%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET734+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 : n032.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 15:26:13 EDT 2023 % Result : Theorem 20.84s 3.64s % Output : Proof 21.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.28 % Computer : n032.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 300 % 0.08/0.28 % DateTime : Sat Aug 26 09:10:13 EDT 2023 % 0.08/0.28 % CPUTime : % 0.12/0.49 ________ _____ % 0.12/0.49 ___ __ \_________(_)________________________________ % 0.12/0.49 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.12/0.49 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.12/0.49 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.12/0.49 % 0.12/0.49 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.12/0.49 (2023-06-19) % 0.12/0.49 % 0.12/0.49 (c) Philipp Rümmer, 2009-2023 % 0.12/0.49 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.12/0.49 Amanda Stjerna. % 0.12/0.49 Free software under BSD-3-Clause. % 0.12/0.49 % 0.12/0.49 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.12/0.49 % 0.12/0.50 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.12/0.51 Running up to 7 provers in parallel. % 0.12/0.52 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.12/0.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.12/0.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.12/0.52 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.12/0.52 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.12/0.52 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.12/0.52 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.51/1.08 Prover 4: Preprocessing ... % 3.51/1.08 Prover 1: Preprocessing ... % 3.51/1.14 Prover 3: Preprocessing ... % 3.51/1.14 Prover 6: Preprocessing ... % 3.51/1.14 Prover 2: Preprocessing ... % 3.51/1.14 Prover 5: Preprocessing ... % 3.51/1.14 Prover 0: Preprocessing ... % 11.62/2.31 Prover 5: Proving ... % 11.62/2.36 Prover 2: Proving ... % 12.10/2.41 Prover 6: Proving ... % 12.78/2.47 Prover 3: Constructing countermodel ... % 12.97/2.52 Prover 1: Constructing countermodel ... % 15.11/2.96 Prover 4: Constructing countermodel ... % 16.80/3.10 Prover 0: Proving ... % 20.84/3.60 Prover 4: Found proof (size 37) % 20.84/3.62 Prover 4: proved (3089ms) % 20.84/3.62 Prover 5: stopped % 20.84/3.63 Prover 2: stopped % 20.84/3.63 Prover 3: stopped % 20.84/3.63 Prover 6: stopped % 20.84/3.63 Prover 1: stopped % 20.84/3.64 Prover 0: proved (3122ms) % 20.84/3.64 % 20.84/3.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.84/3.64 % 20.84/3.65 % SZS output start Proof for theBenchmark % 20.84/3.65 Assumptions after simplification: % 20.84/3.65 --------------------------------- % 20.84/3.65 % 20.84/3.65 (compose_function) % 20.84/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.84/3.72 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 20.84/3.72 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 20.84/3.72 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 20.84/3.72 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] % 20.84/3.72 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 % 20.84/3.72 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = % 20.84/3.72 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.84/3.72 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 20.84/3.72 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 20.84/3.72 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 20.84/3.72 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 20.84/3.72 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 20.84/3.72 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 20.84/3.72 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! % 20.84/3.72 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 20.84/3.72 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 20.84/3.72 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 20.84/3.72 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 20.84/3.72 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : % 20.84/3.72 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ % 20.84/3.72 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 % 20.84/3.72 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.84/3.72 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 20.84/3.72 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 20.84/3.72 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 20.84/3.72 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? % 20.84/3.72 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 20.84/3.72 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 20.84/3.72 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = % 20.84/3.72 0)))))) % 20.84/3.72 % 20.84/3.72 (identity) % 20.84/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.84/3.73 (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 20.84/3.73 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: % 20.84/3.73 $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ~ % 20.84/3.73 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0, % 20.84/3.73 v3, v3) = v4 & member(v3, v1) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] % 20.84/3.73 : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ~ % 20.84/3.73 $i(v2) | ~ $i(v1) | ~ $i(v0) | apply(v0, v2, v2) = 0) % 20.84/3.73 % 20.84/3.73 (surjective) % 20.84/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.84/3.73 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 20.84/3.73 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4) % 20.84/3.73 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6)) % 20.84/3.73 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ % 20.84/3.74 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 20.84/3.74 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) % 20.84/3.74 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 20.84/3.74 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4))) % 20.84/3.74 % 20.84/3.74 (thII25) % 20.84/3.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 20.84/3.74 int] : ( ~ (v5 = 0) & surjective(v1, v2, v3) = v5 & identity(v4, v3) = 0 & % 20.84/3.74 compose_function(v1, v0, v3, v2, v3) = v4 & maps(v1, v2, v3) = 0 & maps(v0, % 20.84/3.74 v3, v2) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.84/3.74 % 20.84/3.74 (function-axioms) % 20.84/3.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 20.84/3.76 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 20.84/3.76 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 20.84/3.76 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 20.84/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.84/3.76 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 20.84/3.76 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 20.84/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.84/3.76 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 20.84/3.76 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 20.84/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.84/3.76 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 20.84/3.76 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 20.84/3.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 20.84/3.76 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 20.84/3.76 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 20.84/3.76 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.84/3.76 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 20.84/3.76 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.84/3.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.84/3.76 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 20.84/3.76 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 20.84/3.76 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 20.84/3.76 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 20.84/3.76 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 20.84/3.76 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.84/3.76 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 20.84/3.76 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.84/3.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 20.84/3.76 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 20.84/3.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.84/3.76 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 20.84/3.76 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.84/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 20.84/3.76 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 20.84/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.84/3.76 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 20.84/3.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 20.84/3.76 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 20.84/3.76 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.84/3.76 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 20.84/3.76 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.84/3.76 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 20.84/3.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 20.84/3.76 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 20.84/3.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.84/3.76 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 20.84/3.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.84/3.76 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 20.84/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 20.84/3.76 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 20.84/3.76 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 20.84/3.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 20.84/3.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 20.84/3.76 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.84/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 20.84/3.76 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.84/3.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.84/3.76 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 20.84/3.76 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 20.84/3.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 20.84/3.76 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 20.84/3.76 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 20.84/3.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 20.84/3.76 (power_set(v2) = v0)) % 20.84/3.76 % 20.84/3.76 Further assumptions not needed in the proof: % 20.84/3.76 -------------------------------------------- % 20.84/3.77 compose_predicate, decreasing_function, difference, empty_set, equal_maps, % 20.84/3.77 equal_set, image2, image3, increasing_function, injective, intersection, % 20.84/3.77 inverse_function, inverse_image2, inverse_image3, inverse_predicate, % 20.84/3.77 isomorphism, maps, one_to_one, power_set, product, singleton, subset, sum, % 20.84/3.77 union, unordered_pair % 20.84/3.77 % 20.84/3.77 Those formulas are unsatisfiable: % 20.84/3.77 --------------------------------- % 20.84/3.77 % 20.84/3.77 Begin of proof % 20.84/3.77 | % 20.84/3.77 | ALPHA: (compose_function) implies: % 20.84/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.84/3.77 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (compose_function(v0, v1, % 20.84/3.77 | v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ~ $i(v6) | ~ % 20.84/3.77 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.84/3.77 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? [v12: % 20.84/3.77 | int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 20.84/3.77 | apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, % 20.84/3.77 | v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ % 20.84/3.77 | (v9 = 0) | ~ (v8 = 0)))))) % 20.84/3.77 | % 20.84/3.77 | ALPHA: (identity) implies: % 20.84/3.77 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) | % 20.84/3.77 | ~ (member(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.84/3.77 | apply(v0, v2, v2) = 0) % 20.84/3.77 | % 20.84/3.77 | ALPHA: (surjective) implies: % 20.84/3.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.84/3.77 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.84/3.77 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ % 20.84/3.77 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) % 20.84/3.77 | & member(v5, v1) = v6)) & ! [v5: $i] : ( ~ (member(v5, v1) = % 20.84/3.77 | 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v5, % 20.84/3.78 | v4) = v6)))) % 20.84/3.78 | % 20.84/3.78 | ALPHA: (function-axioms) implies: % 20.84/3.78 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.84/3.78 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 20.84/3.78 | = v0)) % 20.84/3.78 | % 20.84/3.78 | DELTA: instantiating (thII25) with fresh symbols all_32_0, all_32_1, all_32_2, % 20.84/3.78 | all_32_3, all_32_4, all_32_5 gives: % 20.84/3.78 | (5) ~ (all_32_0 = 0) & surjective(all_32_4, all_32_3, all_32_2) = all_32_0 % 20.84/3.78 | & identity(all_32_1, all_32_2) = 0 & compose_function(all_32_4, % 20.84/3.78 | all_32_5, all_32_2, all_32_3, all_32_2) = all_32_1 & maps(all_32_4, % 20.84/3.78 | all_32_3, all_32_2) = 0 & maps(all_32_5, all_32_2, all_32_3) = 0 & % 20.84/3.78 | $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & % 20.84/3.78 | $i(all_32_5) % 20.84/3.78 | % 20.84/3.78 | ALPHA: (5) implies: % 20.84/3.78 | (6) ~ (all_32_0 = 0) % 20.84/3.78 | (7) $i(all_32_5) % 20.84/3.78 | (8) $i(all_32_4) % 20.84/3.78 | (9) $i(all_32_3) % 20.84/3.78 | (10) $i(all_32_2) % 20.84/3.78 | (11) $i(all_32_1) % 20.84/3.78 | (12) compose_function(all_32_4, all_32_5, all_32_2, all_32_3, all_32_2) = % 20.84/3.78 | all_32_1 % 20.84/3.78 | (13) identity(all_32_1, all_32_2) = 0 % 20.84/3.78 | (14) surjective(all_32_4, all_32_3, all_32_2) = all_32_0 % 20.84/3.78 | % 20.84/3.78 | GROUND_INST: instantiating (3) with all_32_4, all_32_3, all_32_2, all_32_0, % 20.84/3.78 | simplifying with (8), (9), (10), (14) gives: % 20.84/3.79 | (15) all_32_0 = 0 | ? [v0: $i] : (member(v0, all_32_2) = 0 & $i(v0) & ! % 20.84/3.79 | [v1: $i] : ( ~ (apply(all_32_4, v1, v0) = 0) | ~ $i(v1) | ? [v2: % 20.84/3.79 | int] : ( ~ (v2 = 0) & member(v1, all_32_3) = v2)) & ! [v1: $i] % 20.84/3.79 | : ( ~ (member(v1, all_32_3) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ % 20.84/3.79 | (v2 = 0) & apply(all_32_4, v1, v0) = v2))) % 20.84/3.79 | % 20.84/3.79 | BETA: splitting (15) gives: % 20.84/3.79 | % 20.84/3.79 | Case 1: % 20.84/3.79 | | % 20.84/3.79 | | (16) all_32_0 = 0 % 20.84/3.79 | | % 20.84/3.79 | | REDUCE: (6), (16) imply: % 20.84/3.79 | | (17) $false % 20.84/3.79 | | % 20.84/3.79 | | CLOSE: (17) is inconsistent. % 20.84/3.79 | | % 20.84/3.79 | Case 2: % 20.84/3.79 | | % 20.84/3.79 | | (18) ? [v0: $i] : (member(v0, all_32_2) = 0 & $i(v0) & ! [v1: $i] : ( ~ % 20.84/3.79 | | (apply(all_32_4, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ % 20.84/3.79 | | (v2 = 0) & member(v1, all_32_3) = v2)) & ! [v1: $i] : ( ~ % 20.84/3.79 | | (member(v1, all_32_3) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 % 20.84/3.79 | | = 0) & apply(all_32_4, v1, v0) = v2))) % 20.84/3.79 | | % 20.84/3.79 | | DELTA: instantiating (18) with fresh symbol all_48_0 gives: % 21.77/3.79 | | (19) member(all_48_0, all_32_2) = 0 & $i(all_48_0) & ! [v0: $i] : ( ~ % 21.77/3.79 | | (apply(all_32_4, v0, all_48_0) = 0) | ~ $i(v0) | ? [v1: int] : ( % 21.77/3.79 | | ~ (v1 = 0) & member(v0, all_32_3) = v1)) & ! [v0: $i] : ( ~ % 21.77/3.79 | | (member(v0, all_32_3) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 21.77/3.79 | | 0) & apply(all_32_4, v0, all_48_0) = v1)) % 21.77/3.79 | | % 21.77/3.79 | | ALPHA: (19) implies: % 21.77/3.79 | | (20) $i(all_48_0) % 21.77/3.79 | | (21) member(all_48_0, all_32_2) = 0 % 21.77/3.80 | | (22) ! [v0: $i] : ( ~ (apply(all_32_4, v0, all_48_0) = 0) | ~ $i(v0) | % 21.77/3.80 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_3) = v1)) % 21.77/3.80 | | % 21.77/3.80 | | GROUND_INST: instantiating (2) with all_32_1, all_32_2, all_48_0, % 21.77/3.80 | | simplifying with (10), (11), (13), (20), (21) gives: % 21.77/3.80 | | (23) apply(all_32_1, all_48_0, all_48_0) = 0 % 21.77/3.80 | | % 21.77/3.80 | | GROUND_INST: instantiating (1) with all_32_4, all_32_5, all_32_2, all_32_3, % 21.77/3.80 | | all_32_2, all_48_0, all_48_0, all_32_1, simplifying with (7), % 21.77/3.80 | | (8), (9), (10), (12), (20), (23) gives: % 21.77/3.80 | | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4: % 21.77/3.80 | | int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = 0 & % 21.77/3.80 | | apply(all_32_4, v2, all_48_0) = 0 & apply(all_32_5, all_48_0, % 21.77/3.80 | | v2) = 0 & member(v2, all_32_3) = 0) | (member(all_48_0, % 21.77/3.80 | | all_32_2) = v1 & member(all_48_0, all_32_2) = v0 & ( ~ (v1 = % 21.77/3.80 | | 0) | ~ (v0 = 0))))) % 21.77/3.80 | | % 21.77/3.80 | | DELTA: instantiating (24) with fresh symbols all_78_0, all_78_1, all_78_2, % 21.77/3.80 | | all_78_3, all_78_4, all_78_5 gives: % 21.77/3.80 | | (25) $i(all_78_3) & ((all_78_0 = 0 & all_78_1 = 0 & all_78_2 = 0 & % 21.77/3.80 | | apply(all_32_4, all_78_3, all_48_0) = 0 & apply(all_32_5, % 21.77/3.80 | | all_48_0, all_78_3) = 0 & member(all_78_3, all_32_3) = 0) | % 21.77/3.80 | | (member(all_48_0, all_32_2) = all_78_4 & member(all_48_0, % 21.77/3.80 | | all_32_2) = all_78_5 & ( ~ (all_78_4 = 0) | ~ (all_78_5 = % 21.77/3.80 | | 0)))) % 21.77/3.80 | | % 21.77/3.80 | | ALPHA: (25) implies: % 21.77/3.80 | | (26) $i(all_78_3) % 21.77/3.81 | | (27) (all_78_0 = 0 & all_78_1 = 0 & all_78_2 = 0 & apply(all_32_4, % 21.77/3.81 | | all_78_3, all_48_0) = 0 & apply(all_32_5, all_48_0, all_78_3) = % 21.77/3.81 | | 0 & member(all_78_3, all_32_3) = 0) | (member(all_48_0, all_32_2) % 21.77/3.81 | | = all_78_4 & member(all_48_0, all_32_2) = all_78_5 & ( ~ (all_78_4 % 21.77/3.81 | | = 0) | ~ (all_78_5 = 0))) % 21.77/3.81 | | % 21.77/3.81 | | BETA: splitting (27) gives: % 21.77/3.81 | | % 21.77/3.81 | | Case 1: % 21.77/3.81 | | | % 21.77/3.81 | | | (28) all_78_0 = 0 & all_78_1 = 0 & all_78_2 = 0 & apply(all_32_4, % 21.77/3.81 | | | all_78_3, all_48_0) = 0 & apply(all_32_5, all_48_0, all_78_3) = % 21.77/3.81 | | | 0 & member(all_78_3, all_32_3) = 0 % 21.77/3.81 | | | % 21.77/3.81 | | | ALPHA: (28) implies: % 21.77/3.81 | | | (29) member(all_78_3, all_32_3) = 0 % 21.77/3.81 | | | (30) apply(all_32_4, all_78_3, all_48_0) = 0 % 21.77/3.81 | | | % 21.77/3.81 | | | GROUND_INST: instantiating (22) with all_78_3, simplifying with (26), (30) % 21.77/3.81 | | | gives: % 21.77/3.81 | | | (31) ? [v0: int] : ( ~ (v0 = 0) & member(all_78_3, all_32_3) = v0) % 21.77/3.81 | | | % 21.77/3.81 | | | DELTA: instantiating (31) with fresh symbol all_90_0 gives: % 21.77/3.81 | | | (32) ~ (all_90_0 = 0) & member(all_78_3, all_32_3) = all_90_0 % 21.77/3.81 | | | % 21.77/3.81 | | | ALPHA: (32) implies: % 21.77/3.81 | | | (33) ~ (all_90_0 = 0) % 21.77/3.81 | | | (34) member(all_78_3, all_32_3) = all_90_0 % 21.77/3.81 | | | % 21.77/3.81 | | | GROUND_INST: instantiating (4) with 0, all_90_0, all_32_3, all_78_3, % 21.77/3.81 | | | simplifying with (29), (34) gives: % 21.77/3.81 | | | (35) all_90_0 = 0 % 21.77/3.81 | | | % 21.77/3.81 | | | REDUCE: (33), (35) imply: % 21.77/3.81 | | | (36) $false % 21.77/3.81 | | | % 21.77/3.81 | | | CLOSE: (36) is inconsistent. % 21.77/3.81 | | | % 21.77/3.81 | | Case 2: % 21.77/3.81 | | | % 21.77/3.81 | | | (37) member(all_48_0, all_32_2) = all_78_4 & member(all_48_0, all_32_2) % 21.77/3.81 | | | = all_78_5 & ( ~ (all_78_4 = 0) | ~ (all_78_5 = 0)) % 21.77/3.81 | | | % 21.77/3.81 | | | ALPHA: (37) implies: % 21.77/3.81 | | | (38) member(all_48_0, all_32_2) = all_78_5 % 21.77/3.82 | | | (39) member(all_48_0, all_32_2) = all_78_4 % 21.77/3.82 | | | (40) ~ (all_78_4 = 0) | ~ (all_78_5 = 0) % 21.77/3.82 | | | % 21.77/3.82 | | | GROUND_INST: instantiating (4) with 0, all_78_4, all_32_2, all_48_0, % 21.77/3.82 | | | simplifying with (21), (39) gives: % 21.77/3.82 | | | (41) all_78_4 = 0 % 21.77/3.82 | | | % 21.77/3.82 | | | GROUND_INST: instantiating (4) with all_78_5, all_78_4, all_32_2, % 21.77/3.82 | | | all_48_0, simplifying with (38), (39) gives: % 21.77/3.82 | | | (42) all_78_4 = all_78_5 % 21.77/3.82 | | | % 21.77/3.82 | | | COMBINE_EQS: (41), (42) imply: % 21.77/3.82 | | | (43) all_78_5 = 0 % 21.77/3.82 | | | % 21.77/3.82 | | | BETA: splitting (40) gives: % 21.77/3.82 | | | % 21.77/3.82 | | | Case 1: % 21.77/3.82 | | | | % 21.77/3.82 | | | | (44) ~ (all_78_4 = 0) % 21.77/3.82 | | | | % 21.77/3.82 | | | | REDUCE: (41), (44) imply: % 21.77/3.82 | | | | (45) $false % 21.77/3.82 | | | | % 21.77/3.82 | | | | CLOSE: (45) is inconsistent. % 21.77/3.82 | | | | % 21.77/3.82 | | | Case 2: % 21.77/3.82 | | | | % 21.77/3.82 | | | | (46) ~ (all_78_5 = 0) % 21.77/3.82 | | | | % 21.77/3.82 | | | | REDUCE: (43), (46) imply: % 21.77/3.82 | | | | (47) $false % 21.77/3.82 | | | | % 21.77/3.82 | | | | CLOSE: (47) is inconsistent. % 21.77/3.82 | | | | % 21.77/3.82 | | | End of split % 21.77/3.82 | | | % 21.77/3.82 | | End of split % 21.77/3.82 | | % 21.77/3.82 | End of split % 21.77/3.82 | % 21.77/3.82 End of proof % 21.77/3.82 % SZS output end Proof for theBenchmark % 21.77/3.82 % 21.77/3.82 3326ms %------------------------------------------------------------------------------