%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET751+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 : n020.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 15:26:17 EDT 2023 % Result : Theorem 9.83s 2.16s % Output : Proof 13.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET751+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 08:57:44 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.29/1.12 Prover 1: Preprocessing ... % 3.29/1.12 Prover 4: Preprocessing ... % 3.63/1.16 Prover 2: Preprocessing ... % 3.63/1.16 Prover 3: Preprocessing ... % 3.63/1.16 Prover 0: Preprocessing ... % 3.63/1.17 Prover 6: Preprocessing ... % 3.63/1.17 Prover 5: Preprocessing ... % 8.93/1.94 Prover 5: Proving ... % 9.19/1.96 Prover 2: Proving ... % 9.19/2.02 Prover 6: Proving ... % 9.19/2.03 Prover 3: Constructing countermodel ... % 9.83/2.09 Prover 1: Constructing countermodel ... % 9.83/2.16 Prover 3: proved (1528ms) % 9.83/2.16 % 9.83/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.83/2.16 % 9.83/2.17 Prover 6: stopped % 9.83/2.17 Prover 2: stopped % 9.83/2.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.83/2.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.83/2.17 Prover 5: stopped % 9.83/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.83/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.66/2.25 Prover 10: Preprocessing ... % 10.66/2.26 Prover 8: Preprocessing ... % 10.66/2.26 Prover 11: Preprocessing ... % 10.66/2.27 Prover 7: Preprocessing ... % 11.85/2.40 Prover 7: Warning: ignoring some quantifiers % 11.85/2.40 Prover 10: Warning: ignoring some quantifiers % 11.85/2.41 Prover 1: Found proof (size 26) % 11.85/2.41 Prover 1: proved (1784ms) % 11.85/2.41 Prover 11: stopped % 12.60/2.43 Prover 7: Constructing countermodel ... % 12.60/2.45 Prover 10: Constructing countermodel ... % 12.60/2.45 Prover 7: stopped % 12.60/2.46 Prover 10: stopped % 13.12/2.57 Prover 4: Constructing countermodel ... % 13.75/2.58 Prover 0: Proving ... % 13.75/2.58 Prover 0: stopped % 13.75/2.58 Prover 8: Warning: ignoring some quantifiers % 13.75/2.59 Prover 4: stopped % 13.75/2.60 Prover 8: Constructing countermodel ... % 13.86/2.60 Prover 8: stopped % 13.86/2.60 % 13.86/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.86/2.60 % 13.86/2.61 % SZS output start Proof for theBenchmark % 13.86/2.61 Assumptions after simplification: % 13.86/2.61 --------------------------------- % 13.86/2.61 % 13.86/2.61 (image2) % 13.92/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 13.92/2.64 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 13.92/2.64 $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) = 0) | ~ $i(v5) | % 13.92/2.64 ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : ! % 13.92/2.64 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, v1) = v3) | ~ % 13.92/2.64 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 13.92/2.64 (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4))) % 13.92/2.64 % 13.92/2.64 (subset) % 13.92/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 13.92/2.64 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 13.92/2.64 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 13.92/2.64 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 13.92/2.64 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 13.92/2.64 % 13.92/2.64 (thIIa01) % 13.92/2.64 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.92/2.64 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & image2(v0, v4) = v6 & % 13.92/2.64 image2(v0, v3) = v5 & maps(v0, v1, v2) = 0 & subset(v5, v6) = v7 & % 13.92/2.64 subset(v4, v1) = 0 & subset(v3, v4) = 0 & subset(v3, v1) = 0 & $i(v6) & % 13.92/2.64 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.92/2.64 % 13.92/2.64 (function-axioms) % 13.92/2.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.92/2.65 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 13.92/2.65 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 13.92/2.65 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.92/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.92/2.65 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 13.92/2.65 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.92/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.92/2.65 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 13.92/2.65 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.92/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.92/2.65 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 13.92/2.65 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 13.92/2.65 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 13.92/2.65 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 13.92/2.65 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 13.92/2.65 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.92/2.65 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 13.92/2.65 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.92/2.65 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.92/2.65 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 13.92/2.65 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.92/2.65 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 13.92/2.65 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.92/2.65 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 13.92/2.65 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.92/2.65 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 13.92/2.65 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.92/2.65 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 13.92/2.65 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 13.92/2.65 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.92/2.65 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 13.92/2.65 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.92/2.65 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 13.92/2.65 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 13.92/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.92/2.65 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 13.92/2.65 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.92/2.65 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 13.92/2.65 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.92/2.65 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 13.92/2.65 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.92/2.65 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 13.92/2.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.92/2.65 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 13.92/2.65 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.92/2.66 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 13.92/2.66 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.92/2.66 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 13.92/2.66 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 13.92/2.66 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.92/2.66 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 13.92/2.66 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.92/2.66 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 13.92/2.66 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.92/2.66 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 13.92/2.66 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.92/2.66 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.92/2.66 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 13.92/2.66 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 13.92/2.66 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 13.92/2.66 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 13.92/2.66 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 13.92/2.66 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 13.92/2.66 (power_set(v2) = v0)) % 13.92/2.66 % 13.92/2.66 Further assumptions not needed in the proof: % 13.92/2.66 -------------------------------------------- % 13.92/2.66 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 13.92/2.66 equal_maps, equal_set, identity, image3, increasing_function, injective, % 13.92/2.66 intersection, inverse_function, inverse_image2, inverse_image3, % 13.92/2.66 inverse_predicate, isomorphism, maps, one_to_one, power_set, product, singleton, % 13.92/2.66 sum, surjective, union, unordered_pair % 13.92/2.66 % 13.92/2.66 Those formulas are unsatisfiable: % 13.92/2.66 --------------------------------- % 13.92/2.66 % 13.92/2.66 Begin of proof % 13.92/2.66 | % 13.92/2.66 | ALPHA: (subset) implies: % 13.92/2.66 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 13.92/2.66 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 13.92/2.66 | member(v2, v1) = 0)) % 13.92/2.66 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 13.92/2.66 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 13.92/2.66 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 13.92/2.66 | % 13.92/2.66 | ALPHA: (image2) implies: % 13.92/2.66 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, % 13.92/2.66 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 13.92/2.66 | $i(v0) | ? [v4: $i] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & % 13.92/2.66 | $i(v4))) % 13.92/2.66 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 13.92/2.66 | (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 13.92/2.66 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) % 13.92/2.66 | = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = % 13.92/2.66 | v6))) % 13.92/2.66 | % 13.92/2.66 | ALPHA: (function-axioms) implies: % 13.92/2.66 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.92/2.66 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 13.92/2.66 | = v0)) % 13.92/2.66 | % 13.92/2.66 | DELTA: instantiating (thIIa01) with fresh symbols all_32_0, all_32_1, % 13.92/2.66 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6, all_32_7 gives: % 13.92/2.66 | (6) ~ (all_32_0 = 0) & image2(all_32_7, all_32_3) = all_32_1 & % 13.92/2.66 | image2(all_32_7, all_32_4) = all_32_2 & maps(all_32_7, all_32_6, % 13.92/2.66 | all_32_5) = 0 & subset(all_32_2, all_32_1) = all_32_0 & % 13.92/2.66 | subset(all_32_3, all_32_6) = 0 & subset(all_32_4, all_32_3) = 0 & % 13.92/2.66 | subset(all_32_4, all_32_6) = 0 & $i(all_32_1) & $i(all_32_2) & % 13.92/2.66 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) & % 13.92/2.66 | $i(all_32_7) % 13.92/2.66 | % 13.92/2.66 | ALPHA: (6) implies: % 13.92/2.67 | (7) ~ (all_32_0 = 0) % 13.92/2.67 | (8) $i(all_32_7) % 13.92/2.67 | (9) $i(all_32_4) % 13.92/2.67 | (10) $i(all_32_3) % 13.92/2.67 | (11) $i(all_32_2) % 13.92/2.67 | (12) $i(all_32_1) % 13.92/2.67 | (13) subset(all_32_4, all_32_3) = 0 % 13.92/2.67 | (14) subset(all_32_2, all_32_1) = all_32_0 % 13.92/2.67 | (15) image2(all_32_7, all_32_4) = all_32_2 % 13.92/2.67 | (16) image2(all_32_7, all_32_3) = all_32_1 % 13.92/2.67 | % 13.92/2.67 | GROUND_INST: instantiating (1) with all_32_4, all_32_3, simplifying with (9), % 13.92/2.67 | (10), (13) gives: % 13.92/2.67 | (17) ! [v0: $i] : ( ~ (member(v0, all_32_4) = 0) | ~ $i(v0) | member(v0, % 13.92/2.67 | all_32_3) = 0) % 13.92/2.67 | % 13.92/2.67 | GROUND_INST: instantiating (2) with all_32_2, all_32_1, all_32_0, simplifying % 13.92/2.67 | with (11), (12), (14) gives: % 13.92/2.67 | (18) all_32_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 13.92/2.67 | all_32_1) = v1 & member(v0, all_32_2) = 0 & $i(v0)) % 13.92/2.67 | % 13.92/2.67 | BETA: splitting (18) gives: % 13.92/2.67 | % 13.92/2.67 | Case 1: % 13.92/2.67 | | % 13.92/2.67 | | (19) all_32_0 = 0 % 13.92/2.67 | | % 13.92/2.67 | | REDUCE: (7), (19) imply: % 13.92/2.67 | | (20) $false % 13.92/2.67 | | % 13.92/2.67 | | CLOSE: (20) is inconsistent. % 13.92/2.67 | | % 13.92/2.67 | Case 2: % 13.92/2.67 | | % 13.92/2.67 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) = % 13.92/2.67 | | v1 & member(v0, all_32_2) = 0 & $i(v0)) % 13.92/2.67 | | % 13.92/2.67 | | DELTA: instantiating (21) with fresh symbols all_46_0, all_46_1 gives: % 13.92/2.67 | | (22) ~ (all_46_0 = 0) & member(all_46_1, all_32_1) = all_46_0 & % 13.92/2.67 | | member(all_46_1, all_32_2) = 0 & $i(all_46_1) % 13.92/2.67 | | % 13.92/2.67 | | ALPHA: (22) implies: % 13.92/2.67 | | (23) ~ (all_46_0 = 0) % 13.92/2.67 | | (24) $i(all_46_1) % 13.92/2.67 | | (25) member(all_46_1, all_32_2) = 0 % 13.92/2.67 | | (26) member(all_46_1, all_32_1) = all_46_0 % 13.92/2.67 | | % 13.92/2.67 | | GROUND_INST: instantiating (3) with all_32_7, all_32_4, all_46_1, all_32_2, % 13.92/2.67 | | simplifying with (8), (9), (15), (24), (25) gives: % 13.92/2.67 | | (27) ? [v0: $i] : (apply(all_32_7, v0, all_46_1) = 0 & member(v0, % 13.92/2.67 | | all_32_4) = 0 & $i(v0)) % 13.92/2.67 | | % 13.92/2.67 | | GROUND_INST: instantiating (4) with all_32_7, all_32_3, all_46_1, all_32_1, % 13.92/2.67 | | all_46_0, simplifying with (8), (10), (16), (24), (26) gives: % 13.92/2.67 | | (28) all_46_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_7, v0, all_46_1) = 0) % 13.92/2.67 | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_3) = % 13.92/2.67 | | v1)) % 13.92/2.68 | | % 13.92/2.68 | | DELTA: instantiating (27) with fresh symbol all_53_0 gives: % 13.92/2.68 | | (29) apply(all_32_7, all_53_0, all_46_1) = 0 & member(all_53_0, all_32_4) % 13.92/2.68 | | = 0 & $i(all_53_0) % 13.92/2.68 | | % 13.92/2.68 | | ALPHA: (29) implies: % 13.92/2.68 | | (30) $i(all_53_0) % 13.92/2.68 | | (31) member(all_53_0, all_32_4) = 0 % 13.92/2.68 | | (32) apply(all_32_7, all_53_0, all_46_1) = 0 % 13.92/2.68 | | % 13.92/2.68 | | BETA: splitting (28) gives: % 13.92/2.68 | | % 13.92/2.68 | | Case 1: % 13.92/2.68 | | | % 13.92/2.68 | | | (33) all_46_0 = 0 % 13.92/2.68 | | | % 13.92/2.68 | | | REDUCE: (23), (33) imply: % 13.92/2.68 | | | (34) $false % 13.92/2.68 | | | % 13.92/2.68 | | | CLOSE: (34) is inconsistent. % 13.92/2.68 | | | % 13.92/2.68 | | Case 2: % 13.92/2.68 | | | % 13.92/2.68 | | | (35) ! [v0: $i] : ( ~ (apply(all_32_7, v0, all_46_1) = 0) | ~ $i(v0) % 13.92/2.68 | | | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_3) = v1)) % 13.92/2.68 | | | % 13.92/2.68 | | | GROUND_INST: instantiating (17) with all_53_0, simplifying with (30), (31) % 13.92/2.68 | | | gives: % 13.92/2.68 | | | (36) member(all_53_0, all_32_3) = 0 % 13.92/2.68 | | | % 13.92/2.68 | | | GROUND_INST: instantiating (35) with all_53_0, simplifying with (30), (32) % 13.92/2.68 | | | gives: % 13.92/2.68 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & member(all_53_0, all_32_3) = v0) % 13.92/2.68 | | | % 13.92/2.68 | | | DELTA: instantiating (37) with fresh symbol all_66_0 gives: % 13.92/2.68 | | | (38) ~ (all_66_0 = 0) & member(all_53_0, all_32_3) = all_66_0 % 13.92/2.68 | | | % 13.92/2.68 | | | ALPHA: (38) implies: % 13.92/2.68 | | | (39) ~ (all_66_0 = 0) % 13.92/2.68 | | | (40) member(all_53_0, all_32_3) = all_66_0 % 13.92/2.68 | | | % 13.92/2.68 | | | GROUND_INST: instantiating (5) with 0, all_66_0, all_32_3, all_53_0, % 13.92/2.68 | | | simplifying with (36), (40) gives: % 13.92/2.68 | | | (41) all_66_0 = 0 % 13.92/2.68 | | | % 13.92/2.68 | | | REDUCE: (39), (41) imply: % 13.92/2.68 | | | (42) $false % 13.92/2.68 | | | % 13.92/2.68 | | | CLOSE: (42) is inconsistent. % 13.92/2.68 | | | % 13.92/2.68 | | End of split % 13.92/2.68 | | % 13.92/2.68 | End of split % 13.92/2.68 | % 13.92/2.68 End of proof % 13.92/2.68 % SZS output end Proof for theBenchmark % 13.92/2.68 % 13.92/2.68 2074ms %------------------------------------------------------------------------------