%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET756+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 : n031.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 13.54s 2.56s % Output : Proof 16.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET756+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n031.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 09:48:53 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.51/1.21 Prover 4: Preprocessing ... % 3.51/1.21 Prover 1: Preprocessing ... % 3.90/1.24 Prover 6: Preprocessing ... % 3.90/1.24 Prover 5: Preprocessing ... % 3.90/1.24 Prover 3: Preprocessing ... % 3.90/1.24 Prover 0: Preprocessing ... % 3.90/1.24 Prover 2: Preprocessing ... % 8.66/1.93 Prover 5: Proving ... % 8.66/2.01 Prover 2: Proving ... % 9.84/2.05 Prover 1: Constructing countermodel ... % 9.84/2.06 Prover 6: Proving ... % 10.30/2.13 Prover 3: Constructing countermodel ... % 13.54/2.56 Prover 3: proved (1933ms) % 13.54/2.56 % 13.54/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.54/2.56 % 13.54/2.58 Prover 5: stopped % 13.54/2.59 Prover 2: stopped % 13.54/2.59 Prover 6: stopped % 13.54/2.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.54/2.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.54/2.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.54/2.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.86/2.68 Prover 10: Preprocessing ... % 13.86/2.68 Prover 1: Found proof (size 105) % 13.86/2.69 Prover 1: proved (2068ms) % 13.86/2.69 Prover 8: Preprocessing ... % 13.86/2.71 Prover 7: Preprocessing ... % 14.73/2.72 Prover 10: stopped % 14.73/2.73 Prover 11: Preprocessing ... % 14.85/2.75 Prover 4: Constructing countermodel ... % 14.85/2.77 Prover 4: stopped % 14.85/2.78 Prover 7: stopped % 14.85/2.78 Prover 0: Proving ... % 14.85/2.78 Prover 0: stopped % 15.48/2.83 Prover 11: stopped % 15.48/2.88 Prover 8: Warning: ignoring some quantifiers % 15.83/2.89 Prover 8: Constructing countermodel ... % 15.83/2.90 Prover 8: stopped % 15.83/2.90 % 15.83/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.83/2.90 % 15.83/2.91 % SZS output start Proof for theBenchmark % 15.83/2.91 Assumptions after simplification: % 15.83/2.91 --------------------------------- % 15.83/2.91 % 15.83/2.91 (equal_set) % 15.83/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 15.83/2.94 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 15.83/2.94 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 15.83/2.94 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 15.83/2.94 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 15.83/2.94 % 15.83/2.94 (inverse_image2) % 15.83/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.83/2.94 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | % 15.83/2.94 ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v2, v5) = 0) | ~ $i(v5) % 15.83/2.94 | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : ! % 15.83/2.94 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (inverse_image2(v0, v1) = v3) | ~ % 15.83/2.94 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 15.83/2.94 (apply(v0, v2, v4) = 0 & member(v4, v1) = 0 & $i(v4))) % 15.83/2.94 % 15.83/2.94 (subset) % 15.83/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 15.83/2.94 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 15.83/2.94 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 15.83/2.94 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 15.83/2.94 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 15.83/2.94 % 15.83/2.94 (thIIa06) % 15.83/2.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.83/2.95 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 15.83/2.95 : ( ~ (v10 = 0) & inverse_image2(v0, v5) = v6 & inverse_image2(v0, v4) = v8 & % 15.83/2.95 inverse_image2(v0, v3) = v7 & maps(v0, v1, v2) = 0 & union(v7, v8) = v9 & % 15.83/2.95 union(v3, v4) = v5 & equal_set(v6, v9) = v10 & subset(v4, v2) = 0 & % 15.83/2.95 subset(v3, v2) = 0 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 15.83/2.95 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.83/2.95 % 15.83/2.95 (union) % 15.83/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.83/2.95 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 15.83/2.95 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 15.83/2.95 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 15.83/2.95 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 15.83/2.95 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 15.83/2.95 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 15.83/2.95 % 15.83/2.95 (function-axioms) % 15.83/2.96 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.83/2.96 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 15.83/2.96 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 15.83/2.96 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.83/2.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.96 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 15.83/2.96 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.83/2.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.96 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 15.83/2.96 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.83/2.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.96 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 15.83/2.96 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.83/2.96 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 15.83/2.96 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 15.83/2.96 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 15.83/2.96 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.83/2.96 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 15.83/2.96 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.83/2.96 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.83/2.96 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 15.83/2.96 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.83/2.96 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 15.83/2.96 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.83/2.96 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 15.83/2.96 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.83/2.96 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 15.83/2.96 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.83/2.96 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 15.83/2.96 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 15.83/2.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.83/2.96 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 15.83/2.96 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.83/2.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.83/2.96 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 15.83/2.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.96 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 15.83/2.96 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.83/2.96 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 15.83/2.96 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.83/2.96 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 15.83/2.96 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.83/2.96 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 15.83/2.96 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.83/2.96 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 15.83/2.96 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.83/2.96 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 15.83/2.96 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.83/2.96 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 15.83/2.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 15.83/2.96 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.83/2.96 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 15.83/2.96 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.83/2.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 15.83/2.96 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.83/2.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 15.83/2.96 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.83/2.96 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.83/2.96 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 15.83/2.96 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 15.83/2.96 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 15.83/2.96 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.83/2.96 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 15.83/2.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 15.83/2.96 (power_set(v2) = v0)) % 15.83/2.96 % 15.83/2.96 Further assumptions not needed in the proof: % 15.83/2.96 -------------------------------------------- % 15.83/2.96 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 15.83/2.96 equal_maps, identity, image2, image3, increasing_function, injective, % 15.83/2.96 intersection, inverse_function, inverse_image3, inverse_predicate, isomorphism, % 15.83/2.96 maps, one_to_one, power_set, product, singleton, sum, surjective, unordered_pair % 15.83/2.96 % 15.83/2.96 Those formulas are unsatisfiable: % 15.83/2.96 --------------------------------- % 15.83/2.96 % 15.83/2.96 Begin of proof % 15.83/2.96 | % 15.83/2.96 | ALPHA: (subset) implies: % 15.83/2.96 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.83/2.96 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 15.83/2.96 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 15.83/2.96 | % 15.83/2.96 | ALPHA: (equal_set) implies: % 15.83/2.96 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 15.83/2.96 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 15.83/2.96 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 15.83/2.96 | 0)))) % 15.83/2.96 | % 15.83/2.96 | ALPHA: (union) implies: % 15.83/2.96 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 15.83/2.96 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 15.83/2.96 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 15.83/2.96 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 15.83/2.97 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.83/2.97 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 15.83/2.97 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 15.83/2.97 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 15.83/2.97 | v5)) % 15.83/2.97 | % 15.83/2.97 | ALPHA: (inverse_image2) implies: % 15.83/2.97 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.83/2.97 | (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | % 15.83/2.97 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v2, v4) = 0 & % 15.83/2.97 | member(v4, v1) = 0 & $i(v4))) % 16.23/2.97 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.23/2.97 | (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | % 16.23/2.97 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v2, % 16.23/2.97 | v5) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, % 16.23/2.97 | v1) = v6))) % 16.23/2.97 | % 16.23/2.97 | ALPHA: (function-axioms) implies: % 16.23/2.97 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.23/2.97 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 16.23/2.97 | = v0)) % 16.23/2.97 | % 16.23/2.97 | DELTA: instantiating (thIIa06) with fresh symbols all_32_0, all_32_1, % 16.23/2.97 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8, % 16.23/2.97 | all_32_9, all_32_10 gives: % 16.23/2.97 | (8) ~ (all_32_0 = 0) & inverse_image2(all_32_10, all_32_5) = all_32_4 & % 16.23/2.97 | inverse_image2(all_32_10, all_32_6) = all_32_2 & % 16.23/2.97 | inverse_image2(all_32_10, all_32_7) = all_32_3 & maps(all_32_10, % 16.23/2.97 | all_32_9, all_32_8) = 0 & union(all_32_3, all_32_2) = all_32_1 & % 16.23/2.97 | union(all_32_7, all_32_6) = all_32_5 & equal_set(all_32_4, all_32_1) = % 16.23/2.97 | all_32_0 & subset(all_32_6, all_32_8) = 0 & subset(all_32_7, all_32_8) % 16.23/2.97 | = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & % 16.23/2.97 | $i(all_32_5) & $i(all_32_6) & $i(all_32_7) & $i(all_32_8) & % 16.23/2.97 | $i(all_32_9) & $i(all_32_10) % 16.23/2.97 | % 16.23/2.97 | ALPHA: (8) implies: % 16.23/2.97 | (9) ~ (all_32_0 = 0) % 16.23/2.97 | (10) $i(all_32_10) % 16.23/2.97 | (11) $i(all_32_7) % 16.23/2.97 | (12) $i(all_32_6) % 16.23/2.97 | (13) $i(all_32_5) % 16.23/2.97 | (14) $i(all_32_4) % 16.23/2.97 | (15) $i(all_32_3) % 16.23/2.97 | (16) $i(all_32_2) % 16.23/2.97 | (17) $i(all_32_1) % 16.23/2.97 | (18) equal_set(all_32_4, all_32_1) = all_32_0 % 16.23/2.97 | (19) union(all_32_7, all_32_6) = all_32_5 % 16.23/2.97 | (20) union(all_32_3, all_32_2) = all_32_1 % 16.23/2.97 | (21) inverse_image2(all_32_10, all_32_7) = all_32_3 % 16.23/2.97 | (22) inverse_image2(all_32_10, all_32_6) = all_32_2 % 16.23/2.97 | (23) inverse_image2(all_32_10, all_32_5) = all_32_4 % 16.23/2.97 | % 16.23/2.97 | GROUND_INST: instantiating (2) with all_32_4, all_32_1, all_32_0, simplifying % 16.23/2.97 | with (14), (17), (18) gives: % 16.23/2.97 | (24) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_32_1, % 16.23/2.97 | all_32_4) = v1 & subset(all_32_4, all_32_1) = v0 & ( ~ (v1 = 0) | % 16.23/2.97 | ~ (v0 = 0))) % 16.23/2.97 | % 16.23/2.97 | BETA: splitting (24) gives: % 16.23/2.97 | % 16.23/2.97 | Case 1: % 16.23/2.97 | | % 16.23/2.97 | | (25) all_32_0 = 0 % 16.23/2.97 | | % 16.23/2.97 | | REDUCE: (9), (25) imply: % 16.23/2.97 | | (26) $false % 16.23/2.98 | | % 16.23/2.98 | | CLOSE: (26) is inconsistent. % 16.23/2.98 | | % 16.23/2.98 | Case 2: % 16.23/2.98 | | % 16.23/2.98 | | (27) ? [v0: any] : ? [v1: any] : (subset(all_32_1, all_32_4) = v1 & % 16.23/2.98 | | subset(all_32_4, all_32_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.23/2.98 | | % 16.23/2.98 | | DELTA: instantiating (27) with fresh symbols all_45_0, all_45_1 gives: % 16.23/2.98 | | (28) subset(all_32_1, all_32_4) = all_45_0 & subset(all_32_4, all_32_1) = % 16.23/2.98 | | all_45_1 & ( ~ (all_45_0 = 0) | ~ (all_45_1 = 0)) % 16.23/2.98 | | % 16.23/2.98 | | ALPHA: (28) implies: % 16.23/2.98 | | (29) subset(all_32_4, all_32_1) = all_45_1 % 16.23/2.98 | | (30) subset(all_32_1, all_32_4) = all_45_0 % 16.23/2.98 | | (31) ~ (all_45_0 = 0) | ~ (all_45_1 = 0) % 16.23/2.98 | | % 16.23/2.98 | | GROUND_INST: instantiating (1) with all_32_4, all_32_1, all_45_1, % 16.23/2.98 | | simplifying with (14), (17), (29) gives: % 16.23/2.98 | | (32) all_45_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.23/2.98 | | member(v0, all_32_1) = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 16.23/2.98 | | % 16.23/2.98 | | GROUND_INST: instantiating (1) with all_32_1, all_32_4, all_45_0, % 16.23/2.98 | | simplifying with (14), (17), (30) gives: % 16.23/2.98 | | (33) all_45_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.23/2.98 | | member(v0, all_32_1) = 0 & member(v0, all_32_4) = v1 & $i(v0)) % 16.23/2.98 | | % 16.23/2.98 | | BETA: splitting (31) gives: % 16.23/2.98 | | % 16.23/2.98 | | Case 1: % 16.23/2.98 | | | % 16.23/2.98 | | | (34) ~ (all_45_0 = 0) % 16.23/2.98 | | | % 16.23/2.98 | | | BETA: splitting (33) gives: % 16.23/2.98 | | | % 16.23/2.98 | | | Case 1: % 16.23/2.98 | | | | % 16.23/2.98 | | | | (35) all_45_0 = 0 % 16.23/2.98 | | | | % 16.23/2.98 | | | | REDUCE: (34), (35) imply: % 16.23/2.98 | | | | (36) $false % 16.23/2.98 | | | | % 16.23/2.98 | | | | CLOSE: (36) is inconsistent. % 16.23/2.98 | | | | % 16.23/2.98 | | | Case 2: % 16.23/2.98 | | | | % 16.23/2.98 | | | | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) % 16.29/2.98 | | | | = 0 & member(v0, all_32_4) = v1 & $i(v0)) % 16.29/2.98 | | | | % 16.29/2.98 | | | | DELTA: instantiating (37) with fresh symbols all_58_0, all_58_1 gives: % 16.29/2.98 | | | | (38) ~ (all_58_0 = 0) & member(all_58_1, all_32_1) = 0 & % 16.29/2.98 | | | | member(all_58_1, all_32_4) = all_58_0 & $i(all_58_1) % 16.29/2.98 | | | | % 16.29/2.98 | | | | ALPHA: (38) implies: % 16.29/2.98 | | | | (39) ~ (all_58_0 = 0) % 16.29/2.98 | | | | (40) $i(all_58_1) % 16.29/2.98 | | | | (41) member(all_58_1, all_32_4) = all_58_0 % 16.29/2.98 | | | | (42) member(all_58_1, all_32_1) = 0 % 16.29/2.98 | | | | % 16.29/2.98 | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_5, all_58_1, % 16.29/2.98 | | | | all_32_4, all_58_0, simplifying with (10), (13), (23), % 16.29/2.98 | | | | (40), (41) gives: % 16.29/2.98 | | | | (43) all_58_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_10, all_58_1, v0) % 16.29/2.98 | | | | = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 16.29/2.98 | | | | all_32_5) = v1)) % 16.29/2.98 | | | | % 16.29/2.98 | | | | GROUND_INST: instantiating (3) with all_58_1, all_32_3, all_32_2, % 16.29/2.98 | | | | all_32_1, simplifying with (15), (16), (20), (40), (42) % 16.29/2.98 | | | | gives: % 16.29/2.98 | | | | (44) ? [v0: any] : ? [v1: any] : (member(all_58_1, all_32_2) = v1 & % 16.29/2.98 | | | | member(all_58_1, all_32_3) = v0 & (v1 = 0 | v0 = 0)) % 16.29/2.98 | | | | % 16.29/2.98 | | | | DELTA: instantiating (44) with fresh symbols all_65_0, all_65_1 gives: % 16.29/2.98 | | | | (45) member(all_58_1, all_32_2) = all_65_0 & member(all_58_1, % 16.29/2.98 | | | | all_32_3) = all_65_1 & (all_65_0 = 0 | all_65_1 = 0) % 16.29/2.98 | | | | % 16.29/2.98 | | | | ALPHA: (45) implies: % 16.29/2.98 | | | | (46) member(all_58_1, all_32_3) = all_65_1 % 16.29/2.98 | | | | (47) member(all_58_1, all_32_2) = all_65_0 % 16.29/2.98 | | | | (48) all_65_0 = 0 | all_65_1 = 0 % 16.29/2.98 | | | | % 16.29/2.98 | | | | BETA: splitting (43) gives: % 16.29/2.98 | | | | % 16.29/2.98 | | | | Case 1: % 16.29/2.98 | | | | | % 16.29/2.98 | | | | | (49) all_58_0 = 0 % 16.29/2.98 | | | | | % 16.29/2.98 | | | | | REDUCE: (39), (49) imply: % 16.29/2.98 | | | | | (50) $false % 16.29/2.98 | | | | | % 16.29/2.98 | | | | | CLOSE: (50) is inconsistent. % 16.29/2.98 | | | | | % 16.29/2.98 | | | | Case 2: % 16.29/2.98 | | | | | % 16.29/2.99 | | | | | (51) ! [v0: $i] : ( ~ (apply(all_32_10, all_58_1, v0) = 0) | ~ % 16.29/2.99 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_5) % 16.29/2.99 | | | | | = v1)) % 16.29/2.99 | | | | | % 16.29/2.99 | | | | | BETA: splitting (48) gives: % 16.29/2.99 | | | | | % 16.29/2.99 | | | | | Case 1: % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | (52) all_65_0 = 0 % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | REDUCE: (47), (52) imply: % 16.29/2.99 | | | | | | (53) member(all_58_1, all_32_2) = 0 % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | GROUND_INST: instantiating (5) with all_32_10, all_32_6, all_58_1, % 16.29/2.99 | | | | | | all_32_2, simplifying with (10), (12), (22), (40), (53) % 16.29/2.99 | | | | | | gives: % 16.29/2.99 | | | | | | (54) ? [v0: $i] : (apply(all_32_10, all_58_1, v0) = 0 & % 16.29/2.99 | | | | | | member(v0, all_32_6) = 0 & $i(v0)) % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | DELTA: instantiating (54) with fresh symbol all_94_0 gives: % 16.29/2.99 | | | | | | (55) apply(all_32_10, all_58_1, all_94_0) = 0 & member(all_94_0, % 16.29/2.99 | | | | | | all_32_6) = 0 & $i(all_94_0) % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | ALPHA: (55) implies: % 16.29/2.99 | | | | | | (56) $i(all_94_0) % 16.29/2.99 | | | | | | (57) member(all_94_0, all_32_6) = 0 % 16.29/2.99 | | | | | | (58) apply(all_32_10, all_58_1, all_94_0) = 0 % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | GROUND_INST: instantiating (51) with all_94_0, simplifying with % 16.29/2.99 | | | | | | (56), (58) gives: % 16.29/2.99 | | | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & member(all_94_0, all_32_5) = % 16.29/2.99 | | | | | | v0) % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | DELTA: instantiating (59) with fresh symbol all_102_0 gives: % 16.29/2.99 | | | | | | (60) ~ (all_102_0 = 0) & member(all_94_0, all_32_5) = all_102_0 % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | ALPHA: (60) implies: % 16.29/2.99 | | | | | | (61) ~ (all_102_0 = 0) % 16.29/2.99 | | | | | | (62) member(all_94_0, all_32_5) = all_102_0 % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | GROUND_INST: instantiating (4) with all_94_0, all_32_7, all_32_6, % 16.29/2.99 | | | | | | all_32_5, all_102_0, simplifying with (11), (12), (19), % 16.29/2.99 | | | | | | (56), (62) gives: % 16.29/2.99 | | | | | | (63) all_102_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 16.29/2.99 | | | | | | ~ (v0 = 0) & member(all_94_0, all_32_6) = v1 & % 16.29/2.99 | | | | | | member(all_94_0, all_32_7) = v0) % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | BETA: splitting (63) gives: % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | Case 1: % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | (64) all_102_0 = 0 % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | REDUCE: (61), (64) imply: % 16.29/2.99 | | | | | | | (65) $false % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | CLOSE: (65) is inconsistent. % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | Case 2: % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | (66) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 16.29/2.99 | | | | | | | member(all_94_0, all_32_6) = v1 & member(all_94_0, % 16.29/2.99 | | | | | | | all_32_7) = v0) % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | DELTA: instantiating (66) with fresh symbols all_118_0, all_118_1 % 16.29/2.99 | | | | | | | gives: % 16.29/2.99 | | | | | | | (67) ~ (all_118_0 = 0) & ~ (all_118_1 = 0) & member(all_94_0, % 16.29/2.99 | | | | | | | all_32_6) = all_118_0 & member(all_94_0, all_32_7) = % 16.29/2.99 | | | | | | | all_118_1 % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | ALPHA: (67) implies: % 16.29/2.99 | | | | | | | (68) ~ (all_118_0 = 0) % 16.29/2.99 | | | | | | | (69) member(all_94_0, all_32_6) = all_118_0 % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | GROUND_INST: instantiating (7) with 0, all_118_0, all_32_6, % 16.29/2.99 | | | | | | | all_94_0, simplifying with (57), (69) gives: % 16.29/2.99 | | | | | | | (70) all_118_0 = 0 % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | REDUCE: (68), (70) imply: % 16.29/2.99 | | | | | | | (71) $false % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | | CLOSE: (71) is inconsistent. % 16.29/2.99 | | | | | | | % 16.29/2.99 | | | | | | End of split % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | Case 2: % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | (72) all_65_1 = 0 % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | REDUCE: (46), (72) imply: % 16.29/2.99 | | | | | | (73) member(all_58_1, all_32_3) = 0 % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | GROUND_INST: instantiating (5) with all_32_10, all_32_7, all_58_1, % 16.29/2.99 | | | | | | all_32_3, simplifying with (10), (11), (21), (40), (73) % 16.29/2.99 | | | | | | gives: % 16.29/2.99 | | | | | | (74) ? [v0: $i] : (apply(all_32_10, all_58_1, v0) = 0 & % 16.29/2.99 | | | | | | member(v0, all_32_7) = 0 & $i(v0)) % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | DELTA: instantiating (74) with fresh symbol all_99_0 gives: % 16.29/2.99 | | | | | | (75) apply(all_32_10, all_58_1, all_99_0) = 0 & member(all_99_0, % 16.29/2.99 | | | | | | all_32_7) = 0 & $i(all_99_0) % 16.29/2.99 | | | | | | % 16.29/2.99 | | | | | | ALPHA: (75) implies: % 16.29/2.99 | | | | | | (76) $i(all_99_0) % 16.29/3.00 | | | | | | (77) member(all_99_0, all_32_7) = 0 % 16.29/3.00 | | | | | | (78) apply(all_32_10, all_58_1, all_99_0) = 0 % 16.29/3.00 | | | | | | % 16.29/3.00 | | | | | | GROUND_INST: instantiating (51) with all_99_0, simplifying with % 16.29/3.00 | | | | | | (76), (78) gives: % 16.29/3.00 | | | | | | (79) ? [v0: int] : ( ~ (v0 = 0) & member(all_99_0, all_32_5) = % 16.29/3.00 | | | | | | v0) % 16.29/3.00 | | | | | | % 16.29/3.00 | | | | | | DELTA: instantiating (79) with fresh symbol all_109_0 gives: % 16.29/3.00 | | | | | | (80) ~ (all_109_0 = 0) & member(all_99_0, all_32_5) = all_109_0 % 16.29/3.00 | | | | | | % 16.29/3.00 | | | | | | ALPHA: (80) implies: % 16.29/3.00 | | | | | | (81) ~ (all_109_0 = 0) % 16.29/3.00 | | | | | | (82) member(all_99_0, all_32_5) = all_109_0 % 16.29/3.00 | | | | | | % 16.29/3.00 | | | | | | GROUND_INST: instantiating (4) with all_99_0, all_32_7, all_32_6, % 16.29/3.00 | | | | | | all_32_5, all_109_0, simplifying with (11), (12), (19), % 16.29/3.00 | | | | | | (76), (82) gives: % 16.29/3.00 | | | | | | (83) all_109_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 16.29/3.00 | | | | | | ~ (v0 = 0) & member(all_99_0, all_32_6) = v1 & % 16.29/3.00 | | | | | | member(all_99_0, all_32_7) = v0) % 16.29/3.00 | | | | | | % 16.29/3.00 | | | | | | BETA: splitting (83) gives: % 16.29/3.00 | | | | | | % 16.29/3.00 | | | | | | Case 1: % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | (84) all_109_0 = 0 % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | REDUCE: (81), (84) imply: % 16.29/3.00 | | | | | | | (85) $false % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | CLOSE: (85) is inconsistent. % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | Case 2: % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | (86) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 16.29/3.00 | | | | | | | member(all_99_0, all_32_6) = v1 & member(all_99_0, % 16.29/3.00 | | | | | | | all_32_7) = v0) % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | DELTA: instantiating (86) with fresh symbols all_118_0, all_118_1 % 16.29/3.00 | | | | | | | gives: % 16.29/3.00 | | | | | | | (87) ~ (all_118_0 = 0) & ~ (all_118_1 = 0) & member(all_99_0, % 16.29/3.00 | | | | | | | all_32_6) = all_118_0 & member(all_99_0, all_32_7) = % 16.29/3.00 | | | | | | | all_118_1 % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | ALPHA: (87) implies: % 16.29/3.00 | | | | | | | (88) ~ (all_118_1 = 0) % 16.29/3.00 | | | | | | | (89) member(all_99_0, all_32_7) = all_118_1 % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | GROUND_INST: instantiating (7) with 0, all_118_1, all_32_7, % 16.29/3.00 | | | | | | | all_99_0, simplifying with (77), (89) gives: % 16.29/3.00 | | | | | | | (90) all_118_1 = 0 % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | REDUCE: (88), (90) imply: % 16.29/3.00 | | | | | | | (91) $false % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | | CLOSE: (91) is inconsistent. % 16.29/3.00 | | | | | | | % 16.29/3.00 | | | | | | End of split % 16.29/3.00 | | | | | | % 16.29/3.00 | | | | | End of split % 16.29/3.00 | | | | | % 16.29/3.00 | | | | End of split % 16.29/3.00 | | | | % 16.29/3.00 | | | End of split % 16.29/3.00 | | | % 16.29/3.00 | | Case 2: % 16.29/3.00 | | | % 16.29/3.00 | | | (92) ~ (all_45_1 = 0) % 16.29/3.00 | | | % 16.29/3.00 | | | BETA: splitting (32) gives: % 16.29/3.00 | | | % 16.29/3.00 | | | Case 1: % 16.29/3.00 | | | | % 16.29/3.00 | | | | (93) all_45_1 = 0 % 16.29/3.00 | | | | % 16.29/3.00 | | | | REDUCE: (92), (93) imply: % 16.29/3.00 | | | | (94) $false % 16.29/3.00 | | | | % 16.29/3.00 | | | | CLOSE: (94) is inconsistent. % 16.29/3.00 | | | | % 16.29/3.00 | | | Case 2: % 16.29/3.00 | | | | % 16.29/3.00 | | | | (95) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) % 16.29/3.00 | | | | = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 16.29/3.00 | | | | % 16.29/3.00 | | | | DELTA: instantiating (95) with fresh symbols all_79_0, all_79_1 gives: % 16.29/3.00 | | | | (96) ~ (all_79_0 = 0) & member(all_79_1, all_32_1) = all_79_0 & % 16.29/3.00 | | | | member(all_79_1, all_32_4) = 0 & $i(all_79_1) % 16.29/3.00 | | | | % 16.29/3.00 | | | | ALPHA: (96) implies: % 16.29/3.00 | | | | (97) ~ (all_79_0 = 0) % 16.29/3.00 | | | | (98) $i(all_79_1) % 16.29/3.00 | | | | (99) member(all_79_1, all_32_4) = 0 % 16.29/3.00 | | | | (100) member(all_79_1, all_32_1) = all_79_0 % 16.29/3.00 | | | | % 16.29/3.00 | | | | GROUND_INST: instantiating (5) with all_32_10, all_32_5, all_79_1, % 16.29/3.00 | | | | all_32_4, simplifying with (10), (13), (23), (98), (99) % 16.29/3.00 | | | | gives: % 16.29/3.00 | | | | (101) ? [v0: $i] : (apply(all_32_10, all_79_1, v0) = 0 & member(v0, % 16.29/3.00 | | | | all_32_5) = 0 & $i(v0)) % 16.29/3.00 | | | | % 16.29/3.00 | | | | GROUND_INST: instantiating (4) with all_79_1, all_32_3, all_32_2, % 16.29/3.00 | | | | all_32_1, all_79_0, simplifying with (15), (16), (20), % 16.29/3.00 | | | | (98), (100) gives: % 16.29/3.00 | | | | (102) all_79_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 16.29/3.00 | | | | (v0 = 0) & member(all_79_1, all_32_2) = v1 & member(all_79_1, % 16.29/3.01 | | | | all_32_3) = v0) % 16.29/3.01 | | | | % 16.29/3.01 | | | | DELTA: instantiating (101) with fresh symbol all_86_0 gives: % 16.29/3.01 | | | | (103) apply(all_32_10, all_79_1, all_86_0) = 0 & member(all_86_0, % 16.29/3.01 | | | | all_32_5) = 0 & $i(all_86_0) % 16.29/3.01 | | | | % 16.29/3.01 | | | | ALPHA: (103) implies: % 16.29/3.01 | | | | (104) $i(all_86_0) % 16.29/3.01 | | | | (105) member(all_86_0, all_32_5) = 0 % 16.29/3.01 | | | | (106) apply(all_32_10, all_79_1, all_86_0) = 0 % 16.29/3.01 | | | | % 16.29/3.01 | | | | BETA: splitting (102) gives: % 16.29/3.01 | | | | % 16.29/3.01 | | | | Case 1: % 16.29/3.01 | | | | | % 16.29/3.01 | | | | | (107) all_79_0 = 0 % 16.29/3.01 | | | | | % 16.29/3.01 | | | | | REDUCE: (97), (107) imply: % 16.29/3.01 | | | | | (108) $false % 16.29/3.01 | | | | | % 16.29/3.01 | | | | | CLOSE: (108) is inconsistent. % 16.29/3.01 | | | | | % 16.29/3.01 | | | | Case 2: % 16.29/3.01 | | | | | % 16.29/3.01 | | | | | (109) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 16.29/3.01 | | | | | member(all_79_1, all_32_2) = v1 & member(all_79_1, % 16.29/3.01 | | | | | all_32_3) = v0) % 16.29/3.01 | | | | | % 16.29/3.01 | | | | | DELTA: instantiating (109) with fresh symbols all_92_0, all_92_1 % 16.29/3.01 | | | | | gives: % 16.29/3.01 | | | | | (110) ~ (all_92_0 = 0) & ~ (all_92_1 = 0) & member(all_79_1, % 16.29/3.01 | | | | | all_32_2) = all_92_0 & member(all_79_1, all_32_3) = % 16.29/3.01 | | | | | all_92_1 % 16.29/3.01 | | | | | % 16.29/3.01 | | | | | ALPHA: (110) implies: % 16.29/3.01 | | | | | (111) ~ (all_92_1 = 0) % 16.29/3.01 | | | | | (112) ~ (all_92_0 = 0) % 16.29/3.01 | | | | | (113) member(all_79_1, all_32_3) = all_92_1 % 16.29/3.01 | | | | | (114) member(all_79_1, all_32_2) = all_92_0 % 16.29/3.01 | | | | | % 16.29/3.01 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_7, all_79_1, % 16.29/3.01 | | | | | all_32_3, all_92_1, simplifying with (10), (11), (21), % 16.29/3.01 | | | | | (98), (113) gives: % 16.44/3.01 | | | | | (115) all_92_1 = 0 | ! [v0: $i] : ( ~ (apply(all_32_10, all_79_1, % 16.44/3.01 | | | | | v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 16.44/3.01 | | | | | member(v0, all_32_7) = v1)) % 16.44/3.01 | | | | | % 16.44/3.01 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_6, all_79_1, % 16.44/3.01 | | | | | all_32_2, all_92_0, simplifying with (10), (12), (22), % 16.44/3.01 | | | | | (98), (114) gives: % 16.44/3.01 | | | | | (116) all_92_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_10, all_79_1, % 16.44/3.01 | | | | | v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 16.44/3.01 | | | | | member(v0, all_32_6) = v1)) % 16.44/3.01 | | | | | % 16.44/3.01 | | | | | GROUND_INST: instantiating (3) with all_86_0, all_32_7, all_32_6, % 16.44/3.01 | | | | | all_32_5, simplifying with (11), (12), (19), (104), (105) % 16.44/3.01 | | | | | gives: % 16.44/3.01 | | | | | (117) ? [v0: any] : ? [v1: any] : (member(all_86_0, all_32_6) = % 16.44/3.01 | | | | | v1 & member(all_86_0, all_32_7) = v0 & (v1 = 0 | v0 = 0)) % 16.44/3.01 | | | | | % 16.44/3.01 | | | | | DELTA: instantiating (117) with fresh symbols all_99_0, all_99_1 % 16.44/3.01 | | | | | gives: % 16.44/3.01 | | | | | (118) member(all_86_0, all_32_6) = all_99_0 & member(all_86_0, % 16.44/3.01 | | | | | all_32_7) = all_99_1 & (all_99_0 = 0 | all_99_1 = 0) % 16.44/3.01 | | | | | % 16.44/3.01 | | | | | ALPHA: (118) implies: % 16.44/3.01 | | | | | (119) member(all_86_0, all_32_7) = all_99_1 % 16.44/3.01 | | | | | (120) member(all_86_0, all_32_6) = all_99_0 % 16.44/3.01 | | | | | (121) all_99_0 = 0 | all_99_1 = 0 % 16.44/3.01 | | | | | % 16.44/3.01 | | | | | BETA: splitting (116) gives: % 16.44/3.01 | | | | | % 16.44/3.01 | | | | | Case 1: % 16.44/3.01 | | | | | | % 16.44/3.01 | | | | | | (122) all_92_0 = 0 % 16.44/3.01 | | | | | | % 16.44/3.01 | | | | | | REDUCE: (112), (122) imply: % 16.44/3.01 | | | | | | (123) $false % 16.44/3.01 | | | | | | % 16.44/3.01 | | | | | | CLOSE: (123) is inconsistent. % 16.44/3.01 | | | | | | % 16.44/3.01 | | | | | Case 2: % 16.44/3.01 | | | | | | % 16.44/3.01 | | | | | | (124) ! [v0: $i] : ( ~ (apply(all_32_10, all_79_1, v0) = 0) | ~ % 16.44/3.01 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 16.44/3.01 | | | | | | all_32_6) = v1)) % 16.44/3.01 | | | | | | % 16.44/3.01 | | | | | | GROUND_INST: instantiating (124) with all_86_0, simplifying with % 16.44/3.01 | | | | | | (104), (106) gives: % 16.44/3.01 | | | | | | (125) ? [v0: int] : ( ~ (v0 = 0) & member(all_86_0, all_32_6) = % 16.44/3.01 | | | | | | v0) % 16.44/3.01 | | | | | | % 16.44/3.01 | | | | | | BETA: splitting (115) gives: % 16.44/3.01 | | | | | | % 16.44/3.01 | | | | | | Case 1: % 16.44/3.01 | | | | | | | % 16.44/3.01 | | | | | | | (126) all_92_1 = 0 % 16.44/3.01 | | | | | | | % 16.44/3.01 | | | | | | | REDUCE: (111), (126) imply: % 16.44/3.01 | | | | | | | (127) $false % 16.44/3.01 | | | | | | | % 16.44/3.01 | | | | | | | CLOSE: (127) is inconsistent. % 16.44/3.01 | | | | | | | % 16.44/3.01 | | | | | | Case 2: % 16.44/3.01 | | | | | | | % 16.44/3.01 | | | | | | | (128) ! [v0: $i] : ( ~ (apply(all_32_10, all_79_1, v0) = 0) | % 16.44/3.01 | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 16.44/3.01 | | | | | | | all_32_7) = v1)) % 16.44/3.01 | | | | | | | % 16.44/3.01 | | | | | | | GROUND_INST: instantiating (128) with all_86_0, simplifying with % 16.44/3.01 | | | | | | | (104), (106) gives: % 16.44/3.01 | | | | | | | (129) ? [v0: int] : ( ~ (v0 = 0) & member(all_86_0, all_32_7) % 16.44/3.01 | | | | | | | = v0) % 16.44/3.01 | | | | | | | % 16.44/3.01 | | | | | | | DELTA: instantiating (125) with fresh symbol all_110_0 gives: % 16.44/3.01 | | | | | | | (130) ~ (all_110_0 = 0) & member(all_86_0, all_32_6) = % 16.44/3.01 | | | | | | | all_110_0 % 16.44/3.01 | | | | | | | % 16.44/3.01 | | | | | | | ALPHA: (130) implies: % 16.44/3.02 | | | | | | | (131) ~ (all_110_0 = 0) % 16.44/3.02 | | | | | | | (132) member(all_86_0, all_32_6) = all_110_0 % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | | DELTA: instantiating (129) with fresh symbol all_112_0 gives: % 16.44/3.02 | | | | | | | (133) ~ (all_112_0 = 0) & member(all_86_0, all_32_7) = % 16.44/3.02 | | | | | | | all_112_0 % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | | ALPHA: (133) implies: % 16.44/3.02 | | | | | | | (134) ~ (all_112_0 = 0) % 16.44/3.02 | | | | | | | (135) member(all_86_0, all_32_7) = all_112_0 % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | | GROUND_INST: instantiating (7) with all_99_1, all_112_0, all_32_7, % 16.44/3.02 | | | | | | | all_86_0, simplifying with (119), (135) gives: % 16.44/3.02 | | | | | | | (136) all_112_0 = all_99_1 % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | | GROUND_INST: instantiating (7) with all_99_0, all_110_0, all_32_6, % 16.44/3.02 | | | | | | | all_86_0, simplifying with (120), (132) gives: % 16.44/3.02 | | | | | | | (137) all_110_0 = all_99_0 % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | | REDUCE: (134), (136) imply: % 16.44/3.02 | | | | | | | (138) ~ (all_99_1 = 0) % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | | REDUCE: (131), (137) imply: % 16.44/3.02 | | | | | | | (139) ~ (all_99_0 = 0) % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | | BETA: splitting (121) gives: % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | | Case 1: % 16.44/3.02 | | | | | | | | % 16.44/3.02 | | | | | | | | (140) all_99_0 = 0 % 16.44/3.02 | | | | | | | | % 16.44/3.02 | | | | | | | | REDUCE: (139), (140) imply: % 16.44/3.02 | | | | | | | | (141) $false % 16.44/3.02 | | | | | | | | % 16.44/3.02 | | | | | | | | CLOSE: (141) is inconsistent. % 16.44/3.02 | | | | | | | | % 16.44/3.02 | | | | | | | Case 2: % 16.44/3.02 | | | | | | | | % 16.44/3.02 | | | | | | | | (142) all_99_1 = 0 % 16.44/3.02 | | | | | | | | % 16.44/3.02 | | | | | | | | REDUCE: (138), (142) imply: % 16.44/3.02 | | | | | | | | (143) $false % 16.44/3.02 | | | | | | | | % 16.44/3.02 | | | | | | | | CLOSE: (143) is inconsistent. % 16.44/3.02 | | | | | | | | % 16.44/3.02 | | | | | | | End of split % 16.44/3.02 | | | | | | | % 16.44/3.02 | | | | | | End of split % 16.44/3.02 | | | | | | % 16.44/3.02 | | | | | End of split % 16.44/3.02 | | | | | % 16.44/3.02 | | | | End of split % 16.44/3.02 | | | | % 16.44/3.02 | | | End of split % 16.44/3.02 | | | % 16.44/3.02 | | End of split % 16.44/3.02 | | % 16.44/3.02 | End of split % 16.44/3.02 | % 16.44/3.02 End of proof % 16.44/3.02 % SZS output end Proof for theBenchmark % 16.44/3.02 % 16.44/3.02 2419ms %------------------------------------------------------------------------------