%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET753+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 : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 15:26:18 EDT 2023 % Result : Theorem 11.62s 2.35s % Output : Proof 15.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET753+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n004.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 15:54:22 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 3.80/1.25 Prover 1: Preprocessing ... % 4.08/1.28 Prover 4: Preprocessing ... % 4.08/1.29 Prover 0: Preprocessing ... % 4.08/1.29 Prover 2: Preprocessing ... % 4.08/1.29 Prover 3: Preprocessing ... % 4.08/1.29 Prover 5: Preprocessing ... % 4.08/1.29 Prover 6: Preprocessing ... % 8.79/2.01 Prover 5: Proving ... % 9.45/2.11 Prover 3: Constructing countermodel ... % 9.45/2.13 Prover 2: Proving ... % 10.49/2.18 Prover 6: Proving ... % 10.49/2.18 Prover 1: Constructing countermodel ... % 11.62/2.34 Prover 3: proved (1712ms) % 11.62/2.34 % 11.62/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.62/2.35 % 11.62/2.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.88/2.36 Prover 5: stopped % 11.88/2.36 Prover 6: stopped % 11.88/2.36 Prover 2: stopped % 11.88/2.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.88/2.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.88/2.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.88/2.42 Prover 8: Preprocessing ... % 12.40/2.43 Prover 7: Preprocessing ... % 12.40/2.47 Prover 10: Preprocessing ... % 12.64/2.48 Prover 11: Preprocessing ... % 13.36/2.58 Prover 7: Warning: ignoring some quantifiers % 13.36/2.60 Prover 10: Warning: ignoring some quantifiers % 13.36/2.62 Prover 7: Constructing countermodel ... % 13.36/2.63 Prover 10: Constructing countermodel ... % 13.36/2.66 Prover 1: Found proof (size 44) % 13.36/2.66 Prover 1: proved (2036ms) % 13.36/2.66 Prover 7: stopped % 13.36/2.67 Prover 10: stopped % 13.36/2.68 Prover 11: stopped % 13.36/2.70 Prover 0: Proving ... % 13.36/2.70 Prover 0: stopped % 14.20/2.72 Prover 4: Constructing countermodel ... % 14.20/2.75 Prover 4: stopped % 14.66/2.76 Prover 8: Warning: ignoring some quantifiers % 14.66/2.77 Prover 8: Constructing countermodel ... % 14.66/2.77 Prover 8: stopped % 14.66/2.77 % 14.66/2.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.66/2.77 % 14.66/2.78 % SZS output start Proof for theBenchmark % 14.66/2.79 Assumptions after simplification: % 14.66/2.79 --------------------------------- % 14.66/2.79 % 14.66/2.79 (image2) % 14.66/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 14.66/2.81 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 14.66/2.81 $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) = 0) | ~ $i(v5) | % 14.66/2.81 ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : ! % 14.66/2.81 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, v1) = v3) | ~ % 14.66/2.81 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 14.66/2.81 (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4))) % 14.66/2.81 % 14.66/2.81 (intersection) % 14.66/2.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 14.66/2.82 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 14.66/2.82 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 14.66/2.82 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 14.66/2.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 14.66/2.82 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 14.66/2.82 0 & member(v0, v1) = 0)) % 14.66/2.82 % 14.66/2.82 (subset) % 14.66/2.82 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 14.66/2.82 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 14.66/2.82 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 14.66/2.82 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 14.66/2.82 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 14.66/2.82 % 14.66/2.82 (thIIa03) % 14.66/2.82 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.66/2.82 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 14.66/2.82 : ( ~ (v10 = 0) & image2(v0, v5) = v6 & image2(v0, v4) = v8 & image2(v0, v3) = % 14.66/2.82 v7 & maps(v0, v1, v2) = 0 & intersection(v7, v8) = v9 & intersection(v3, v4) % 14.66/2.82 = v5 & subset(v6, v9) = v10 & subset(v4, v1) = 0 & subset(v3, v1) = 0 & % 14.66/2.82 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 14.66/2.82 $i(v1) & $i(v0)) % 14.66/2.82 % 14.66/2.82 (function-axioms) % 15.01/2.83 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.01/2.83 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 15.01/2.83 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 15.01/2.83 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.01/2.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.01/2.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 15.01/2.83 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.01/2.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.01/2.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 15.01/2.83 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.01/2.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.01/2.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 15.01/2.83 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.01/2.83 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 15.01/2.83 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 15.01/2.83 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 15.01/2.83 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.01/2.83 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 15.01/2.83 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.01/2.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.01/2.83 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 15.01/2.83 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.01/2.83 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 15.01/2.83 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.01/2.83 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 15.01/2.83 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.01/2.83 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 15.01/2.83 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.01/2.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 15.01/2.83 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 15.01/2.83 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.01/2.83 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 15.01/2.83 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.01/2.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.01/2.83 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 15.01/2.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.01/2.83 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 15.01/2.83 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.01/2.83 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 15.01/2.83 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.01/2.83 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 15.01/2.83 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.01/2.83 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 15.01/2.83 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.01/2.83 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 15.01/2.83 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.01/2.83 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 15.01/2.83 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.01/2.83 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 15.01/2.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 15.01/2.83 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.01/2.83 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 15.01/2.83 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.01/2.83 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 15.01/2.83 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.01/2.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 15.01/2.83 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.01/2.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.01/2.83 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 15.01/2.83 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 15.01/2.83 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 15.01/2.83 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.01/2.83 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 15.01/2.83 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 15.01/2.83 (power_set(v2) = v0)) % 15.01/2.83 % 15.01/2.83 Further assumptions not needed in the proof: % 15.01/2.83 -------------------------------------------- % 15.01/2.83 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 15.01/2.83 equal_maps, equal_set, identity, image3, increasing_function, injective, % 15.01/2.83 inverse_function, inverse_image2, inverse_image3, inverse_predicate, % 15.01/2.83 isomorphism, maps, one_to_one, power_set, product, singleton, sum, surjective, % 15.01/2.83 union, unordered_pair % 15.01/2.83 % 15.01/2.83 Those formulas are unsatisfiable: % 15.01/2.83 --------------------------------- % 15.01/2.83 % 15.01/2.83 Begin of proof % 15.01/2.83 | % 15.01/2.83 | ALPHA: (subset) implies: % 15.01/2.83 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.01/2.83 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 15.01/2.83 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 15.01/2.83 | % 15.01/2.83 | ALPHA: (intersection) implies: % 15.01/2.84 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.01/2.84 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 15.01/2.84 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 15.01/2.84 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.01/2.84 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 15.01/2.84 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 15.01/2.84 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 15.01/2.84 | 0)))) % 15.01/2.84 | % 15.01/2.84 | ALPHA: (image2) implies: % 15.01/2.84 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, % 15.01/2.84 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 15.01/2.84 | $i(v0) | ? [v4: $i] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & % 15.01/2.84 | $i(v4))) % 15.01/2.84 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.01/2.84 | (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 15.01/2.84 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) % 15.01/2.84 | = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = % 15.01/2.84 | v6))) % 15.01/2.84 | % 15.01/2.84 | ALPHA: (function-axioms) implies: % 15.01/2.84 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.01/2.84 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 15.01/2.84 | = v0)) % 15.01/2.84 | % 15.01/2.84 | DELTA: instantiating (thIIa03) with fresh symbols all_32_0, all_32_1, % 15.01/2.84 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8, % 15.01/2.84 | all_32_9, all_32_10 gives: % 15.01/2.84 | (7) ~ (all_32_0 = 0) & image2(all_32_10, all_32_5) = all_32_4 & % 15.01/2.84 | image2(all_32_10, all_32_6) = all_32_2 & image2(all_32_10, all_32_7) = % 15.01/2.84 | all_32_3 & maps(all_32_10, all_32_9, all_32_8) = 0 & % 15.01/2.84 | intersection(all_32_3, all_32_2) = all_32_1 & intersection(all_32_7, % 15.01/2.84 | all_32_6) = all_32_5 & subset(all_32_4, all_32_1) = all_32_0 & % 15.01/2.84 | subset(all_32_6, all_32_9) = 0 & subset(all_32_7, all_32_9) = 0 & % 15.01/2.84 | $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & % 15.01/2.84 | $i(all_32_5) & $i(all_32_6) & $i(all_32_7) & $i(all_32_8) & % 15.01/2.84 | $i(all_32_9) & $i(all_32_10) % 15.01/2.84 | % 15.01/2.84 | ALPHA: (7) implies: % 15.01/2.84 | (8) ~ (all_32_0 = 0) % 15.01/2.84 | (9) $i(all_32_10) % 15.01/2.84 | (10) $i(all_32_7) % 15.01/2.84 | (11) $i(all_32_6) % 15.01/2.84 | (12) $i(all_32_5) % 15.01/2.84 | (13) $i(all_32_4) % 15.01/2.84 | (14) $i(all_32_3) % 15.01/2.84 | (15) $i(all_32_2) % 15.01/2.84 | (16) $i(all_32_1) % 15.01/2.84 | (17) subset(all_32_4, all_32_1) = all_32_0 % 15.01/2.84 | (18) intersection(all_32_7, all_32_6) = all_32_5 % 15.01/2.84 | (19) intersection(all_32_3, all_32_2) = all_32_1 % 15.01/2.84 | (20) image2(all_32_10, all_32_7) = all_32_3 % 15.01/2.84 | (21) image2(all_32_10, all_32_6) = all_32_2 % 15.01/2.84 | (22) image2(all_32_10, all_32_5) = all_32_4 % 15.01/2.84 | % 15.01/2.84 | GROUND_INST: instantiating (1) with all_32_4, all_32_1, all_32_0, simplifying % 15.01/2.85 | with (13), (16), (17) gives: % 15.01/2.85 | (23) all_32_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 15.01/2.85 | all_32_1) = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 15.01/2.85 | % 15.01/2.85 | BETA: splitting (23) gives: % 15.01/2.85 | % 15.01/2.85 | Case 1: % 15.01/2.85 | | % 15.01/2.85 | | (24) all_32_0 = 0 % 15.01/2.85 | | % 15.01/2.85 | | REDUCE: (8), (24) imply: % 15.01/2.85 | | (25) $false % 15.01/2.85 | | % 15.01/2.85 | | CLOSE: (25) is inconsistent. % 15.01/2.85 | | % 15.01/2.85 | Case 2: % 15.01/2.85 | | % 15.01/2.85 | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) = % 15.01/2.85 | | v1 & member(v0, all_32_4) = 0 & $i(v0)) % 15.01/2.85 | | % 15.01/2.85 | | DELTA: instantiating (26) with fresh symbols all_45_0, all_45_1 gives: % 15.01/2.85 | | (27) ~ (all_45_0 = 0) & member(all_45_1, all_32_1) = all_45_0 & % 15.01/2.85 | | member(all_45_1, all_32_4) = 0 & $i(all_45_1) % 15.01/2.85 | | % 15.01/2.85 | | ALPHA: (27) implies: % 15.01/2.85 | | (28) ~ (all_45_0 = 0) % 15.01/2.85 | | (29) $i(all_45_1) % 15.01/2.85 | | (30) member(all_45_1, all_32_4) = 0 % 15.01/2.85 | | (31) member(all_45_1, all_32_1) = all_45_0 % 15.01/2.85 | | % 15.01/2.85 | | GROUND_INST: instantiating (4) with all_32_10, all_32_5, all_45_1, all_32_4, % 15.01/2.85 | | simplifying with (9), (12), (22), (29), (30) gives: % 15.01/2.85 | | (32) ? [v0: $i] : (apply(all_32_10, v0, all_45_1) = 0 & member(v0, % 15.01/2.85 | | all_32_5) = 0 & $i(v0)) % 15.01/2.85 | | % 15.01/2.85 | | GROUND_INST: instantiating (3) with all_45_1, all_32_3, all_32_2, all_32_1, % 15.01/2.85 | | all_45_0, simplifying with (14), (15), (19), (29), (31) gives: % 15.01/2.85 | | (33) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_45_1, % 15.01/2.85 | | all_32_2) = v1 & member(all_45_1, all_32_3) = v0 & ( ~ (v1 = 0) % 15.01/2.85 | | | ~ (v0 = 0))) % 15.01/2.85 | | % 15.01/2.85 | | DELTA: instantiating (32) with fresh symbol all_52_0 gives: % 15.01/2.85 | | (34) apply(all_32_10, all_52_0, all_45_1) = 0 & member(all_52_0, % 15.01/2.85 | | all_32_5) = 0 & $i(all_52_0) % 15.01/2.85 | | % 15.01/2.85 | | ALPHA: (34) implies: % 15.01/2.85 | | (35) $i(all_52_0) % 15.01/2.85 | | (36) member(all_52_0, all_32_5) = 0 % 15.01/2.85 | | (37) apply(all_32_10, all_52_0, all_45_1) = 0 % 15.01/2.85 | | % 15.01/2.85 | | BETA: splitting (33) gives: % 15.01/2.85 | | % 15.01/2.85 | | Case 1: % 15.01/2.85 | | | % 15.01/2.85 | | | (38) all_45_0 = 0 % 15.01/2.85 | | | % 15.01/2.85 | | | REDUCE: (28), (38) imply: % 15.01/2.85 | | | (39) $false % 15.01/2.85 | | | % 15.01/2.85 | | | CLOSE: (39) is inconsistent. % 15.01/2.85 | | | % 15.01/2.85 | | Case 2: % 15.01/2.85 | | | % 15.01/2.85 | | | (40) ? [v0: any] : ? [v1: any] : (member(all_45_1, all_32_2) = v1 & % 15.01/2.85 | | | member(all_45_1, all_32_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 15.01/2.85 | | | % 15.01/2.85 | | | DELTA: instantiating (40) with fresh symbols all_58_0, all_58_1 gives: % 15.01/2.85 | | | (41) member(all_45_1, all_32_2) = all_58_0 & member(all_45_1, all_32_3) % 15.01/2.85 | | | = all_58_1 & ( ~ (all_58_0 = 0) | ~ (all_58_1 = 0)) % 15.01/2.85 | | | % 15.01/2.85 | | | ALPHA: (41) implies: % 15.01/2.85 | | | (42) member(all_45_1, all_32_3) = all_58_1 % 15.01/2.85 | | | (43) member(all_45_1, all_32_2) = all_58_0 % 15.01/2.85 | | | (44) ~ (all_58_0 = 0) | ~ (all_58_1 = 0) % 15.01/2.85 | | | % 15.01/2.86 | | | GROUND_INST: instantiating (5) with all_32_10, all_32_7, all_45_1, % 15.01/2.86 | | | all_32_3, all_58_1, simplifying with (9), (10), (20), (29), % 15.01/2.86 | | | (42) gives: % 15.01/2.86 | | | (45) all_58_1 = 0 | ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_45_1) = % 15.01/2.86 | | | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 15.01/2.86 | | | all_32_7) = v1)) % 15.01/2.86 | | | % 15.01/2.86 | | | GROUND_INST: instantiating (5) with all_32_10, all_32_6, all_45_1, % 15.01/2.86 | | | all_32_2, all_58_0, simplifying with (9), (11), (21), (29), % 15.01/2.86 | | | (43) gives: % 15.01/2.86 | | | (46) all_58_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_45_1) = % 15.01/2.86 | | | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 15.01/2.86 | | | all_32_6) = v1)) % 15.01/2.86 | | | % 15.01/2.86 | | | GROUND_INST: instantiating (2) with all_52_0, all_32_7, all_32_6, % 15.01/2.86 | | | all_32_5, simplifying with (10), (11), (18), (35), (36) % 15.01/2.86 | | | gives: % 15.01/2.86 | | | (47) member(all_52_0, all_32_6) = 0 & member(all_52_0, all_32_7) = 0 % 15.01/2.86 | | | % 15.01/2.86 | | | ALPHA: (47) implies: % 15.01/2.86 | | | (48) member(all_52_0, all_32_7) = 0 % 15.01/2.86 | | | (49) member(all_52_0, all_32_6) = 0 % 15.01/2.86 | | | % 15.01/2.86 | | | BETA: splitting (44) gives: % 15.01/2.86 | | | % 15.01/2.86 | | | Case 1: % 15.01/2.86 | | | | % 15.01/2.86 | | | | (50) ~ (all_58_0 = 0) % 15.01/2.86 | | | | % 15.01/2.86 | | | | BETA: splitting (46) gives: % 15.01/2.86 | | | | % 15.01/2.86 | | | | Case 1: % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | (51) all_58_0 = 0 % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | REDUCE: (50), (51) imply: % 15.01/2.86 | | | | | (52) $false % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | CLOSE: (52) is inconsistent. % 15.01/2.86 | | | | | % 15.01/2.86 | | | | Case 2: % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | (53) ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_45_1) = 0) | ~ % 15.01/2.86 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_6) % 15.01/2.86 | | | | | = v1)) % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | GROUND_INST: instantiating (53) with all_52_0, simplifying with (35), % 15.01/2.86 | | | | | (37) gives: % 15.01/2.86 | | | | | (54) ? [v0: int] : ( ~ (v0 = 0) & member(all_52_0, all_32_6) = v0) % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | DELTA: instantiating (54) with fresh symbol all_91_0 gives: % 15.01/2.86 | | | | | (55) ~ (all_91_0 = 0) & member(all_52_0, all_32_6) = all_91_0 % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | ALPHA: (55) implies: % 15.01/2.86 | | | | | (56) ~ (all_91_0 = 0) % 15.01/2.86 | | | | | (57) member(all_52_0, all_32_6) = all_91_0 % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | GROUND_INST: instantiating (6) with 0, all_91_0, all_32_6, all_52_0, % 15.01/2.86 | | | | | simplifying with (49), (57) gives: % 15.01/2.86 | | | | | (58) all_91_0 = 0 % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | REDUCE: (56), (58) imply: % 15.01/2.86 | | | | | (59) $false % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | CLOSE: (59) is inconsistent. % 15.01/2.86 | | | | | % 15.01/2.86 | | | | End of split % 15.01/2.86 | | | | % 15.01/2.86 | | | Case 2: % 15.01/2.86 | | | | % 15.01/2.86 | | | | (60) ~ (all_58_1 = 0) % 15.01/2.86 | | | | % 15.01/2.86 | | | | BETA: splitting (45) gives: % 15.01/2.86 | | | | % 15.01/2.86 | | | | Case 1: % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | (61) all_58_1 = 0 % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | REDUCE: (60), (61) imply: % 15.01/2.86 | | | | | (62) $false % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | CLOSE: (62) is inconsistent. % 15.01/2.86 | | | | | % 15.01/2.86 | | | | Case 2: % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | (63) ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_45_1) = 0) | ~ % 15.01/2.86 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_7) % 15.01/2.86 | | | | | = v1)) % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | GROUND_INST: instantiating (63) with all_52_0, simplifying with (35), % 15.01/2.86 | | | | | (37) gives: % 15.01/2.86 | | | | | (64) ? [v0: int] : ( ~ (v0 = 0) & member(all_52_0, all_32_7) = v0) % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | DELTA: instantiating (64) with fresh symbol all_91_0 gives: % 15.01/2.86 | | | | | (65) ~ (all_91_0 = 0) & member(all_52_0, all_32_7) = all_91_0 % 15.01/2.86 | | | | | % 15.01/2.86 | | | | | ALPHA: (65) implies: % 15.01/2.86 | | | | | (66) ~ (all_91_0 = 0) % 15.01/2.87 | | | | | (67) member(all_52_0, all_32_7) = all_91_0 % 15.01/2.87 | | | | | % 15.01/2.87 | | | | | GROUND_INST: instantiating (6) with 0, all_91_0, all_32_7, all_52_0, % 15.01/2.87 | | | | | simplifying with (48), (67) gives: % 15.01/2.87 | | | | | (68) all_91_0 = 0 % 15.01/2.87 | | | | | % 15.01/2.87 | | | | | REDUCE: (66), (68) imply: % 15.01/2.87 | | | | | (69) $false % 15.01/2.87 | | | | | % 15.01/2.87 | | | | | CLOSE: (69) is inconsistent. % 15.01/2.87 | | | | | % 15.01/2.87 | | | | End of split % 15.01/2.87 | | | | % 15.01/2.87 | | | End of split % 15.01/2.87 | | | % 15.01/2.87 | | End of split % 15.01/2.87 | | % 15.01/2.87 | End of split % 15.01/2.87 | % 15.01/2.87 End of proof % 15.01/2.87 % SZS output end Proof for theBenchmark % 15.01/2.87 % 15.01/2.87 2260ms %------------------------------------------------------------------------------