%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET754+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 : n021.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 15:26:18 EDT 2023 % Result : Theorem 11.09s 2.25s % Output : Proof 13.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET754+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 : n021.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 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 13:44:41 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.15/1.21 Prover 4: Preprocessing ... % 3.15/1.21 Prover 1: Preprocessing ... % 3.67/1.24 Prover 3: Preprocessing ... % 3.67/1.24 Prover 0: Preprocessing ... % 3.67/1.24 Prover 2: Preprocessing ... % 3.67/1.24 Prover 6: Preprocessing ... % 3.67/1.24 Prover 5: Preprocessing ... % 8.78/1.95 Prover 5: Proving ... % 8.78/1.95 Prover 2: Proving ... % 9.19/1.98 Prover 6: Proving ... % 9.19/1.98 Prover 3: Constructing countermodel ... % 9.19/2.00 Prover 1: Constructing countermodel ... % 11.09/2.24 Prover 3: proved (1587ms) % 11.09/2.24 % 11.09/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.09/2.25 % 11.18/2.26 Prover 5: stopped % 11.18/2.28 Prover 6: stopped % 11.18/2.28 Prover 2: stopped % 11.18/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.18/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.18/2.30 Prover 1: Found proof (size 37) % 11.18/2.30 Prover 1: proved (1636ms) % 11.18/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.18/2.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.65/2.33 Prover 7: Preprocessing ... % 11.65/2.35 Prover 8: Preprocessing ... % 12.05/2.39 Prover 10: Preprocessing ... % 12.05/2.40 Prover 7: stopped % 12.05/2.41 Prover 11: Preprocessing ... % 12.05/2.42 Prover 10: stopped % 12.92/2.50 Prover 4: Constructing countermodel ... % 12.92/2.50 Prover 11: stopped % 12.92/2.52 Prover 4: stopped % 13.35/2.55 Prover 0: Proving ... % 13.35/2.55 Prover 0: stopped % 13.35/2.55 Prover 8: Warning: ignoring some quantifiers % 13.35/2.57 Prover 8: Constructing countermodel ... % 13.35/2.57 Prover 8: stopped % 13.35/2.57 % 13.35/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.35/2.57 % 13.35/2.58 % SZS output start Proof for theBenchmark % 13.35/2.58 Assumptions after simplification: % 13.35/2.58 --------------------------------- % 13.35/2.58 % 13.35/2.58 (image2) % 13.35/2.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 13.35/2.60 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 13.35/2.60 $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) = 0) | ~ $i(v5) | % 13.35/2.60 ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : ! % 13.35/2.60 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, v1) = v3) | ~ % 13.35/2.60 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 13.35/2.60 (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4))) % 13.35/2.60 % 13.35/2.60 (inverse_image2) % 13.35/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 13.35/2.61 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | % 13.35/2.61 ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v2, v5) = 0) | ~ $i(v5) % 13.35/2.61 | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : ! % 13.35/2.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (inverse_image2(v0, v1) = v3) | ~ % 13.35/2.61 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 13.35/2.61 (apply(v0, v2, v4) = 0 & member(v4, v1) = 0 & $i(v4))) % 13.35/2.61 % 13.35/2.61 (maps) % 13.65/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.65/2.61 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 13.65/2.61 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, % 13.65/2.61 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = % 13.65/2.61 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4) % 13.65/2.61 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( % 13.65/2.61 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 13.65/2.61 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( % 13.65/2.61 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) % 13.65/2.61 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 13.65/2.61 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 13.65/2.61 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) % 13.65/2.61 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~ % 13.65/2.61 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 & % 13.65/2.61 $i(v4))))) % 13.65/2.61 % 13.65/2.61 (subset) % 13.65/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 13.65/2.62 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 13.65/2.62 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 13.65/2.62 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 13.65/2.62 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 13.65/2.62 % 13.65/2.62 (thIIa04) % 13.65/2.62 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.65/2.62 $i] : ? [v6: int] : ( ~ (v6 = 0) & inverse_image2(v0, v4) = v5 & image2(v0, % 13.65/2.62 v3) = v4 & maps(v0, v1, v2) = 0 & subset(v3, v5) = v6 & subset(v3, v1) = 0 % 13.65/2.62 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.65/2.62 % 13.65/2.62 (function-axioms) % 13.65/2.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.65/2.63 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 13.65/2.63 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 13.65/2.63 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.65/2.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.65/2.63 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 13.65/2.63 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.65/2.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.65/2.63 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 13.65/2.63 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.65/2.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.65/2.63 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 13.65/2.63 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.65/2.63 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 13.65/2.63 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 13.65/2.63 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 13.65/2.63 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.65/2.63 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 13.65/2.63 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.65/2.63 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.65/2.63 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 13.65/2.63 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.65/2.63 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 13.65/2.63 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.65/2.63 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 13.65/2.63 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.65/2.63 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 13.65/2.63 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.65/2.63 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 13.65/2.63 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 13.65/2.63 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.65/2.63 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 13.65/2.63 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.65/2.63 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 13.65/2.63 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 13.65/2.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.65/2.63 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 13.65/2.63 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.65/2.63 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 13.65/2.63 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.65/2.63 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 13.65/2.63 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.65/2.63 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 13.65/2.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.65/2.63 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 13.65/2.63 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.65/2.63 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 13.65/2.63 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.65/2.63 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 13.65/2.63 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 13.65/2.63 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.65/2.63 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 13.65/2.63 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.65/2.63 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 13.65/2.63 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.65/2.63 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 13.65/2.63 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.65/2.63 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.65/2.63 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 13.65/2.63 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 13.65/2.63 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 13.65/2.63 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 13.65/2.63 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 13.65/2.63 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 13.65/2.63 (power_set(v2) = v0)) % 13.65/2.63 % 13.65/2.63 Further assumptions not needed in the proof: % 13.65/2.63 -------------------------------------------- % 13.65/2.63 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 13.65/2.63 equal_maps, equal_set, identity, image3, increasing_function, injective, % 13.65/2.63 intersection, inverse_function, inverse_image3, inverse_predicate, isomorphism, % 13.65/2.63 one_to_one, power_set, product, singleton, sum, surjective, union, % 13.65/2.63 unordered_pair % 13.65/2.63 % 13.65/2.63 Those formulas are unsatisfiable: % 13.65/2.63 --------------------------------- % 13.65/2.63 % 13.65/2.63 Begin of proof % 13.65/2.63 | % 13.65/2.63 | ALPHA: (subset) implies: % 13.65/2.63 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 13.65/2.63 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 13.65/2.63 | member(v2, v1) = 0)) % 13.65/2.63 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 13.65/2.63 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 13.65/2.63 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 13.65/2.63 | % 13.65/2.63 | ALPHA: (maps) implies: % 13.65/2.64 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | % 13.65/2.64 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : ! % 13.65/2.64 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, % 13.65/2.64 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 13.65/2.64 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 13.65/2.64 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ % 13.65/2.64 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) % 13.65/2.64 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 13.65/2.64 | member(v4, v2) = 0 & $i(v4))))) % 13.65/2.64 | % 13.65/2.64 | ALPHA: (image2) implies: % 13.65/2.64 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 13.65/2.64 | (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 13.65/2.64 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) % 13.65/2.64 | = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = % 13.65/2.64 | v6))) % 13.65/2.64 | % 13.65/2.64 | ALPHA: (inverse_image2) implies: % 13.65/2.64 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 13.65/2.64 | (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | % 13.65/2.64 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v2, % 13.65/2.64 | v5) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, % 13.65/2.64 | v1) = v6))) % 13.65/2.64 | % 13.65/2.64 | ALPHA: (function-axioms) implies: % 13.65/2.64 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.65/2.64 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 13.65/2.64 | = v0)) % 13.65/2.64 | % 13.65/2.64 | DELTA: instantiating (thIIa04) with fresh symbols all_32_0, all_32_1, % 13.65/2.64 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6 gives: % 13.65/2.64 | (7) ~ (all_32_0 = 0) & inverse_image2(all_32_6, all_32_2) = all_32_1 & % 13.65/2.64 | image2(all_32_6, all_32_3) = all_32_2 & maps(all_32_6, all_32_5, % 13.65/2.64 | all_32_4) = 0 & subset(all_32_3, all_32_1) = all_32_0 & % 13.65/2.64 | subset(all_32_3, all_32_5) = 0 & $i(all_32_1) & $i(all_32_2) & % 13.65/2.64 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) % 13.65/2.64 | % 13.65/2.64 | ALPHA: (7) implies: % 13.65/2.64 | (8) ~ (all_32_0 = 0) % 13.65/2.64 | (9) $i(all_32_6) % 13.65/2.64 | (10) $i(all_32_5) % 13.65/2.64 | (11) $i(all_32_4) % 13.65/2.64 | (12) $i(all_32_3) % 13.65/2.64 | (13) $i(all_32_2) % 13.65/2.64 | (14) $i(all_32_1) % 13.65/2.64 | (15) subset(all_32_3, all_32_5) = 0 % 13.65/2.64 | (16) subset(all_32_3, all_32_1) = all_32_0 % 13.65/2.64 | (17) maps(all_32_6, all_32_5, all_32_4) = 0 % 13.65/2.64 | (18) image2(all_32_6, all_32_3) = all_32_2 % 13.65/2.64 | (19) inverse_image2(all_32_6, all_32_2) = all_32_1 % 13.65/2.64 | % 13.65/2.64 | GROUND_INST: instantiating (1) with all_32_3, all_32_5, simplifying with (10), % 13.65/2.64 | (12), (15) gives: % 13.65/2.64 | (20) ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | member(v0, % 13.65/2.64 | all_32_5) = 0) % 13.65/2.64 | % 13.65/2.64 | GROUND_INST: instantiating (2) with all_32_3, all_32_1, all_32_0, simplifying % 13.65/2.64 | with (12), (14), (16) gives: % 13.65/2.65 | (21) all_32_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 13.65/2.65 | all_32_1) = v1 & member(v0, all_32_3) = 0 & $i(v0)) % 13.65/2.65 | % 13.65/2.65 | GROUND_INST: instantiating (3) with all_32_6, all_32_5, all_32_4, simplifying % 13.65/2.65 | with (9), (10), (11), (17) gives: % 13.65/2.65 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 13.65/2.65 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) | % 13.65/2.65 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 13.65/2.65 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_4) = v4 & % 13.65/2.65 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 13.65/2.65 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_5) = 0) | ~ % 13.65/2.65 | $i(v0) | ? [v1: $i] : (apply(all_32_6, v0, v1) = 0 & member(v1, % 13.65/2.65 | all_32_4) = 0 & $i(v1))) % 13.65/2.65 | % 13.65/2.65 | ALPHA: (22) implies: % 13.65/2.65 | (23) ! [v0: $i] : ( ~ (member(v0, all_32_5) = 0) | ~ $i(v0) | ? [v1: $i] % 13.65/2.65 | : (apply(all_32_6, v0, v1) = 0 & member(v1, all_32_4) = 0 & $i(v1))) % 13.65/2.65 | % 13.65/2.65 | BETA: splitting (21) gives: % 13.65/2.65 | % 13.65/2.65 | Case 1: % 13.65/2.65 | | % 13.65/2.65 | | (24) all_32_0 = 0 % 13.65/2.65 | | % 13.65/2.65 | | REDUCE: (8), (24) imply: % 13.65/2.65 | | (25) $false % 13.65/2.65 | | % 13.65/2.65 | | CLOSE: (25) is inconsistent. % 13.65/2.65 | | % 13.65/2.65 | Case 2: % 13.65/2.65 | | % 13.65/2.65 | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) = % 13.65/2.65 | | v1 & member(v0, all_32_3) = 0 & $i(v0)) % 13.65/2.65 | | % 13.65/2.65 | | DELTA: instantiating (26) with fresh symbols all_44_0, all_44_1 gives: % 13.65/2.65 | | (27) ~ (all_44_0 = 0) & member(all_44_1, all_32_1) = all_44_0 & % 13.65/2.65 | | member(all_44_1, all_32_3) = 0 & $i(all_44_1) % 13.65/2.65 | | % 13.65/2.65 | | ALPHA: (27) implies: % 13.65/2.65 | | (28) ~ (all_44_0 = 0) % 13.65/2.65 | | (29) $i(all_44_1) % 13.65/2.65 | | (30) member(all_44_1, all_32_3) = 0 % 13.65/2.65 | | (31) member(all_44_1, all_32_1) = all_44_0 % 13.65/2.65 | | % 13.65/2.65 | | GROUND_INST: instantiating (20) with all_44_1, simplifying with (29), (30) % 13.65/2.65 | | gives: % 13.65/2.65 | | (32) member(all_44_1, all_32_5) = 0 % 13.65/2.65 | | % 13.65/2.65 | | GROUND_INST: instantiating (5) with all_32_6, all_32_2, all_44_1, all_32_1, % 13.65/2.65 | | all_44_0, simplifying with (9), (13), (19), (29), (31) gives: % 13.65/2.65 | | (33) all_44_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_6, all_44_1, v0) = 0) % 13.65/2.65 | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_2) = % 13.65/2.65 | | v1)) % 13.65/2.65 | | % 13.65/2.65 | | BETA: splitting (33) gives: % 13.65/2.65 | | % 13.65/2.65 | | Case 1: % 13.65/2.65 | | | % 13.65/2.65 | | | (34) all_44_0 = 0 % 13.65/2.65 | | | % 13.65/2.65 | | | REDUCE: (28), (34) imply: % 13.65/2.65 | | | (35) $false % 13.65/2.65 | | | % 13.65/2.65 | | | CLOSE: (35) is inconsistent. % 13.65/2.65 | | | % 13.65/2.65 | | Case 2: % 13.65/2.65 | | | % 13.65/2.66 | | | (36) ! [v0: $i] : ( ~ (apply(all_32_6, all_44_1, v0) = 0) | ~ $i(v0) % 13.65/2.66 | | | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_2) = v1)) % 13.65/2.66 | | | % 13.65/2.66 | | | GROUND_INST: instantiating (23) with all_44_1, simplifying with (29), (32) % 13.65/2.66 | | | gives: % 13.65/2.66 | | | (37) ? [v0: $i] : (apply(all_32_6, all_44_1, v0) = 0 & member(v0, % 13.65/2.66 | | | all_32_4) = 0 & $i(v0)) % 13.65/2.66 | | | % 13.65/2.66 | | | DELTA: instantiating (37) with fresh symbol all_62_0 gives: % 13.65/2.66 | | | (38) apply(all_32_6, all_44_1, all_62_0) = 0 & member(all_62_0, % 13.65/2.66 | | | all_32_4) = 0 & $i(all_62_0) % 13.65/2.66 | | | % 13.65/2.66 | | | ALPHA: (38) implies: % 13.65/2.66 | | | (39) $i(all_62_0) % 13.65/2.66 | | | (40) apply(all_32_6, all_44_1, all_62_0) = 0 % 13.65/2.66 | | | % 13.65/2.66 | | | GROUND_INST: instantiating (36) with all_62_0, simplifying with (39), (40) % 13.65/2.66 | | | gives: % 13.65/2.66 | | | (41) ? [v0: int] : ( ~ (v0 = 0) & member(all_62_0, all_32_2) = v0) % 13.65/2.66 | | | % 13.65/2.66 | | | DELTA: instantiating (41) with fresh symbol all_69_0 gives: % 13.65/2.66 | | | (42) ~ (all_69_0 = 0) & member(all_62_0, all_32_2) = all_69_0 % 13.65/2.66 | | | % 13.65/2.66 | | | ALPHA: (42) implies: % 13.65/2.66 | | | (43) ~ (all_69_0 = 0) % 13.65/2.66 | | | (44) member(all_62_0, all_32_2) = all_69_0 % 13.65/2.66 | | | % 13.65/2.66 | | | GROUND_INST: instantiating (4) with all_32_6, all_32_3, all_62_0, % 13.65/2.66 | | | all_32_2, all_69_0, simplifying with (9), (12), (18), (39), % 13.65/2.66 | | | (44) gives: % 13.65/2.66 | | | (45) all_69_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_6, v0, all_62_0) = % 13.65/2.66 | | | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 13.65/2.66 | | | all_32_3) = v1)) % 13.65/2.66 | | | % 13.65/2.66 | | | BETA: splitting (45) gives: % 13.65/2.66 | | | % 13.65/2.66 | | | Case 1: % 13.65/2.66 | | | | % 13.65/2.66 | | | | (46) all_69_0 = 0 % 13.65/2.66 | | | | % 13.65/2.66 | | | | REDUCE: (43), (46) imply: % 13.65/2.66 | | | | (47) $false % 13.65/2.66 | | | | % 13.65/2.66 | | | | CLOSE: (47) is inconsistent. % 13.65/2.66 | | | | % 13.65/2.66 | | | Case 2: % 13.65/2.66 | | | | % 13.65/2.66 | | | | (48) ! [v0: $i] : ( ~ (apply(all_32_6, v0, all_62_0) = 0) | ~ % 13.65/2.66 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_3) = % 13.65/2.66 | | | | v1)) % 13.65/2.66 | | | | % 13.65/2.66 | | | | GROUND_INST: instantiating (48) with all_44_1, simplifying with (29), % 13.65/2.66 | | | | (40) gives: % 13.65/2.66 | | | | (49) ? [v0: int] : ( ~ (v0 = 0) & member(all_44_1, all_32_3) = v0) % 13.65/2.66 | | | | % 13.65/2.66 | | | | DELTA: instantiating (49) with fresh symbol all_79_0 gives: % 13.65/2.66 | | | | (50) ~ (all_79_0 = 0) & member(all_44_1, all_32_3) = all_79_0 % 13.65/2.66 | | | | % 13.65/2.66 | | | | ALPHA: (50) implies: % 13.65/2.66 | | | | (51) ~ (all_79_0 = 0) % 13.65/2.66 | | | | (52) member(all_44_1, all_32_3) = all_79_0 % 13.65/2.66 | | | | % 13.65/2.66 | | | | GROUND_INST: instantiating (6) with 0, all_79_0, all_32_3, all_44_1, % 13.65/2.66 | | | | simplifying with (30), (52) gives: % 13.65/2.66 | | | | (53) all_79_0 = 0 % 13.65/2.66 | | | | % 13.65/2.66 | | | | REDUCE: (51), (53) imply: % 13.65/2.66 | | | | (54) $false % 13.65/2.66 | | | | % 13.65/2.66 | | | | CLOSE: (54) is inconsistent. % 13.65/2.66 | | | | % 13.65/2.66 | | | End of split % 13.65/2.66 | | | % 13.65/2.66 | | End of split % 13.65/2.66 | | % 13.65/2.66 | End of split % 13.65/2.66 | % 13.65/2.66 End of proof % 13.65/2.66 % SZS output end Proof for theBenchmark % 13.65/2.66 % 13.65/2.66 2037ms %------------------------------------------------------------------------------