%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET757+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 : n019.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 14.11s 2.68s % Output : Proof 17.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET757+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.36 % Computer : n019.cluster.edu % 0.16/0.36 % Model : x86_64 x86_64 % 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.36 % Memory : 8042.1875MB % 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.36 % CPULimit : 300 % 0.16/0.36 % WCLimit : 300 % 0.16/0.36 % DateTime : Sat Aug 26 11:27:43 EDT 2023 % 0.16/0.36 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.19/1.14 Prover 4: Preprocessing ... % 3.19/1.14 Prover 1: Preprocessing ... % 3.19/1.19 Prover 0: Preprocessing ... % 3.19/1.19 Prover 2: Preprocessing ... % 3.19/1.19 Prover 6: Preprocessing ... % 3.19/1.19 Prover 5: Preprocessing ... % 3.19/1.19 Prover 3: Preprocessing ... % 9.09/1.97 Prover 5: Proving ... % 9.22/2.00 Prover 2: Proving ... % 10.18/2.12 Prover 1: Constructing countermodel ... % 10.18/2.13 Prover 6: Proving ... % 10.18/2.14 Prover 3: Constructing countermodel ... % 13.78/2.62 Prover 0: Proving ... % 13.78/2.62 Prover 4: Constructing countermodel ... % 14.11/2.68 Prover 3: proved (2051ms) % 14.11/2.68 % 14.11/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.11/2.68 % 14.11/2.68 Prover 0: stopped % 14.11/2.68 Prover 2: stopped % 14.11/2.68 Prover 6: stopped % 14.11/2.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.11/2.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.11/2.71 Prover 5: stopped % 14.11/2.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.11/2.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.11/2.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.71/2.75 Prover 10: Preprocessing ... % 14.71/2.75 Prover 7: Preprocessing ... % 14.71/2.77 Prover 8: Preprocessing ... % 14.71/2.78 Prover 11: Preprocessing ... % 15.01/2.81 Prover 13: Preprocessing ... % 15.01/2.82 Prover 1: Found proof (size 142) % 15.01/2.82 Prover 1: proved (2195ms) % 15.43/2.84 Prover 4: stopped % 15.56/2.86 Prover 10: Warning: ignoring some quantifiers % 15.56/2.86 Prover 7: Warning: ignoring some quantifiers % 15.56/2.87 Prover 13: stopped % 15.56/2.88 Prover 10: Constructing countermodel ... % 15.56/2.88 Prover 7: Constructing countermodel ... % 15.56/2.89 Prover 11: stopped % 15.56/2.89 Prover 10: stopped % 15.56/2.89 Prover 7: stopped % 15.56/2.97 Prover 8: Warning: ignoring some quantifiers % 15.56/2.98 Prover 8: Constructing countermodel ... % 15.56/2.99 Prover 8: stopped % 15.56/2.99 % 15.56/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.56/2.99 % 15.56/3.01 % SZS output start Proof for theBenchmark % 15.56/3.02 Assumptions after simplification: % 15.56/3.02 --------------------------------- % 15.56/3.02 % 15.56/3.02 (equal_set) % 16.26/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 16.26/3.05 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 16.26/3.05 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 16.26/3.05 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 16.26/3.05 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 16.26/3.05 % 16.26/3.05 (intersection) % 16.26/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 16.26/3.06 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 16.26/3.06 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 16.26/3.06 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 16.26/3.06 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 16.26/3.06 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 16.26/3.06 0 & member(v0, v1) = 0)) % 16.26/3.06 % 16.26/3.06 (inverse_image3) % 16.63/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.63/3.06 int] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = % 16.63/3.06 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ % 16.63/3.06 (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v3, v6) = % 16.63/3.06 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) & % 16.63/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 16.63/3.07 (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~ % 16.63/3.07 $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] : % 16.63/3.07 (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5)))) % 16.63/3.07 % 16.63/3.07 (maps) % 16.63/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.63/3.07 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 16.63/3.07 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, % 16.63/3.07 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = % 16.63/3.07 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4) % 16.63/3.07 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( % 16.63/3.07 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 16.63/3.07 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( % 16.63/3.07 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) % 16.63/3.07 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 16.63/3.07 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 16.63/3.07 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) % 16.63/3.07 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~ % 16.63/3.07 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 & % 16.63/3.07 $i(v4))))) % 16.63/3.07 % 16.63/3.07 (subset) % 16.63/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 16.63/3.08 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 16.63/3.08 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 16.63/3.08 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 16.63/3.08 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 16.63/3.08 % 16.63/3.08 (thIIa07) % 16.63/3.08 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 16.63/3.08 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 16.63/3.08 : ( ~ (v10 = 0) & inverse_image3(v0, v5, v1) = v6 & inverse_image3(v0, v4, v1) % 16.63/3.08 = v8 & inverse_image3(v0, v3, v1) = v7 & maps(v0, v1, v2) = 0 & % 16.63/3.08 intersection(v7, v8) = v9 & intersection(v3, v4) = v5 & equal_set(v6, v9) = % 16.63/3.08 v10 & subset(v4, v2) = 0 & subset(v3, v2) = 0 & $i(v9) & $i(v8) & $i(v7) & % 16.63/3.08 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.63/3.08 % 16.63/3.08 (function-axioms) % 16.63/3.09 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.63/3.09 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 16.63/3.09 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 16.63/3.09 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 16.63/3.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/3.09 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 16.63/3.09 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 16.63/3.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/3.09 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 16.63/3.09 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 16.63/3.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/3.09 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 16.63/3.09 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 16.63/3.09 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 16.63/3.09 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 16.63/3.09 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 16.63/3.09 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.63/3.09 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 16.63/3.09 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.63/3.09 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.63/3.09 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 16.63/3.09 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 16.63/3.09 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 16.63/3.09 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 16.63/3.09 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 16.63/3.09 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.63/3.09 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 16.63/3.09 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.63/3.09 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 16.63/3.09 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 16.63/3.09 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.63/3.09 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 16.63/3.09 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.63/3.09 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 16.63/3.09 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 16.63/3.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.63/3.09 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 16.63/3.09 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.63/3.09 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 16.63/3.09 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.63/3.09 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 16.63/3.09 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.63/3.09 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 16.63/3.09 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.63/3.09 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 16.63/3.09 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.63/3.09 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 16.63/3.09 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.63/3.09 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 16.63/3.09 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 16.63/3.09 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 16.63/3.09 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 16.63/3.09 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.63/3.09 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 16.63/3.09 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.63/3.09 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 16.63/3.09 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.63/3.09 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.63/3.09 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 16.63/3.09 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 16.63/3.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 16.63/3.09 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 16.63/3.09 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 16.63/3.09 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 16.63/3.09 (power_set(v2) = v0)) % 16.63/3.09 % 16.63/3.09 Further assumptions not needed in the proof: % 16.63/3.09 -------------------------------------------- % 16.63/3.09 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 16.63/3.09 equal_maps, identity, image2, image3, increasing_function, injective, % 16.63/3.09 inverse_function, inverse_image2, inverse_predicate, isomorphism, one_to_one, % 16.63/3.09 power_set, product, singleton, sum, surjective, union, unordered_pair % 16.63/3.09 % 16.63/3.09 Those formulas are unsatisfiable: % 16.63/3.09 --------------------------------- % 16.63/3.09 % 16.63/3.09 Begin of proof % 16.63/3.09 | % 16.63/3.09 | ALPHA: (subset) implies: % 16.63/3.10 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 16.63/3.10 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 16.63/3.10 | member(v2, v1) = 0)) % 16.63/3.10 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 16.63/3.10 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 16.63/3.10 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 16.63/3.10 | % 16.63/3.10 | ALPHA: (equal_set) implies: % 16.63/3.10 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 16.63/3.10 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 16.63/3.10 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 16.63/3.10 | 0)))) % 16.63/3.10 | % 16.63/3.10 | ALPHA: (intersection) implies: % 16.63/3.10 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.63/3.10 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 16.63/3.10 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 16.63/3.10 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.63/3.10 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 16.63/3.10 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 16.63/3.10 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 16.63/3.10 | 0)))) % 16.63/3.10 | % 16.63/3.10 | ALPHA: (maps) implies: % 16.63/3.10 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | % 16.63/3.10 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : ! % 16.63/3.10 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, % 16.63/3.10 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 16.63/3.10 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 16.63/3.10 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ % 16.63/3.10 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) % 16.63/3.10 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 16.63/3.10 | member(v4, v2) = 0 & $i(v4))))) % 16.63/3.10 | % 16.63/3.10 | ALPHA: (inverse_image3) implies: % 16.63/3.10 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 16.63/3.10 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ % 16.63/3.10 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? % 16.63/3.10 | [v5: $i] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5)))) % 16.63/3.11 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.63/3.11 | ! [v5: int] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ % 16.63/3.11 | (member(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 16.63/3.11 | | ? [v6: int] : ( ~ (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : % 16.63/3.11 | ( ~ (apply(v0, v3, v6) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) % 16.63/3.11 | & member(v6, v1) = v7))) % 16.63/3.11 | % 16.63/3.11 | ALPHA: (function-axioms) implies: % 16.63/3.11 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.63/3.11 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 16.63/3.11 | = v0)) % 16.63/3.11 | % 16.63/3.11 | DELTA: instantiating (thIIa07) with fresh symbols all_32_0, all_32_1, % 16.63/3.11 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8, % 16.63/3.11 | all_32_9, all_32_10 gives: % 16.63/3.11 | (10) ~ (all_32_0 = 0) & inverse_image3(all_32_10, all_32_5, all_32_9) = % 16.63/3.11 | all_32_4 & inverse_image3(all_32_10, all_32_6, all_32_9) = all_32_2 & % 16.63/3.11 | inverse_image3(all_32_10, all_32_7, all_32_9) = all_32_3 & % 16.63/3.11 | maps(all_32_10, all_32_9, all_32_8) = 0 & intersection(all_32_3, % 16.63/3.11 | all_32_2) = all_32_1 & intersection(all_32_7, all_32_6) = all_32_5 & % 16.63/3.11 | equal_set(all_32_4, all_32_1) = all_32_0 & subset(all_32_6, all_32_8) % 16.63/3.11 | = 0 & subset(all_32_7, all_32_8) = 0 & $i(all_32_1) & $i(all_32_2) & % 16.63/3.11 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) & % 16.63/3.11 | $i(all_32_7) & $i(all_32_8) & $i(all_32_9) & $i(all_32_10) % 16.63/3.11 | % 16.63/3.11 | ALPHA: (10) implies: % 16.63/3.11 | (11) ~ (all_32_0 = 0) % 16.63/3.11 | (12) $i(all_32_10) % 16.63/3.11 | (13) $i(all_32_9) % 16.63/3.11 | (14) $i(all_32_8) % 16.63/3.11 | (15) $i(all_32_7) % 16.63/3.11 | (16) $i(all_32_6) % 16.63/3.11 | (17) $i(all_32_5) % 16.63/3.11 | (18) $i(all_32_4) % 16.63/3.11 | (19) $i(all_32_3) % 16.63/3.11 | (20) $i(all_32_2) % 16.63/3.11 | (21) $i(all_32_1) % 16.63/3.11 | (22) subset(all_32_7, all_32_8) = 0 % 16.63/3.11 | (23) subset(all_32_6, all_32_8) = 0 % 16.63/3.11 | (24) equal_set(all_32_4, all_32_1) = all_32_0 % 16.63/3.11 | (25) intersection(all_32_7, all_32_6) = all_32_5 % 16.63/3.11 | (26) intersection(all_32_3, all_32_2) = all_32_1 % 16.63/3.11 | (27) maps(all_32_10, all_32_9, all_32_8) = 0 % 16.63/3.11 | (28) inverse_image3(all_32_10, all_32_7, all_32_9) = all_32_3 % 16.63/3.11 | (29) inverse_image3(all_32_10, all_32_6, all_32_9) = all_32_2 % 16.63/3.11 | (30) inverse_image3(all_32_10, all_32_5, all_32_9) = all_32_4 % 16.63/3.11 | % 16.63/3.11 | GROUND_INST: instantiating (1) with all_32_7, all_32_8, simplifying with (14), % 16.63/3.11 | (15), (22) gives: % 16.63/3.11 | (31) ! [v0: $i] : ( ~ (member(v0, all_32_7) = 0) | ~ $i(v0) | member(v0, % 16.63/3.11 | all_32_8) = 0) % 16.63/3.11 | % 16.63/3.12 | GROUND_INST: instantiating (1) with all_32_6, all_32_8, simplifying with (14), % 16.63/3.12 | (16), (23) gives: % 16.63/3.12 | (32) ! [v0: $i] : ( ~ (member(v0, all_32_6) = 0) | ~ $i(v0) | member(v0, % 16.63/3.12 | all_32_8) = 0) % 16.63/3.12 | % 16.63/3.12 | GROUND_INST: instantiating (3) with all_32_4, all_32_1, all_32_0, simplifying % 16.63/3.12 | with (18), (21), (24) gives: % 16.63/3.12 | (33) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_32_1, % 16.63/3.12 | all_32_4) = v1 & subset(all_32_4, all_32_1) = v0 & ( ~ (v1 = 0) | % 16.63/3.12 | ~ (v0 = 0))) % 16.63/3.12 | % 16.63/3.12 | GROUND_INST: instantiating (6) with all_32_10, all_32_9, all_32_8, simplifying % 16.63/3.12 | with (12), (13), (14), (27) gives: % 16.63/3.12 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 16.63/3.12 | (apply(all_32_10, v0, v2) = 0) | ~ (apply(all_32_10, v0, v1) = 0) | % 16.63/3.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 16.63/3.12 | [v5: any] : (member(v2, all_32_8) = v5 & member(v1, all_32_8) = v4 & % 16.63/3.12 | member(v0, all_32_9) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 16.63/3.12 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_9) = 0) | ~ % 16.63/3.12 | $i(v0) | ? [v1: $i] : (apply(all_32_10, v0, v1) = 0 & member(v1, % 16.63/3.12 | all_32_8) = 0 & $i(v1))) % 16.63/3.12 | % 16.63/3.12 | ALPHA: (34) implies: % 16.63/3.12 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 16.63/3.12 | (apply(all_32_10, v0, v2) = 0) | ~ (apply(all_32_10, v0, v1) = 0) | % 16.63/3.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 16.63/3.12 | [v5: any] : (member(v2, all_32_8) = v5 & member(v1, all_32_8) = v4 & % 16.63/3.12 | member(v0, all_32_9) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 16.63/3.12 | 0)))) % 16.63/3.12 | % 16.63/3.12 | BETA: splitting (33) gives: % 16.63/3.12 | % 16.63/3.12 | Case 1: % 16.63/3.12 | | % 16.63/3.12 | | (36) all_32_0 = 0 % 16.63/3.12 | | % 16.63/3.12 | | REDUCE: (11), (36) imply: % 16.63/3.12 | | (37) $false % 16.63/3.12 | | % 16.63/3.12 | | CLOSE: (37) is inconsistent. % 16.63/3.12 | | % 16.63/3.12 | Case 2: % 16.63/3.12 | | % 16.63/3.12 | | (38) ? [v0: any] : ? [v1: any] : (subset(all_32_1, all_32_4) = v1 & % 16.63/3.12 | | subset(all_32_4, all_32_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.63/3.12 | | % 16.63/3.12 | | DELTA: instantiating (38) with fresh symbols all_45_0, all_45_1 gives: % 16.63/3.12 | | (39) subset(all_32_1, all_32_4) = all_45_0 & subset(all_32_4, all_32_1) = % 16.63/3.12 | | all_45_1 & ( ~ (all_45_0 = 0) | ~ (all_45_1 = 0)) % 16.63/3.12 | | % 16.63/3.12 | | ALPHA: (39) implies: % 16.63/3.12 | | (40) subset(all_32_4, all_32_1) = all_45_1 % 16.63/3.12 | | (41) subset(all_32_1, all_32_4) = all_45_0 % 16.63/3.12 | | (42) ~ (all_45_0 = 0) | ~ (all_45_1 = 0) % 16.63/3.12 | | % 16.63/3.12 | | GROUND_INST: instantiating (2) with all_32_4, all_32_1, all_45_1, % 16.63/3.12 | | simplifying with (18), (21), (40) gives: % 16.63/3.12 | | (43) all_45_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.63/3.12 | | member(v0, all_32_1) = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 16.63/3.12 | | % 16.63/3.12 | | GROUND_INST: instantiating (2) with all_32_1, all_32_4, all_45_0, % 16.63/3.12 | | simplifying with (18), (21), (41) gives: % 16.63/3.13 | | (44) all_45_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.63/3.13 | | member(v0, all_32_1) = 0 & member(v0, all_32_4) = v1 & $i(v0)) % 16.63/3.13 | | % 16.63/3.13 | | BETA: splitting (42) gives: % 16.63/3.13 | | % 16.63/3.13 | | Case 1: % 16.63/3.13 | | | % 16.63/3.13 | | | (45) ~ (all_45_0 = 0) % 16.63/3.13 | | | % 16.63/3.13 | | | BETA: splitting (44) gives: % 16.63/3.13 | | | % 16.63/3.13 | | | Case 1: % 16.63/3.13 | | | | % 16.63/3.13 | | | | (46) all_45_0 = 0 % 16.63/3.13 | | | | % 16.63/3.13 | | | | REDUCE: (45), (46) imply: % 16.63/3.13 | | | | (47) $false % 16.63/3.13 | | | | % 16.63/3.13 | | | | CLOSE: (47) is inconsistent. % 16.63/3.13 | | | | % 16.63/3.13 | | | Case 2: % 16.63/3.13 | | | | % 16.63/3.13 | | | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) % 16.63/3.13 | | | | = 0 & member(v0, all_32_4) = v1 & $i(v0)) % 16.63/3.13 | | | | % 16.63/3.13 | | | | DELTA: instantiating (48) with fresh symbols all_58_0, all_58_1 gives: % 16.63/3.13 | | | | (49) ~ (all_58_0 = 0) & member(all_58_1, all_32_1) = 0 & % 16.63/3.13 | | | | member(all_58_1, all_32_4) = all_58_0 & $i(all_58_1) % 16.63/3.13 | | | | % 16.63/3.13 | | | | ALPHA: (49) implies: % 16.63/3.13 | | | | (50) ~ (all_58_0 = 0) % 16.63/3.13 | | | | (51) $i(all_58_1) % 16.63/3.13 | | | | (52) member(all_58_1, all_32_4) = all_58_0 % 16.63/3.13 | | | | (53) member(all_58_1, all_32_1) = 0 % 16.63/3.13 | | | | % 16.63/3.13 | | | | GROUND_INST: instantiating (8) with all_32_10, all_32_5, all_32_9, % 16.63/3.13 | | | | all_58_1, all_32_4, all_58_0, simplifying with (12), (13), % 16.63/3.13 | | | | (17), (30), (51), (52) gives: % 16.63/3.13 | | | | (54) all_58_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, % 16.63/3.13 | | | | all_32_9) = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, % 16.63/3.13 | | | | all_58_1, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 16.63/3.13 | | | | 0) & member(v0, all_32_5) = v1)) % 16.63/3.13 | | | | % 16.63/3.13 | | | | GROUND_INST: instantiating (4) with all_58_1, all_32_3, all_32_2, % 16.63/3.13 | | | | all_32_1, simplifying with (19), (20), (26), (51), (53) % 16.63/3.13 | | | | gives: % 16.63/3.13 | | | | (55) member(all_58_1, all_32_2) = 0 & member(all_58_1, all_32_3) = 0 % 16.63/3.13 | | | | % 16.63/3.13 | | | | ALPHA: (55) implies: % 16.63/3.13 | | | | (56) member(all_58_1, all_32_3) = 0 % 16.63/3.13 | | | | (57) member(all_58_1, all_32_2) = 0 % 16.63/3.13 | | | | % 16.63/3.13 | | | | GROUND_INST: instantiating (7) with all_32_10, all_32_7, all_32_9, % 16.63/3.13 | | | | all_58_1, all_32_3, simplifying with (12), (13), (15), % 16.63/3.13 | | | | (28), (51), (56) gives: % 16.63/3.13 | | | | (58) member(all_58_1, all_32_9) = 0 & ? [v0: $i] : (apply(all_32_10, % 16.63/3.13 | | | | all_58_1, v0) = 0 & member(v0, all_32_7) = 0 & $i(v0)) % 16.63/3.13 | | | | % 16.63/3.13 | | | | ALPHA: (58) implies: % 16.63/3.13 | | | | (59) ? [v0: $i] : (apply(all_32_10, all_58_1, v0) = 0 & member(v0, % 16.63/3.13 | | | | all_32_7) = 0 & $i(v0)) % 16.63/3.13 | | | | % 16.63/3.13 | | | | GROUND_INST: instantiating (7) with all_32_10, all_32_6, all_32_9, % 16.63/3.13 | | | | all_58_1, all_32_2, simplifying with (12), (13), (16), % 16.63/3.13 | | | | (29), (51), (57) gives: % 16.63/3.13 | | | | (60) member(all_58_1, all_32_9) = 0 & ? [v0: $i] : (apply(all_32_10, % 16.63/3.13 | | | | all_58_1, v0) = 0 & member(v0, all_32_6) = 0 & $i(v0)) % 16.63/3.13 | | | | % 16.63/3.13 | | | | ALPHA: (60) implies: % 16.63/3.13 | | | | (61) member(all_58_1, all_32_9) = 0 % 16.63/3.13 | | | | (62) ? [v0: $i] : (apply(all_32_10, all_58_1, v0) = 0 & member(v0, % 16.63/3.13 | | | | all_32_6) = 0 & $i(v0)) % 16.63/3.13 | | | | % 16.63/3.13 | | | | DELTA: instantiating (59) with fresh symbol all_72_0 gives: % 16.63/3.13 | | | | (63) apply(all_32_10, all_58_1, all_72_0) = 0 & member(all_72_0, % 16.63/3.13 | | | | all_32_7) = 0 & $i(all_72_0) % 16.63/3.13 | | | | % 16.63/3.13 | | | | ALPHA: (63) implies: % 16.63/3.13 | | | | (64) $i(all_72_0) % 16.63/3.13 | | | | (65) member(all_72_0, all_32_7) = 0 % 16.63/3.13 | | | | (66) apply(all_32_10, all_58_1, all_72_0) = 0 % 16.63/3.13 | | | | % 16.63/3.13 | | | | DELTA: instantiating (62) with fresh symbol all_74_0 gives: % 16.63/3.13 | | | | (67) apply(all_32_10, all_58_1, all_74_0) = 0 & member(all_74_0, % 16.63/3.13 | | | | all_32_6) = 0 & $i(all_74_0) % 16.63/3.13 | | | | % 16.63/3.13 | | | | ALPHA: (67) implies: % 16.63/3.13 | | | | (68) $i(all_74_0) % 16.63/3.13 | | | | (69) member(all_74_0, all_32_6) = 0 % 16.63/3.13 | | | | (70) apply(all_32_10, all_58_1, all_74_0) = 0 % 16.63/3.13 | | | | % 16.63/3.13 | | | | BETA: splitting (54) gives: % 16.63/3.13 | | | | % 16.63/3.13 | | | | Case 1: % 16.63/3.13 | | | | | % 16.63/3.14 | | | | | (71) all_58_0 = 0 % 16.63/3.14 | | | | | % 16.63/3.14 | | | | | REDUCE: (50), (71) imply: % 16.63/3.14 | | | | | (72) $false % 16.63/3.14 | | | | | % 16.63/3.14 | | | | | CLOSE: (72) is inconsistent. % 16.63/3.14 | | | | | % 16.63/3.14 | | | | Case 2: % 16.63/3.14 | | | | | % 16.63/3.14 | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_9) = v0) % 16.63/3.14 | | | | | | ! [v0: $i] : ( ~ (apply(all_32_10, all_58_1, v0) = 0) | ~ % 16.63/3.14 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_5) % 16.63/3.14 | | | | | = v1)) % 16.63/3.14 | | | | | % 16.63/3.14 | | | | | BETA: splitting (73) gives: % 16.63/3.14 | | | | | % 16.63/3.14 | | | | | Case 1: % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_9) = % 16.63/3.14 | | | | | | v0) % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | DELTA: instantiating (74) with fresh symbol all_83_0 gives: % 16.63/3.14 | | | | | | (75) ~ (all_83_0 = 0) & member(all_58_1, all_32_9) = all_83_0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | ALPHA: (75) implies: % 16.63/3.14 | | | | | | (76) ~ (all_83_0 = 0) % 16.63/3.14 | | | | | | (77) member(all_58_1, all_32_9) = all_83_0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | GROUND_INST: instantiating (9) with 0, all_83_0, all_32_9, all_58_1, % 16.63/3.14 | | | | | | simplifying with (61), (77) gives: % 16.63/3.14 | | | | | | (78) all_83_0 = 0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | REDUCE: (76), (78) imply: % 16.63/3.14 | | | | | | (79) $false % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | CLOSE: (79) is inconsistent. % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | Case 2: % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | (80) ! [v0: $i] : ( ~ (apply(all_32_10, all_58_1, v0) = 0) | ~ % 16.63/3.14 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 16.63/3.14 | | | | | | all_32_5) = v1)) % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | GROUND_INST: instantiating (31) with all_72_0, simplifying with % 16.63/3.14 | | | | | | (64), (65) gives: % 16.63/3.14 | | | | | | (81) member(all_72_0, all_32_8) = 0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | GROUND_INST: instantiating (32) with all_74_0, simplifying with % 16.63/3.14 | | | | | | (68), (69) gives: % 16.63/3.14 | | | | | | (82) member(all_74_0, all_32_8) = 0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | GROUND_INST: instantiating (80) with all_72_0, simplifying with % 16.63/3.14 | | | | | | (64), (66) gives: % 16.63/3.14 | | | | | | (83) ? [v0: int] : ( ~ (v0 = 0) & member(all_72_0, all_32_5) = % 16.63/3.14 | | | | | | v0) % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | GROUND_INST: instantiating (35) with all_58_1, all_72_0, all_74_0, % 16.63/3.14 | | | | | | simplifying with (51), (64), (66), (68), (70) gives: % 16.63/3.14 | | | | | | (84) all_74_0 = all_72_0 | ? [v0: any] : ? [v1: any] : ? [v2: % 16.63/3.14 | | | | | | any] : (member(all_74_0, all_32_8) = v2 & member(all_72_0, % 16.63/3.14 | | | | | | all_32_8) = v1 & member(all_58_1, all_32_9) = v0 & ( ~ % 16.63/3.14 | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | GROUND_INST: instantiating (80) with all_74_0, simplifying with % 16.63/3.14 | | | | | | (68), (70) gives: % 16.63/3.14 | | | | | | (85) ? [v0: int] : ( ~ (v0 = 0) & member(all_74_0, all_32_5) = % 16.63/3.14 | | | | | | v0) % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | DELTA: instantiating (85) with fresh symbol all_89_0 gives: % 16.63/3.14 | | | | | | (86) ~ (all_89_0 = 0) & member(all_74_0, all_32_5) = all_89_0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | ALPHA: (86) implies: % 16.63/3.14 | | | | | | (87) member(all_74_0, all_32_5) = all_89_0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | DELTA: instantiating (83) with fresh symbol all_91_0 gives: % 16.63/3.14 | | | | | | (88) ~ (all_91_0 = 0) & member(all_72_0, all_32_5) = all_91_0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | ALPHA: (88) implies: % 16.63/3.14 | | | | | | (89) ~ (all_91_0 = 0) % 16.63/3.14 | | | | | | (90) member(all_72_0, all_32_5) = all_91_0 % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | BETA: splitting (84) gives: % 16.63/3.14 | | | | | | % 16.63/3.14 | | | | | | Case 1: % 16.63/3.14 | | | | | | | % 16.63/3.14 | | | | | | | (91) all_74_0 = all_72_0 % 16.63/3.14 | | | | | | | % 16.63/3.14 | | | | | | | REDUCE: (87), (91) imply: % 16.63/3.14 | | | | | | | (92) member(all_72_0, all_32_5) = all_89_0 % 16.63/3.14 | | | | | | | % 16.63/3.14 | | | | | | | REDUCE: (69), (91) imply: % 16.63/3.14 | | | | | | | (93) member(all_72_0, all_32_6) = 0 % 16.63/3.14 | | | | | | | % 16.63/3.14 | | | | | | | GROUND_INST: instantiating (9) with all_89_0, all_91_0, all_32_5, % 16.63/3.14 | | | | | | | all_72_0, simplifying with (90), (92) gives: % 16.63/3.14 | | | | | | | (94) all_91_0 = all_89_0 % 16.63/3.14 | | | | | | | % 16.63/3.14 | | | | | | | REDUCE: (89), (94) imply: % 16.63/3.14 | | | | | | | (95) ~ (all_89_0 = 0) % 16.63/3.14 | | | | | | | % 16.63/3.14 | | | | | | | GROUND_INST: instantiating (5) with all_72_0, all_32_7, all_32_6, % 16.63/3.14 | | | | | | | all_32_5, all_89_0, simplifying with (15), (16), % 16.63/3.14 | | | | | | | (25), (64), (92) gives: % 16.63/3.14 | | | | | | | (96) all_89_0 = 0 | ? [v0: any] : ? [v1: any] : % 16.63/3.14 | | | | | | | (member(all_72_0, all_32_6) = v1 & member(all_72_0, % 16.63/3.14 | | | | | | | all_32_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.63/3.14 | | | | | | | % 16.63/3.14 | | | | | | | BETA: splitting (96) gives: % 16.63/3.14 | | | | | | | % 16.63/3.14 | | | | | | | Case 1: % 16.63/3.14 | | | | | | | | % 16.63/3.14 | | | | | | | | (97) all_89_0 = 0 % 16.63/3.14 | | | | | | | | % 16.63/3.14 | | | | | | | | REDUCE: (95), (97) imply: % 16.63/3.14 | | | | | | | | (98) $false % 16.63/3.14 | | | | | | | | % 16.63/3.14 | | | | | | | | CLOSE: (98) is inconsistent. % 16.63/3.14 | | | | | | | | % 16.63/3.14 | | | | | | | Case 2: % 16.63/3.14 | | | | | | | | % 16.63/3.14 | | | | | | | | (99) ? [v0: any] : ? [v1: any] : (member(all_72_0, % 16.63/3.14 | | | | | | | | all_32_6) = v1 & member(all_72_0, all_32_7) = v0 & ( % 16.63/3.14 | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 16.63/3.14 | | | | | | | | % 16.63/3.14 | | | | | | | | DELTA: instantiating (99) with fresh symbols all_118_0, % 16.63/3.14 | | | | | | | | all_118_1 gives: % 16.63/3.14 | | | | | | | | (100) member(all_72_0, all_32_6) = all_118_0 & % 16.63/3.14 | | | | | | | | member(all_72_0, all_32_7) = all_118_1 & ( ~ (all_118_0 % 16.63/3.14 | | | | | | | | = 0) | ~ (all_118_1 = 0)) % 16.63/3.14 | | | | | | | | % 16.63/3.14 | | | | | | | | ALPHA: (100) implies: % 16.63/3.15 | | | | | | | | (101) member(all_72_0, all_32_7) = all_118_1 % 16.63/3.15 | | | | | | | | (102) member(all_72_0, all_32_6) = all_118_0 % 16.63/3.15 | | | | | | | | (103) ~ (all_118_0 = 0) | ~ (all_118_1 = 0) % 16.63/3.15 | | | | | | | | % 16.63/3.15 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_118_1, all_32_7, % 16.63/3.15 | | | | | | | | all_72_0, simplifying with (65), (101) gives: % 16.63/3.15 | | | | | | | | (104) all_118_1 = 0 % 16.63/3.15 | | | | | | | | % 16.63/3.15 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_118_0, all_32_6, % 16.63/3.15 | | | | | | | | all_72_0, simplifying with (93), (102) gives: % 16.63/3.15 | | | | | | | | (105) all_118_0 = 0 % 16.63/3.15 | | | | | | | | % 16.63/3.15 | | | | | | | | BETA: splitting (103) gives: % 16.63/3.15 | | | | | | | | % 16.63/3.15 | | | | | | | | Case 1: % 16.63/3.15 | | | | | | | | | % 16.63/3.15 | | | | | | | | | (106) ~ (all_118_0 = 0) % 16.63/3.15 | | | | | | | | | % 16.63/3.15 | | | | | | | | | REDUCE: (105), (106) imply: % 16.63/3.15 | | | | | | | | | (107) $false % 16.63/3.15 | | | | | | | | | % 16.63/3.15 | | | | | | | | | CLOSE: (107) is inconsistent. % 16.63/3.15 | | | | | | | | | % 16.63/3.15 | | | | | | | | Case 2: % 16.63/3.15 | | | | | | | | | % 16.63/3.15 | | | | | | | | | (108) ~ (all_118_1 = 0) % 16.63/3.15 | | | | | | | | | % 16.63/3.15 | | | | | | | | | REDUCE: (104), (108) imply: % 16.63/3.15 | | | | | | | | | (109) $false % 16.63/3.15 | | | | | | | | | % 16.63/3.15 | | | | | | | | | CLOSE: (109) is inconsistent. % 16.63/3.15 | | | | | | | | | % 16.63/3.15 | | | | | | | | End of split % 16.63/3.15 | | | | | | | | % 16.63/3.15 | | | | | | | End of split % 16.63/3.15 | | | | | | | % 16.63/3.15 | | | | | | Case 2: % 16.63/3.15 | | | | | | | % 16.63/3.15 | | | | | | | (110) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.63/3.15 | | | | | | | (member(all_74_0, all_32_8) = v2 & member(all_72_0, % 16.63/3.15 | | | | | | | all_32_8) = v1 & member(all_58_1, all_32_9) = v0 & ( % 16.63/3.15 | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 16.63/3.15 | | | | | | | % 16.63/3.15 | | | | | | | DELTA: instantiating (110) with fresh symbols all_99_0, all_99_1, % 16.63/3.15 | | | | | | | all_99_2 gives: % 16.63/3.15 | | | | | | | (111) member(all_74_0, all_32_8) = all_99_0 & member(all_72_0, % 16.63/3.15 | | | | | | | all_32_8) = all_99_1 & member(all_58_1, all_32_9) = % 16.63/3.15 | | | | | | | all_99_2 & ( ~ (all_99_0 = 0) | ~ (all_99_1 = 0) | ~ % 16.63/3.15 | | | | | | | (all_99_2 = 0)) % 16.63/3.15 | | | | | | | % 16.63/3.15 | | | | | | | ALPHA: (111) implies: % 16.63/3.15 | | | | | | | (112) member(all_58_1, all_32_9) = all_99_2 % 16.63/3.15 | | | | | | | (113) member(all_72_0, all_32_8) = all_99_1 % 16.63/3.15 | | | | | | | (114) member(all_74_0, all_32_8) = all_99_0 % 16.63/3.15 | | | | | | | (115) ~ (all_99_0 = 0) | ~ (all_99_1 = 0) | ~ (all_99_2 = 0) % 16.63/3.15 | | | | | | | % 17.06/3.15 | | | | | | | GROUND_INST: instantiating (9) with 0, all_99_2, all_32_9, % 17.06/3.15 | | | | | | | all_58_1, simplifying with (61), (112) gives: % 17.06/3.15 | | | | | | | (116) all_99_2 = 0 % 17.06/3.15 | | | | | | | % 17.06/3.15 | | | | | | | GROUND_INST: instantiating (9) with 0, all_99_1, all_32_8, % 17.06/3.15 | | | | | | | all_72_0, simplifying with (81), (113) gives: % 17.06/3.15 | | | | | | | (117) all_99_1 = 0 % 17.06/3.15 | | | | | | | % 17.06/3.15 | | | | | | | GROUND_INST: instantiating (9) with 0, all_99_0, all_32_8, % 17.06/3.15 | | | | | | | all_74_0, simplifying with (82), (114) gives: % 17.06/3.15 | | | | | | | (118) all_99_0 = 0 % 17.06/3.15 | | | | | | | % 17.06/3.15 | | | | | | | BETA: splitting (115) gives: % 17.06/3.15 | | | | | | | % 17.06/3.15 | | | | | | | Case 1: % 17.06/3.15 | | | | | | | | % 17.06/3.15 | | | | | | | | (119) ~ (all_99_0 = 0) % 17.06/3.15 | | | | | | | | % 17.06/3.15 | | | | | | | | REDUCE: (118), (119) imply: % 17.06/3.15 | | | | | | | | (120) $false % 17.06/3.15 | | | | | | | | % 17.06/3.15 | | | | | | | | CLOSE: (120) is inconsistent. % 17.06/3.15 | | | | | | | | % 17.06/3.15 | | | | | | | Case 2: % 17.06/3.15 | | | | | | | | % 17.06/3.15 | | | | | | | | (121) ~ (all_99_1 = 0) | ~ (all_99_2 = 0) % 17.06/3.15 | | | | | | | | % 17.06/3.15 | | | | | | | | BETA: splitting (121) gives: % 17.06/3.15 | | | | | | | | % 17.06/3.15 | | | | | | | | Case 1: % 17.06/3.15 | | | | | | | | | % 17.06/3.15 | | | | | | | | | (122) ~ (all_99_1 = 0) % 17.06/3.15 | | | | | | | | | % 17.06/3.15 | | | | | | | | | REDUCE: (117), (122) imply: % 17.06/3.15 | | | | | | | | | (123) $false % 17.06/3.15 | | | | | | | | | % 17.06/3.15 | | | | | | | | | CLOSE: (123) is inconsistent. % 17.06/3.15 | | | | | | | | | % 17.06/3.15 | | | | | | | | Case 2: % 17.06/3.15 | | | | | | | | | % 17.06/3.15 | | | | | | | | | (124) ~ (all_99_2 = 0) % 17.06/3.15 | | | | | | | | | % 17.06/3.15 | | | | | | | | | REDUCE: (116), (124) imply: % 17.06/3.15 | | | | | | | | | (125) $false % 17.06/3.15 | | | | | | | | | % 17.06/3.15 | | | | | | | | | CLOSE: (125) is inconsistent. % 17.06/3.15 | | | | | | | | | % 17.06/3.15 | | | | | | | | End of split % 17.06/3.15 | | | | | | | | % 17.06/3.15 | | | | | | | End of split % 17.06/3.15 | | | | | | | % 17.06/3.15 | | | | | | End of split % 17.06/3.15 | | | | | | % 17.06/3.15 | | | | | End of split % 17.06/3.15 | | | | | % 17.06/3.15 | | | | End of split % 17.06/3.15 | | | | % 17.06/3.15 | | | End of split % 17.06/3.15 | | | % 17.06/3.15 | | Case 2: % 17.06/3.15 | | | % 17.06/3.15 | | | (126) ~ (all_45_1 = 0) % 17.06/3.15 | | | % 17.06/3.15 | | | BETA: splitting (43) gives: % 17.06/3.15 | | | % 17.06/3.15 | | | Case 1: % 17.06/3.15 | | | | % 17.06/3.15 | | | | (127) all_45_1 = 0 % 17.06/3.15 | | | | % 17.06/3.15 | | | | REDUCE: (126), (127) imply: % 17.06/3.15 | | | | (128) $false % 17.06/3.15 | | | | % 17.06/3.15 | | | | CLOSE: (128) is inconsistent. % 17.06/3.15 | | | | % 17.06/3.15 | | | Case 2: % 17.06/3.15 | | | | % 17.06/3.15 | | | | (129) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 17.06/3.15 | | | | all_32_1) = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 17.06/3.15 | | | | % 17.06/3.15 | | | | DELTA: instantiating (129) with fresh symbols all_58_0, all_58_1 gives: % 17.06/3.15 | | | | (130) ~ (all_58_0 = 0) & member(all_58_1, all_32_1) = all_58_0 & % 17.06/3.15 | | | | member(all_58_1, all_32_4) = 0 & $i(all_58_1) % 17.06/3.15 | | | | % 17.06/3.15 | | | | ALPHA: (130) implies: % 17.06/3.15 | | | | (131) ~ (all_58_0 = 0) % 17.06/3.15 | | | | (132) $i(all_58_1) % 17.06/3.15 | | | | (133) member(all_58_1, all_32_4) = 0 % 17.06/3.15 | | | | (134) member(all_58_1, all_32_1) = all_58_0 % 17.06/3.15 | | | | % 17.06/3.15 | | | | GROUND_INST: instantiating (7) with all_32_10, all_32_5, all_32_9, % 17.06/3.15 | | | | all_58_1, all_32_4, simplifying with (12), (13), (17), % 17.06/3.15 | | | | (30), (132), (133) gives: % 17.06/3.15 | | | | (135) member(all_58_1, all_32_9) = 0 & ? [v0: $i] : % 17.06/3.15 | | | | (apply(all_32_10, all_58_1, v0) = 0 & member(v0, all_32_5) = 0 % 17.06/3.15 | | | | & $i(v0)) % 17.06/3.15 | | | | % 17.06/3.15 | | | | ALPHA: (135) implies: % 17.06/3.15 | | | | (136) member(all_58_1, all_32_9) = 0 % 17.06/3.15 | | | | (137) ? [v0: $i] : (apply(all_32_10, all_58_1, v0) = 0 & member(v0, % 17.06/3.15 | | | | all_32_5) = 0 & $i(v0)) % 17.06/3.15 | | | | % 17.06/3.15 | | | | GROUND_INST: instantiating (5) with all_58_1, all_32_3, all_32_2, % 17.06/3.15 | | | | all_32_1, all_58_0, simplifying with (19), (20), (26), % 17.06/3.15 | | | | (132), (134) gives: % 17.06/3.16 | | | | (138) all_58_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_58_1, % 17.06/3.16 | | | | all_32_2) = v1 & member(all_58_1, all_32_3) = v0 & ( ~ (v1 % 17.06/3.16 | | | | = 0) | ~ (v0 = 0))) % 17.06/3.16 | | | | % 17.06/3.16 | | | | DELTA: instantiating (137) with fresh symbol all_67_0 gives: % 17.06/3.16 | | | | (139) apply(all_32_10, all_58_1, all_67_0) = 0 & member(all_67_0, % 17.06/3.16 | | | | all_32_5) = 0 & $i(all_67_0) % 17.06/3.16 | | | | % 17.06/3.16 | | | | ALPHA: (139) implies: % 17.06/3.16 | | | | (140) $i(all_67_0) % 17.06/3.16 | | | | (141) member(all_67_0, all_32_5) = 0 % 17.06/3.16 | | | | (142) apply(all_32_10, all_58_1, all_67_0) = 0 % 17.06/3.16 | | | | % 17.06/3.16 | | | | BETA: splitting (138) gives: % 17.06/3.16 | | | | % 17.06/3.16 | | | | Case 1: % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | (143) all_58_0 = 0 % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | REDUCE: (131), (143) imply: % 17.06/3.16 | | | | | (144) $false % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | CLOSE: (144) is inconsistent. % 17.06/3.16 | | | | | % 17.06/3.16 | | | | Case 2: % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | (145) ? [v0: any] : ? [v1: any] : (member(all_58_1, all_32_2) = % 17.06/3.16 | | | | | v1 & member(all_58_1, all_32_3) = v0 & ( ~ (v1 = 0) | ~ % 17.06/3.16 | | | | | (v0 = 0))) % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | DELTA: instantiating (145) with fresh symbols all_73_0, all_73_1 % 17.06/3.16 | | | | | gives: % 17.06/3.16 | | | | | (146) member(all_58_1, all_32_2) = all_73_0 & member(all_58_1, % 17.06/3.16 | | | | | all_32_3) = all_73_1 & ( ~ (all_73_0 = 0) | ~ (all_73_1 = % 17.06/3.16 | | | | | 0)) % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | ALPHA: (146) implies: % 17.06/3.16 | | | | | (147) member(all_58_1, all_32_3) = all_73_1 % 17.06/3.16 | | | | | (148) member(all_58_1, all_32_2) = all_73_0 % 17.06/3.16 | | | | | (149) ~ (all_73_0 = 0) | ~ (all_73_1 = 0) % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | GROUND_INST: instantiating (8) with all_32_10, all_32_7, all_32_9, % 17.06/3.16 | | | | | all_58_1, all_32_3, all_73_1, simplifying with (12), % 17.06/3.16 | | | | | (13), (15), (28), (132), (147) gives: % 17.06/3.16 | | | | | (150) all_73_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, % 17.06/3.16 | | | | | all_32_9) = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, % 17.06/3.16 | | | | | all_58_1, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 17.06/3.16 | | | | | = 0) & member(v0, all_32_7) = v1)) % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | GROUND_INST: instantiating (8) with all_32_10, all_32_6, all_32_9, % 17.06/3.16 | | | | | all_58_1, all_32_2, all_73_0, simplifying with (12), % 17.06/3.16 | | | | | (13), (16), (29), (132), (148) gives: % 17.06/3.16 | | | | | (151) all_73_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, % 17.06/3.16 | | | | | all_32_9) = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, % 17.06/3.16 | | | | | all_58_1, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 17.06/3.16 | | | | | = 0) & member(v0, all_32_6) = v1)) % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | GROUND_INST: instantiating (4) with all_67_0, all_32_7, all_32_6, % 17.06/3.16 | | | | | all_32_5, simplifying with (15), (16), (25), (140), (141) % 17.06/3.16 | | | | | gives: % 17.06/3.16 | | | | | (152) member(all_67_0, all_32_6) = 0 & member(all_67_0, all_32_7) = % 17.06/3.16 | | | | | 0 % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | ALPHA: (152) implies: % 17.06/3.16 | | | | | (153) member(all_67_0, all_32_7) = 0 % 17.06/3.16 | | | | | (154) member(all_67_0, all_32_6) = 0 % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | BETA: splitting (149) gives: % 17.06/3.16 | | | | | % 17.06/3.16 | | | | | Case 1: % 17.06/3.16 | | | | | | % 17.06/3.16 | | | | | | (155) ~ (all_73_0 = 0) % 17.06/3.16 | | | | | | % 17.06/3.16 | | | | | | BETA: splitting (151) gives: % 17.06/3.16 | | | | | | % 17.06/3.16 | | | | | | Case 1: % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | (156) all_73_0 = 0 % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | REDUCE: (155), (156) imply: % 17.06/3.16 | | | | | | | (157) $false % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | CLOSE: (157) is inconsistent. % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | Case 2: % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | (158) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_9) % 17.06/3.16 | | | | | | | = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, all_58_1, % 17.06/3.16 | | | | | | | v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 17.06/3.16 | | | | | | | & member(v0, all_32_6) = v1)) % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | BETA: splitting (158) gives: % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | Case 1: % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | (159) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, % 17.06/3.16 | | | | | | | | all_32_9) = v0) % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | DELTA: instantiating (159) with fresh symbol all_107_0 gives: % 17.06/3.16 | | | | | | | | (160) ~ (all_107_0 = 0) & member(all_58_1, all_32_9) = % 17.06/3.16 | | | | | | | | all_107_0 % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | REF_CLOSE: (9), (136), (160) are inconsistent by sub-proof #1. % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | Case 2: % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | (161) ! [v0: $i] : ( ~ (apply(all_32_10, all_58_1, v0) = 0) % 17.06/3.16 | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 17.06/3.16 | | | | | | | | member(v0, all_32_6) = v1)) % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | GROUND_INST: instantiating (161) with all_67_0, simplifying with % 17.06/3.16 | | | | | | | | (140), (142) gives: % 17.06/3.16 | | | | | | | | (162) ? [v0: int] : ( ~ (v0 = 0) & member(all_67_0, % 17.06/3.16 | | | | | | | | all_32_6) = v0) % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | DELTA: instantiating (162) with fresh symbol all_108_0 gives: % 17.06/3.16 | | | | | | | | (163) ~ (all_108_0 = 0) & member(all_67_0, all_32_6) = % 17.06/3.16 | | | | | | | | all_108_0 % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | ALPHA: (163) implies: % 17.06/3.16 | | | | | | | | (164) ~ (all_108_0 = 0) % 17.06/3.16 | | | | | | | | (165) member(all_67_0, all_32_6) = all_108_0 % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_108_0, all_32_6, % 17.06/3.16 | | | | | | | | all_67_0, simplifying with (154), (165) gives: % 17.06/3.16 | | | | | | | | (166) all_108_0 = 0 % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | REDUCE: (164), (166) imply: % 17.06/3.16 | | | | | | | | (167) $false % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | | CLOSE: (167) is inconsistent. % 17.06/3.16 | | | | | | | | % 17.06/3.16 | | | | | | | End of split % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | End of split % 17.06/3.16 | | | | | | % 17.06/3.16 | | | | | Case 2: % 17.06/3.16 | | | | | | % 17.06/3.16 | | | | | | (168) ~ (all_73_1 = 0) % 17.06/3.16 | | | | | | % 17.06/3.16 | | | | | | BETA: splitting (150) gives: % 17.06/3.16 | | | | | | % 17.06/3.16 | | | | | | Case 1: % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | (169) all_73_1 = 0 % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | REDUCE: (168), (169) imply: % 17.06/3.16 | | | | | | | (170) $false % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | CLOSE: (170) is inconsistent. % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | Case 2: % 17.06/3.16 | | | | | | | % 17.06/3.16 | | | | | | | (171) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_9) % 17.06/3.16 | | | | | | | = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, all_58_1, % 17.06/3.16 | | | | | | | v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 17.06/3.17 | | | | | | | & member(v0, all_32_7) = v1)) % 17.06/3.17 | | | | | | | % 17.06/3.17 | | | | | | | BETA: splitting (171) gives: % 17.06/3.17 | | | | | | | % 17.06/3.17 | | | | | | | Case 1: % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | (172) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, % 17.06/3.17 | | | | | | | | all_32_9) = v0) % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | DELTA: instantiating (172) with fresh symbol all_107_0 gives: % 17.06/3.17 | | | | | | | | (173) ~ (all_107_0 = 0) & member(all_58_1, all_32_9) = % 17.06/3.17 | | | | | | | | all_107_0 % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | REF_CLOSE: (9), (136), (173) are inconsistent by sub-proof #1. % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | Case 2: % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | (174) ! [v0: $i] : ( ~ (apply(all_32_10, all_58_1, v0) = 0) % 17.06/3.17 | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 17.06/3.17 | | | | | | | | member(v0, all_32_7) = v1)) % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | GROUND_INST: instantiating (174) with all_67_0, simplifying with % 17.06/3.17 | | | | | | | | (140), (142) gives: % 17.06/3.17 | | | | | | | | (175) ? [v0: int] : ( ~ (v0 = 0) & member(all_67_0, % 17.06/3.17 | | | | | | | | all_32_7) = v0) % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | DELTA: instantiating (175) with fresh symbol all_108_0 gives: % 17.06/3.17 | | | | | | | | (176) ~ (all_108_0 = 0) & member(all_67_0, all_32_7) = % 17.06/3.17 | | | | | | | | all_108_0 % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | ALPHA: (176) implies: % 17.06/3.17 | | | | | | | | (177) ~ (all_108_0 = 0) % 17.06/3.17 | | | | | | | | (178) member(all_67_0, all_32_7) = all_108_0 % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_108_0, all_32_7, % 17.06/3.17 | | | | | | | | all_67_0, simplifying with (153), (178) gives: % 17.06/3.17 | | | | | | | | (179) all_108_0 = 0 % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | REDUCE: (177), (179) imply: % 17.06/3.17 | | | | | | | | (180) $false % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | | CLOSE: (180) is inconsistent. % 17.06/3.17 | | | | | | | | % 17.06/3.17 | | | | | | | End of split % 17.06/3.17 | | | | | | | % 17.06/3.17 | | | | | | End of split % 17.06/3.17 | | | | | | % 17.06/3.17 | | | | | End of split % 17.06/3.17 | | | | | % 17.06/3.17 | | | | End of split % 17.06/3.17 | | | | % 17.06/3.17 | | | End of split % 17.06/3.17 | | | % 17.06/3.17 | | End of split % 17.06/3.17 | | % 17.06/3.17 | End of split % 17.06/3.17 | % 17.06/3.17 End of proof % 17.06/3.17 % 17.06/3.17 Sub-proof #1 shows that the following formulas are inconsistent: % 17.06/3.17 ---------------------------------------------------------------- % 17.06/3.17 (1) ~ (all_107_0 = 0) & member(all_58_1, all_32_9) = all_107_0 % 17.06/3.17 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.06/3.17 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 17.06/3.17 v0)) % 17.06/3.17 (3) member(all_58_1, all_32_9) = 0 % 17.06/3.17 % 17.06/3.17 Begin of proof % 17.06/3.17 | % 17.06/3.17 | ALPHA: (1) implies: % 17.06/3.17 | (4) ~ (all_107_0 = 0) % 17.06/3.17 | (5) member(all_58_1, all_32_9) = all_107_0 % 17.06/3.17 | % 17.06/3.17 | GROUND_INST: instantiating (2) with 0, all_107_0, all_32_9, all_58_1, % 17.06/3.17 | simplifying with (3), (5) gives: % 17.06/3.17 | (6) all_107_0 = 0 % 17.06/3.17 | % 17.06/3.17 | REDUCE: (4), (6) imply: % 17.06/3.17 | (7) $false % 17.06/3.17 | % 17.06/3.17 | CLOSE: (7) is inconsistent. % 17.06/3.17 | % 17.06/3.17 End of proof % 17.06/3.17 % SZS output end Proof for theBenchmark % 17.06/3.17 % 17.06/3.17 2561ms %------------------------------------------------------------------------------