 15.95/3.08 | | | | GROUND_INST: instantiating (4) with all_82_0, all_84_2, all_32_3, % 15.95/3.08 | | | | all_54_0, simplifying with (54), (56) gives: % 15.95/3.08 | | | | (58) all_84_2 = all_82_0 % 15.95/3.08 | | | | % 15.95/3.08 | | | | COMBINE_EQS: (57), (58) imply: % 15.95/3.08 | | | | (59) all_82_0 = 0 % 15.95/3.08 | | | | % 15.95/3.08 | | | | REDUCE: (53), (59) imply: % 15.95/3.08 | | | | (60) $false % 15.95/3.08 | | | | % 15.95/3.09 | | | | CLOSE: (60) is inconsistent. % 15.95/3.09 | | | | % 15.95/3.09 | | | End of split % 15.95/3.09 | | | % 15.95/3.09 | | End of split % 15.95/3.09 | | % 15.95/3.09 | End of split % 15.95/3.09 | % 15.95/3.09 End of proof % 15.95/3.09 % SZS output end Proof for theBenchmark % 15.95/3.09 % 15.95/3.09 2479ms %------------------------------------------------------------------------------