%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET752+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 15:26:17 EDT 2023 % Result : Theorem 12.56s 2.54s % Output : Proof 15.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET752+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 : n004.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 12:38:08 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.48/1.22 Prover 1: Preprocessing ... % 3.48/1.23 Prover 4: Preprocessing ... % 3.48/1.26 Prover 3: Preprocessing ... % 3.48/1.26 Prover 5: Preprocessing ... % 3.48/1.26 Prover 2: Preprocessing ... % 3.48/1.26 Prover 0: Preprocessing ... % 3.48/1.26 Prover 6: Preprocessing ... % 8.79/2.03 Prover 5: Proving ... % 8.79/2.06 Prover 2: Proving ... % 9.12/2.09 Prover 6: Proving ... % 9.91/2.18 Prover 3: Constructing countermodel ... % 9.91/2.19 Prover 1: Constructing countermodel ... % 12.23/2.53 Prover 3: proved (1896ms) % 12.56/2.54 % 12.56/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.56/2.54 % 12.56/2.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.56/2.55 Prover 5: stopped % 12.56/2.57 Prover 2: stopped % 12.56/2.58 Prover 6: stopped % 12.56/2.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.56/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.56/2.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.39/2.66 Prover 8: Preprocessing ... % 13.39/2.67 Prover 7: Preprocessing ... % 13.39/2.67 Prover 4: Constructing countermodel ... % 13.39/2.69 Prover 10: Preprocessing ... % 13.39/2.69 Prover 11: Preprocessing ... % 13.94/2.73 Prover 1: Found proof (size 104) % 13.94/2.73 Prover 1: proved (2097ms) % 13.94/2.74 Prover 4: stopped % 13.94/2.74 Prover 10: stopped % 13.94/2.75 Prover 7: stopped % 14.21/2.78 Prover 0: Proving ... % 14.21/2.78 Prover 0: stopped % 14.21/2.83 Prover 11: stopped % 14.77/2.90 Prover 8: Warning: ignoring some quantifiers % 14.77/2.91 Prover 8: Constructing countermodel ... % 14.77/2.91 Prover 8: stopped % 14.77/2.91 % 14.77/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.77/2.91 % 15.02/2.93 % SZS output start Proof for theBenchmark % 15.02/2.93 Assumptions after simplification: % 15.02/2.93 --------------------------------- % 15.02/2.93 % 15.02/2.93 (equal_set) % 15.14/2.97 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 15.14/2.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 15.14/2.97 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 15.14/2.97 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 15.14/2.97 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 15.14/2.97 % 15.14/2.97 (image2) % 15.14/2.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.14/2.97 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 15.14/2.97 $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) = 0) | ~ $i(v5) | % 15.14/2.97 ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))) & ! [v0: $i] : ! % 15.14/2.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, v1) = v3) | ~ % 15.14/2.97 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 15.14/2.97 (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & $i(v4))) % 15.14/2.97 % 15.14/2.97 (subset) % 15.14/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 15.14/2.98 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 15.14/2.98 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 15.14/2.98 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 15.14/2.98 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 15.14/2.98 % 15.14/2.98 (thIIa02) % 15.14/2.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.14/2.98 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 15.14/2.98 : ( ~ (v10 = 0) & image2(v0, v5) = v6 & image2(v0, v4) = v8 & image2(v0, v3) = % 15.14/2.98 v7 & maps(v0, v1, v2) = 0 & union(v7, v8) = v9 & union(v3, v4) = v5 & % 15.14/2.98 equal_set(v6, v9) = v10 & subset(v4, v1) = 0 & subset(v3, v1) = 0 & $i(v9) & % 15.14/2.98 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 15.14/2.98 $i(v0)) % 15.14/2.98 % 15.14/2.98 (union) % 15.14/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.14/2.98 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 15.14/2.98 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 15.14/2.98 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 15.14/2.98 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 15.14/2.98 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 15.14/2.98 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 15.14/2.98 % 15.14/2.98 (function-axioms) % 15.14/2.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.14/2.99 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 15.14/2.99 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 15.14/2.99 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.14/2.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.14/2.99 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 15.14/2.99 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.14/2.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.14/2.99 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 15.14/2.99 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.14/2.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.14/2.99 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 15.14/2.99 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.14/2.99 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 15.14/2.99 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 15.14/2.99 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 15.14/2.99 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.14/2.99 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 15.14/2.99 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.14/2.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.14/2.99 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 15.14/2.99 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.14/2.99 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 15.14/2.99 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.14/2.99 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 15.14/2.99 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.14/2.99 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 15.14/2.99 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.14/2.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 15.14/2.99 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 15.14/2.99 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.14/2.99 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 15.14/2.99 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.14/2.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.14/2.99 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 15.14/2.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.14/2.99 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 15.14/2.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.14/2.99 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 15.14/2.99 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.14/2.99 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 15.14/2.99 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.14/2.99 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 15.14/2.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.14/2.99 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 15.14/2.99 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.14/2.99 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 15.14/2.99 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.14/2.99 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 15.14/2.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 15.14/2.99 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.14/2.99 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 15.14/2.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.14/2.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 15.14/2.99 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.14/2.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 15.14/2.99 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.14/2.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.14/2.99 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 15.14/2.99 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 15.14/2.99 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 15.14/2.99 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.14/2.99 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 15.14/2.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 15.14/2.99 (power_set(v2) = v0)) % 15.14/2.99 % 15.14/2.99 Further assumptions not needed in the proof: % 15.14/2.99 -------------------------------------------- % 15.14/2.99 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 15.14/2.99 equal_maps, identity, image3, increasing_function, injective, intersection, % 15.14/2.99 inverse_function, inverse_image2, inverse_image3, inverse_predicate, % 15.14/2.99 isomorphism, maps, one_to_one, power_set, product, singleton, sum, surjective, % 15.14/2.99 unordered_pair % 15.14/2.99 % 15.14/2.99 Those formulas are unsatisfiable: % 15.14/2.99 --------------------------------- % 15.14/2.99 % 15.14/2.99 Begin of proof % 15.14/2.99 | % 15.14/2.99 | ALPHA: (subset) implies: % 15.14/2.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.14/2.99 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 15.14/2.99 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 15.14/2.99 | % 15.14/2.99 | ALPHA: (equal_set) implies: % 15.14/3.00 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 15.14/3.00 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 15.14/3.00 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 15.14/3.00 | 0)))) % 15.14/3.00 | % 15.14/3.00 | ALPHA: (union) implies: % 15.14/3.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 15.14/3.00 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 15.14/3.00 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 15.14/3.00 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 15.14/3.00 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.14/3.00 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 15.14/3.00 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 15.14/3.00 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 15.14/3.00 | v5)) % 15.14/3.00 | % 15.14/3.00 | ALPHA: (image2) implies: % 15.14/3.00 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (image2(v0, % 15.14/3.00 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 15.14/3.00 | $i(v0) | ? [v4: $i] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0 & % 15.14/3.00 | $i(v4))) % 15.14/3.00 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.14/3.00 | (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 15.14/3.00 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (apply(v0, v5, v2) % 15.14/3.00 | = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = % 15.14/3.00 | v6))) % 15.14/3.00 | % 15.14/3.00 | ALPHA: (function-axioms) implies: % 15.14/3.00 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.14/3.00 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 15.14/3.00 | = v0)) % 15.14/3.00 | % 15.14/3.00 | DELTA: instantiating (thIIa02) with fresh symbols all_32_0, all_32_1, % 15.14/3.00 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8, % 15.14/3.00 | all_32_9, all_32_10 gives: % 15.14/3.00 | (8) ~ (all_32_0 = 0) & image2(all_32_10, all_32_5) = all_32_4 & % 15.14/3.00 | image2(all_32_10, all_32_6) = all_32_2 & image2(all_32_10, all_32_7) = % 15.14/3.00 | all_32_3 & maps(all_32_10, all_32_9, all_32_8) = 0 & union(all_32_3, % 15.14/3.00 | all_32_2) = all_32_1 & union(all_32_7, all_32_6) = all_32_5 & % 15.14/3.00 | equal_set(all_32_4, all_32_1) = all_32_0 & subset(all_32_6, all_32_9) = % 15.14/3.00 | 0 & subset(all_32_7, all_32_9) = 0 & $i(all_32_1) & $i(all_32_2) & % 15.14/3.00 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) & % 15.14/3.00 | $i(all_32_7) & $i(all_32_8) & $i(all_32_9) & $i(all_32_10) % 15.14/3.00 | % 15.14/3.00 | ALPHA: (8) implies: % 15.14/3.00 | (9) ~ (all_32_0 = 0) % 15.14/3.00 | (10) $i(all_32_10) % 15.14/3.00 | (11) $i(all_32_7) % 15.14/3.00 | (12) $i(all_32_6) % 15.14/3.00 | (13) $i(all_32_5) % 15.14/3.00 | (14) $i(all_32_4) % 15.14/3.00 | (15) $i(all_32_3) % 15.14/3.00 | (16) $i(all_32_2) % 15.14/3.00 | (17) $i(all_32_1) % 15.14/3.00 | (18) equal_set(all_32_4, all_32_1) = all_32_0 % 15.14/3.00 | (19) union(all_32_7, all_32_6) = all_32_5 % 15.14/3.00 | (20) union(all_32_3, all_32_2) = all_32_1 % 15.14/3.00 | (21) image2(all_32_10, all_32_7) = all_32_3 % 15.14/3.00 | (22) image2(all_32_10, all_32_6) = all_32_2 % 15.14/3.00 | (23) image2(all_32_10, all_32_5) = all_32_4 % 15.14/3.00 | % 15.14/3.01 | GROUND_INST: instantiating (2) with all_32_4, all_32_1, all_32_0, simplifying % 15.14/3.01 | with (14), (17), (18) gives: % 15.14/3.01 | (24) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_32_1, % 15.14/3.01 | all_32_4) = v1 & subset(all_32_4, all_32_1) = v0 & ( ~ (v1 = 0) | % 15.14/3.01 | ~ (v0 = 0))) % 15.14/3.01 | % 15.14/3.01 | BETA: splitting (24) gives: % 15.14/3.01 | % 15.14/3.01 | Case 1: % 15.14/3.01 | | % 15.14/3.01 | | (25) all_32_0 = 0 % 15.14/3.01 | | % 15.14/3.01 | | REDUCE: (9), (25) imply: % 15.14/3.01 | | (26) $false % 15.14/3.01 | | % 15.14/3.01 | | CLOSE: (26) is inconsistent. % 15.14/3.01 | | % 15.14/3.01 | Case 2: % 15.14/3.01 | | % 15.14/3.01 | | (27) ? [v0: any] : ? [v1: any] : (subset(all_32_1, all_32_4) = v1 & % 15.14/3.01 | | subset(all_32_4, all_32_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 15.14/3.01 | | % 15.14/3.01 | | DELTA: instantiating (27) with fresh symbols all_45_0, all_45_1 gives: % 15.14/3.01 | | (28) subset(all_32_1, all_32_4) = all_45_0 & subset(all_32_4, all_32_1) = % 15.14/3.01 | | all_45_1 & ( ~ (all_45_0 = 0) | ~ (all_45_1 = 0)) % 15.14/3.01 | | % 15.14/3.01 | | ALPHA: (28) implies: % 15.14/3.01 | | (29) subset(all_32_4, all_32_1) = all_45_1 % 15.14/3.01 | | (30) subset(all_32_1, all_32_4) = all_45_0 % 15.14/3.01 | | (31) ~ (all_45_0 = 0) | ~ (all_45_1 = 0) % 15.14/3.01 | | % 15.14/3.01 | | GROUND_INST: instantiating (1) with all_32_4, all_32_1, all_45_1, % 15.14/3.01 | | simplifying with (14), (17), (29) gives: % 15.14/3.01 | | (32) all_45_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.14/3.01 | | member(v0, all_32_1) = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 15.14/3.01 | | % 15.14/3.01 | | GROUND_INST: instantiating (1) with all_32_1, all_32_4, all_45_0, % 15.14/3.01 | | simplifying with (14), (17), (30) gives: % 15.14/3.01 | | (33) all_45_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.14/3.01 | | member(v0, all_32_1) = 0 & member(v0, all_32_4) = v1 & $i(v0)) % 15.14/3.01 | | % 15.14/3.01 | | BETA: splitting (31) gives: % 15.14/3.01 | | % 15.14/3.01 | | Case 1: % 15.14/3.01 | | | % 15.14/3.01 | | | (34) ~ (all_45_0 = 0) % 15.14/3.01 | | | % 15.14/3.01 | | | BETA: splitting (33) gives: % 15.14/3.01 | | | % 15.14/3.01 | | | Case 1: % 15.14/3.01 | | | | % 15.14/3.01 | | | | (35) all_45_0 = 0 % 15.14/3.01 | | | | % 15.14/3.01 | | | | REDUCE: (34), (35) imply: % 15.14/3.01 | | | | (36) $false % 15.14/3.01 | | | | % 15.14/3.01 | | | | CLOSE: (36) is inconsistent. % 15.14/3.01 | | | | % 15.14/3.01 | | | Case 2: % 15.14/3.01 | | | | % 15.14/3.01 | | | | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) % 15.14/3.01 | | | | = 0 & member(v0, all_32_4) = v1 & $i(v0)) % 15.14/3.01 | | | | % 15.14/3.01 | | | | DELTA: instantiating (37) with fresh symbols all_58_0, all_58_1 gives: % 15.14/3.01 | | | | (38) ~ (all_58_0 = 0) & member(all_58_1, all_32_1) = 0 & % 15.14/3.01 | | | | member(all_58_1, all_32_4) = all_58_0 & $i(all_58_1) % 15.14/3.01 | | | | % 15.14/3.01 | | | | ALPHA: (38) implies: % 15.14/3.01 | | | | (39) ~ (all_58_0 = 0) % 15.14/3.01 | | | | (40) $i(all_58_1) % 15.14/3.01 | | | | (41) member(all_58_1, all_32_4) = all_58_0 % 15.14/3.01 | | | | (42) member(all_58_1, all_32_1) = 0 % 15.14/3.01 | | | | % 15.14/3.01 | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_5, all_58_1, % 15.14/3.01 | | | | all_32_4, all_58_0, simplifying with (10), (13), (23), % 15.14/3.01 | | | | (40), (41) gives: % 15.14/3.01 | | | | (43) all_58_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_58_1) % 15.14/3.01 | | | | = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 15.14/3.01 | | | | all_32_5) = v1)) % 15.14/3.01 | | | | % 15.14/3.02 | | | | GROUND_INST: instantiating (3) with all_58_1, all_32_3, all_32_2, % 15.14/3.02 | | | | all_32_1, simplifying with (15), (16), (20), (40), (42) % 15.14/3.02 | | | | gives: % 15.14/3.02 | | | | (44) ? [v0: any] : ? [v1: any] : (member(all_58_1, all_32_2) = v1 & % 15.14/3.02 | | | | member(all_58_1, all_32_3) = v0 & (v1 = 0 | v0 = 0)) % 15.14/3.02 | | | | % 15.14/3.02 | | | | DELTA: instantiating (44) with fresh symbols all_65_0, all_65_1 gives: % 15.14/3.02 | | | | (45) member(all_58_1, all_32_2) = all_65_0 & member(all_58_1, % 15.14/3.02 | | | | all_32_3) = all_65_1 & (all_65_0 = 0 | all_65_1 = 0) % 15.14/3.02 | | | | % 15.14/3.02 | | | | ALPHA: (45) implies: % 15.14/3.02 | | | | (46) member(all_58_1, all_32_3) = all_65_1 % 15.14/3.02 | | | | (47) member(all_58_1, all_32_2) = all_65_0 % 15.14/3.02 | | | | (48) all_65_0 = 0 | all_65_1 = 0 % 15.14/3.02 | | | | % 15.14/3.02 | | | | BETA: splitting (43) gives: % 15.14/3.02 | | | | % 15.14/3.02 | | | | Case 1: % 15.14/3.02 | | | | | % 15.14/3.02 | | | | | (49) all_58_0 = 0 % 15.14/3.02 | | | | | % 15.14/3.02 | | | | | REDUCE: (39), (49) imply: % 15.14/3.02 | | | | | (50) $false % 15.14/3.02 | | | | | % 15.14/3.02 | | | | | CLOSE: (50) is inconsistent. % 15.14/3.02 | | | | | % 15.14/3.02 | | | | Case 2: % 15.14/3.02 | | | | | % 15.14/3.02 | | | | | (51) ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_58_1) = 0) | ~ % 15.14/3.02 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_5) % 15.14/3.02 | | | | | = v1)) % 15.14/3.02 | | | | | % 15.14/3.02 | | | | | BETA: splitting (48) gives: % 15.14/3.02 | | | | | % 15.14/3.02 | | | | | Case 1: % 15.14/3.02 | | | | | | % 15.14/3.02 | | | | | | (52) all_65_0 = 0 % 15.14/3.02 | | | | | | % 15.14/3.02 | | | | | | REDUCE: (47), (52) imply: % 15.14/3.02 | | | | | | (53) member(all_58_1, all_32_2) = 0 % 15.14/3.02 | | | | | | % 15.14/3.02 | | | | | | GROUND_INST: instantiating (5) with all_32_10, all_32_6, all_58_1, % 15.14/3.02 | | | | | | all_32_2, simplifying with (10), (12), (22), (40), (53) % 15.14/3.02 | | | | | | gives: % 15.14/3.02 | | | | | | (54) ? [v0: $i] : (apply(all_32_10, v0, all_58_1) = 0 & % 15.14/3.02 | | | | | | member(v0, all_32_6) = 0 & $i(v0)) % 15.14/3.02 | | | | | | % 15.14/3.02 | | | | | | DELTA: instantiating (54) with fresh symbol all_94_0 gives: % 15.14/3.02 | | | | | | (55) apply(all_32_10, all_94_0, all_58_1) = 0 & member(all_94_0, % 15.14/3.02 | | | | | | all_32_6) = 0 & $i(all_94_0) % 15.14/3.02 | | | | | | % 15.14/3.02 | | | | | | ALPHA: (55) implies: % 15.14/3.02 | | | | | | (56) $i(all_94_0) % 15.14/3.02 | | | | | | (57) member(all_94_0, all_32_6) = 0 % 15.14/3.02 | | | | | | (58) apply(all_32_10, all_94_0, all_58_1) = 0 % 15.14/3.02 | | | | | | % 15.14/3.02 | | | | | | GROUND_INST: instantiating (51) with all_94_0, simplifying with % 15.14/3.02 | | | | | | (56), (58) gives: % 15.14/3.02 | | | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & member(all_94_0, all_32_5) = % 15.14/3.02 | | | | | | v0) % 15.14/3.02 | | | | | | % 15.14/3.02 | | | | | | DELTA: instantiating (59) with fresh symbol all_102_0 gives: % 15.14/3.02 | | | | | | (60) ~ (all_102_0 = 0) & member(all_94_0, all_32_5) = all_102_0 % 15.14/3.02 | | | | | | % 15.14/3.02 | | | | | | ALPHA: (60) implies: % 15.14/3.02 | | | | | | (61) ~ (all_102_0 = 0) % 15.14/3.02 | | | | | | (62) member(all_94_0, all_32_5) = all_102_0 % 15.49/3.02 | | | | | | % 15.49/3.02 | | | | | | GROUND_INST: instantiating (4) with all_94_0, all_32_7, all_32_6, % 15.49/3.02 | | | | | | all_32_5, all_102_0, simplifying with (11), (12), (19), % 15.49/3.02 | | | | | | (56), (62) gives: % 15.49/3.02 | | | | | | (63) all_102_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 15.49/3.02 | | | | | | ~ (v0 = 0) & member(all_94_0, all_32_6) = v1 & % 15.49/3.02 | | | | | | member(all_94_0, all_32_7) = v0) % 15.49/3.02 | | | | | | % 15.49/3.02 | | | | | | BETA: splitting (63) gives: % 15.49/3.02 | | | | | | % 15.49/3.02 | | | | | | Case 1: % 15.49/3.02 | | | | | | | % 15.49/3.02 | | | | | | | (64) all_102_0 = 0 % 15.49/3.02 | | | | | | | % 15.49/3.02 | | | | | | | REDUCE: (61), (64) imply: % 15.49/3.02 | | | | | | | (65) $false % 15.49/3.02 | | | | | | | % 15.49/3.02 | | | | | | | CLOSE: (65) is inconsistent. % 15.49/3.02 | | | | | | | % 15.49/3.03 | | | | | | Case 2: % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | (66) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 15.49/3.03 | | | | | | | member(all_94_0, all_32_6) = v1 & member(all_94_0, % 15.49/3.03 | | | | | | | all_32_7) = v0) % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | DELTA: instantiating (66) with fresh symbols all_115_0, all_115_1 % 15.49/3.03 | | | | | | | gives: % 15.49/3.03 | | | | | | | (67) ~ (all_115_0 = 0) & ~ (all_115_1 = 0) & member(all_94_0, % 15.49/3.03 | | | | | | | all_32_6) = all_115_0 & member(all_94_0, all_32_7) = % 15.49/3.03 | | | | | | | all_115_1 % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | ALPHA: (67) implies: % 15.49/3.03 | | | | | | | (68) ~ (all_115_0 = 0) % 15.49/3.03 | | | | | | | (69) member(all_94_0, all_32_6) = all_115_0 % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | GROUND_INST: instantiating (7) with 0, all_115_0, all_32_6, % 15.49/3.03 | | | | | | | all_94_0, simplifying with (57), (69) gives: % 15.49/3.03 | | | | | | | (70) all_115_0 = 0 % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | REDUCE: (68), (70) imply: % 15.49/3.03 | | | | | | | (71) $false % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | CLOSE: (71) is inconsistent. % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | End of split % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | Case 2: % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | (72) all_65_1 = 0 % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | REDUCE: (46), (72) imply: % 15.49/3.03 | | | | | | (73) member(all_58_1, all_32_3) = 0 % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | GROUND_INST: instantiating (5) with all_32_10, all_32_7, all_58_1, % 15.49/3.03 | | | | | | all_32_3, simplifying with (10), (11), (21), (40), (73) % 15.49/3.03 | | | | | | gives: % 15.49/3.03 | | | | | | (74) ? [v0: $i] : (apply(all_32_10, v0, all_58_1) = 0 & % 15.49/3.03 | | | | | | member(v0, all_32_7) = 0 & $i(v0)) % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | DELTA: instantiating (74) with fresh symbol all_99_0 gives: % 15.49/3.03 | | | | | | (75) apply(all_32_10, all_99_0, all_58_1) = 0 & member(all_99_0, % 15.49/3.03 | | | | | | all_32_7) = 0 & $i(all_99_0) % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | ALPHA: (75) implies: % 15.49/3.03 | | | | | | (76) $i(all_99_0) % 15.49/3.03 | | | | | | (77) member(all_99_0, all_32_7) = 0 % 15.49/3.03 | | | | | | (78) apply(all_32_10, all_99_0, all_58_1) = 0 % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | GROUND_INST: instantiating (51) with all_99_0, simplifying with % 15.49/3.03 | | | | | | (76), (78) gives: % 15.49/3.03 | | | | | | (79) ? [v0: int] : ( ~ (v0 = 0) & member(all_99_0, all_32_5) = % 15.49/3.03 | | | | | | v0) % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | DELTA: instantiating (79) with fresh symbol all_109_0 gives: % 15.49/3.03 | | | | | | (80) ~ (all_109_0 = 0) & member(all_99_0, all_32_5) = all_109_0 % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | ALPHA: (80) implies: % 15.49/3.03 | | | | | | (81) ~ (all_109_0 = 0) % 15.49/3.03 | | | | | | (82) member(all_99_0, all_32_5) = all_109_0 % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | GROUND_INST: instantiating (4) with all_99_0, all_32_7, all_32_6, % 15.49/3.03 | | | | | | all_32_5, all_109_0, simplifying with (11), (12), (19), % 15.49/3.03 | | | | | | (76), (82) gives: % 15.49/3.03 | | | | | | (83) all_109_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 15.49/3.03 | | | | | | ~ (v0 = 0) & member(all_99_0, all_32_6) = v1 & % 15.49/3.03 | | | | | | member(all_99_0, all_32_7) = v0) % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | BETA: splitting (83) gives: % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | | Case 1: % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | (84) all_109_0 = 0 % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | REDUCE: (81), (84) imply: % 15.49/3.03 | | | | | | | (85) $false % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | CLOSE: (85) is inconsistent. % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | Case 2: % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | (86) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 15.49/3.03 | | | | | | | member(all_99_0, all_32_6) = v1 & member(all_99_0, % 15.49/3.03 | | | | | | | all_32_7) = v0) % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | DELTA: instantiating (86) with fresh symbols all_122_0, all_122_1 % 15.49/3.03 | | | | | | | gives: % 15.49/3.03 | | | | | | | (87) ~ (all_122_0 = 0) & ~ (all_122_1 = 0) & member(all_99_0, % 15.49/3.03 | | | | | | | all_32_6) = all_122_0 & member(all_99_0, all_32_7) = % 15.49/3.03 | | | | | | | all_122_1 % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | ALPHA: (87) implies: % 15.49/3.03 | | | | | | | (88) ~ (all_122_1 = 0) % 15.49/3.03 | | | | | | | (89) member(all_99_0, all_32_7) = all_122_1 % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | GROUND_INST: instantiating (7) with 0, all_122_1, all_32_7, % 15.49/3.03 | | | | | | | all_99_0, simplifying with (77), (89) gives: % 15.49/3.03 | | | | | | | (90) all_122_1 = 0 % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | REDUCE: (88), (90) imply: % 15.49/3.03 | | | | | | | (91) $false % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | | CLOSE: (91) is inconsistent. % 15.49/3.03 | | | | | | | % 15.49/3.03 | | | | | | End of split % 15.49/3.03 | | | | | | % 15.49/3.03 | | | | | End of split % 15.49/3.03 | | | | | % 15.49/3.03 | | | | End of split % 15.49/3.03 | | | | % 15.49/3.03 | | | End of split % 15.49/3.03 | | | % 15.49/3.03 | | Case 2: % 15.49/3.03 | | | % 15.49/3.03 | | | (92) ~ (all_45_1 = 0) % 15.49/3.03 | | | % 15.49/3.03 | | | BETA: splitting (32) gives: % 15.49/3.03 | | | % 15.49/3.03 | | | Case 1: % 15.49/3.03 | | | | % 15.49/3.03 | | | | (93) all_45_1 = 0 % 15.49/3.03 | | | | % 15.49/3.04 | | | | REDUCE: (92), (93) imply: % 15.49/3.04 | | | | (94) $false % 15.49/3.04 | | | | % 15.49/3.04 | | | | CLOSE: (94) is inconsistent. % 15.49/3.04 | | | | % 15.49/3.04 | | | Case 2: % 15.49/3.04 | | | | % 15.49/3.04 | | | | (95) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) % 15.49/3.04 | | | | = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 15.49/3.04 | | | | % 15.49/3.04 | | | | DELTA: instantiating (95) with fresh symbols all_79_0, all_79_1 gives: % 15.49/3.04 | | | | (96) ~ (all_79_0 = 0) & member(all_79_1, all_32_1) = all_79_0 & % 15.49/3.04 | | | | member(all_79_1, all_32_4) = 0 & $i(all_79_1) % 15.49/3.04 | | | | % 15.49/3.04 | | | | ALPHA: (96) implies: % 15.49/3.04 | | | | (97) ~ (all_79_0 = 0) % 15.49/3.04 | | | | (98) $i(all_79_1) % 15.49/3.04 | | | | (99) member(all_79_1, all_32_4) = 0 % 15.49/3.04 | | | | (100) member(all_79_1, all_32_1) = all_79_0 % 15.49/3.04 | | | | % 15.49/3.04 | | | | GROUND_INST: instantiating (5) with all_32_10, all_32_5, all_79_1, % 15.49/3.04 | | | | all_32_4, simplifying with (10), (13), (23), (98), (99) % 15.49/3.04 | | | | gives: % 15.49/3.04 | | | | (101) ? [v0: $i] : (apply(all_32_10, v0, all_79_1) = 0 & member(v0, % 15.49/3.04 | | | | all_32_5) = 0 & $i(v0)) % 15.49/3.04 | | | | % 15.49/3.04 | | | | GROUND_INST: instantiating (4) with all_79_1, all_32_3, all_32_2, % 15.49/3.04 | | | | all_32_1, all_79_0, simplifying with (15), (16), (20), % 15.49/3.04 | | | | (98), (100) gives: % 15.49/3.04 | | | | (102) all_79_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 15.49/3.04 | | | | (v0 = 0) & member(all_79_1, all_32_2) = v1 & member(all_79_1, % 15.49/3.04 | | | | all_32_3) = v0) % 15.49/3.04 | | | | % 15.49/3.04 | | | | DELTA: instantiating (101) with fresh symbol all_86_0 gives: % 15.49/3.04 | | | | (103) apply(all_32_10, all_86_0, all_79_1) = 0 & member(all_86_0, % 15.49/3.04 | | | | all_32_5) = 0 & $i(all_86_0) % 15.49/3.04 | | | | % 15.49/3.04 | | | | ALPHA: (103) implies: % 15.49/3.04 | | | | (104) $i(all_86_0) % 15.49/3.04 | | | | (105) member(all_86_0, all_32_5) = 0 % 15.49/3.04 | | | | (106) apply(all_32_10, all_86_0, all_79_1) = 0 % 15.49/3.04 | | | | % 15.49/3.04 | | | | BETA: splitting (102) gives: % 15.49/3.04 | | | | % 15.49/3.04 | | | | Case 1: % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | (107) all_79_0 = 0 % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | REDUCE: (97), (107) imply: % 15.49/3.04 | | | | | (108) $false % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | CLOSE: (108) is inconsistent. % 15.49/3.04 | | | | | % 15.49/3.04 | | | | Case 2: % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | (109) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 15.49/3.04 | | | | | member(all_79_1, all_32_2) = v1 & member(all_79_1, % 15.49/3.04 | | | | | all_32_3) = v0) % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | DELTA: instantiating (109) with fresh symbols all_92_0, all_92_1 % 15.49/3.04 | | | | | gives: % 15.49/3.04 | | | | | (110) ~ (all_92_0 = 0) & ~ (all_92_1 = 0) & member(all_79_1, % 15.49/3.04 | | | | | all_32_2) = all_92_0 & member(all_79_1, all_32_3) = % 15.49/3.04 | | | | | all_92_1 % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | ALPHA: (110) implies: % 15.49/3.04 | | | | | (111) ~ (all_92_1 = 0) % 15.49/3.04 | | | | | (112) ~ (all_92_0 = 0) % 15.49/3.04 | | | | | (113) member(all_79_1, all_32_3) = all_92_1 % 15.49/3.04 | | | | | (114) member(all_79_1, all_32_2) = all_92_0 % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_7, all_79_1, % 15.49/3.04 | | | | | all_32_3, all_92_1, simplifying with (10), (11), (21), % 15.49/3.04 | | | | | (98), (113) gives: % 15.49/3.04 | | | | | (115) all_92_1 = 0 | ! [v0: $i] : ( ~ (apply(all_32_10, v0, % 15.49/3.04 | | | | | all_79_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 15.49/3.04 | | | | | 0) & member(v0, all_32_7) = v1)) % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | GROUND_INST: instantiating (6) with all_32_10, all_32_6, all_79_1, % 15.49/3.04 | | | | | all_32_2, all_92_0, simplifying with (10), (12), (22), % 15.49/3.04 | | | | | (98), (114) gives: % 15.49/3.04 | | | | | (116) all_92_0 = 0 | ! [v0: $i] : ( ~ (apply(all_32_10, v0, % 15.49/3.04 | | | | | all_79_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 15.49/3.04 | | | | | 0) & member(v0, all_32_6) = v1)) % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | GROUND_INST: instantiating (3) with all_86_0, all_32_7, all_32_6, % 15.49/3.04 | | | | | all_32_5, simplifying with (11), (12), (19), (104), (105) % 15.49/3.04 | | | | | gives: % 15.49/3.04 | | | | | (117) ? [v0: any] : ? [v1: any] : (member(all_86_0, all_32_6) = % 15.49/3.04 | | | | | v1 & member(all_86_0, all_32_7) = v0 & (v1 = 0 | v0 = 0)) % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | DELTA: instantiating (117) with fresh symbols all_99_0, all_99_1 % 15.49/3.04 | | | | | gives: % 15.49/3.04 | | | | | (118) member(all_86_0, all_32_6) = all_99_0 & member(all_86_0, % 15.49/3.04 | | | | | all_32_7) = all_99_1 & (all_99_0 = 0 | all_99_1 = 0) % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | ALPHA: (118) implies: % 15.49/3.04 | | | | | (119) member(all_86_0, all_32_7) = all_99_1 % 15.49/3.04 | | | | | (120) member(all_86_0, all_32_6) = all_99_0 % 15.49/3.04 | | | | | (121) all_99_0 = 0 | all_99_1 = 0 % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | BETA: splitting (116) gives: % 15.49/3.04 | | | | | % 15.49/3.04 | | | | | Case 1: % 15.49/3.04 | | | | | | % 15.49/3.04 | | | | | | (122) all_92_0 = 0 % 15.49/3.04 | | | | | | % 15.49/3.04 | | | | | | REDUCE: (112), (122) imply: % 15.49/3.04 | | | | | | (123) $false % 15.49/3.04 | | | | | | % 15.49/3.04 | | | | | | CLOSE: (123) is inconsistent. % 15.49/3.04 | | | | | | % 15.49/3.04 | | | | | Case 2: % 15.49/3.05 | | | | | | % 15.49/3.05 | | | | | | (124) ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_79_1) = 0) | ~ % 15.49/3.05 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 15.49/3.05 | | | | | | all_32_6) = v1)) % 15.49/3.05 | | | | | | % 15.49/3.05 | | | | | | GROUND_INST: instantiating (124) with all_86_0, simplifying with % 15.49/3.05 | | | | | | (104), (106) gives: % 15.49/3.05 | | | | | | (125) ? [v0: int] : ( ~ (v0 = 0) & member(all_86_0, all_32_6) = % 15.49/3.05 | | | | | | v0) % 15.49/3.05 | | | | | | % 15.49/3.05 | | | | | | BETA: splitting (115) gives: % 15.49/3.05 | | | | | | % 15.49/3.05 | | | | | | Case 1: % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | (126) all_92_1 = 0 % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | REDUCE: (111), (126) imply: % 15.49/3.05 | | | | | | | (127) $false % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | CLOSE: (127) is inconsistent. % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | Case 2: % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | (128) ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_79_1) = 0) | % 15.49/3.05 | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 15.49/3.05 | | | | | | | all_32_7) = v1)) % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | GROUND_INST: instantiating (128) with all_86_0, simplifying with % 15.49/3.05 | | | | | | | (104), (106) gives: % 15.49/3.05 | | | | | | | (129) ? [v0: int] : ( ~ (v0 = 0) & member(all_86_0, all_32_7) % 15.49/3.05 | | | | | | | = v0) % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | DELTA: instantiating (125) with fresh symbol all_110_0 gives: % 15.49/3.05 | | | | | | | (130) ~ (all_110_0 = 0) & member(all_86_0, all_32_6) = % 15.49/3.05 | | | | | | | all_110_0 % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | ALPHA: (130) implies: % 15.49/3.05 | | | | | | | (131) ~ (all_110_0 = 0) % 15.49/3.05 | | | | | | | (132) member(all_86_0, all_32_6) = all_110_0 % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | DELTA: instantiating (129) with fresh symbol all_112_0 gives: % 15.49/3.05 | | | | | | | (133) ~ (all_112_0 = 0) & member(all_86_0, all_32_7) = % 15.49/3.05 | | | | | | | all_112_0 % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | ALPHA: (133) implies: % 15.49/3.05 | | | | | | | (134) ~ (all_112_0 = 0) % 15.49/3.05 | | | | | | | (135) member(all_86_0, all_32_7) = all_112_0 % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | GROUND_INST: instantiating (7) with all_99_1, all_112_0, all_32_7, % 15.49/3.05 | | | | | | | all_86_0, simplifying with (119), (135) gives: % 15.49/3.05 | | | | | | | (136) all_112_0 = all_99_1 % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | GROUND_INST: instantiating (7) with all_99_0, all_110_0, all_32_6, % 15.49/3.05 | | | | | | | all_86_0, simplifying with (120), (132) gives: % 15.49/3.05 | | | | | | | (137) all_110_0 = all_99_0 % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | REDUCE: (134), (136) imply: % 15.49/3.05 | | | | | | | (138) ~ (all_99_1 = 0) % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | REDUCE: (131), (137) imply: % 15.49/3.05 | | | | | | | (139) ~ (all_99_0 = 0) % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | BETA: splitting (121) gives: % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | | Case 1: % 15.49/3.05 | | | | | | | | % 15.49/3.05 | | | | | | | | (140) all_99_0 = 0 % 15.49/3.05 | | | | | | | | % 15.49/3.05 | | | | | | | | REDUCE: (139), (140) imply: % 15.49/3.05 | | | | | | | | (141) $false % 15.49/3.05 | | | | | | | | % 15.49/3.05 | | | | | | | | CLOSE: (141) is inconsistent. % 15.49/3.05 | | | | | | | | % 15.49/3.05 | | | | | | | Case 2: % 15.49/3.05 | | | | | | | | % 15.49/3.05 | | | | | | | | (142) all_99_1 = 0 % 15.49/3.05 | | | | | | | | % 15.49/3.05 | | | | | | | | REDUCE: (138), (142) imply: % 15.49/3.05 | | | | | | | | (143) $false % 15.49/3.05 | | | | | | | | % 15.49/3.05 | | | | | | | | CLOSE: (143) is inconsistent. % 15.49/3.05 | | | | | | | | % 15.49/3.05 | | | | | | | End of split % 15.49/3.05 | | | | | | | % 15.49/3.05 | | | | | | End of split % 15.49/3.05 | | | | | | % 15.49/3.05 | | | | | End of split % 15.49/3.05 | | | | | % 15.49/3.05 | | | | End of split % 15.49/3.05 | | | | % 15.49/3.05 | | | End of split % 15.49/3.05 | | | % 15.49/3.05 | | End of split % 15.49/3.05 | | % 15.49/3.05 | End of split % 15.49/3.05 | % 15.49/3.05 End of proof % 15.49/3.05 % SZS output end Proof for theBenchmark % 15.49/3.05 % 15.49/3.05 2443ms %------------------------------------------------------------------------------