%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET761+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 : n013.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 15:26:20 EDT 2023 % Result : Theorem 13.74s 2.64s % Output : Proof 16.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET761+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n013.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 08:25:32 EDT 2023 % 0.13/0.36 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.44/1.23 Prover 1: Preprocessing ... % 3.44/1.24 Prover 4: Preprocessing ... % 3.44/1.27 Prover 5: Preprocessing ... % 3.44/1.27 Prover 6: Preprocessing ... % 3.44/1.27 Prover 3: Preprocessing ... % 3.44/1.27 Prover 0: Preprocessing ... % 3.44/1.27 Prover 2: Preprocessing ... % 8.84/1.99 Prover 5: Proving ... % 8.84/1.99 Prover 2: Proving ... % 8.84/2.05 Prover 1: Constructing countermodel ... % 8.84/2.05 Prover 3: Constructing countermodel ... % 8.84/2.07 Prover 6: Proving ... % 13.74/2.63 Prover 3: proved (1975ms) % 13.74/2.64 % 13.74/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.74/2.64 % 13.74/2.64 Prover 5: stopped % 13.74/2.65 Prover 2: stopped % 13.74/2.66 Prover 6: stopped % 13.74/2.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.74/2.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.74/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.74/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.74/2.66 Prover 4: Constructing countermodel ... % 13.74/2.71 Prover 0: Proving ... % 13.74/2.71 Prover 0: stopped % 13.74/2.73 Prover 8: Preprocessing ... % 13.74/2.73 Prover 7: Preprocessing ... % 13.74/2.73 Prover 11: Preprocessing ... % 13.74/2.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.74/2.74 Prover 10: Preprocessing ... % 13.74/2.77 Prover 1: Found proof (size 141) % 13.74/2.77 Prover 1: proved (2116ms) % 13.74/2.77 Prover 4: stopped % 14.38/2.78 Prover 13: Preprocessing ... % 14.38/2.79 Prover 7: stopped % 14.38/2.80 Prover 10: stopped % 14.38/2.84 Prover 13: stopped % 15.27/2.86 Prover 11: stopped % 15.42/2.92 Prover 8: Warning: ignoring some quantifiers % 15.66/2.93 Prover 8: Constructing countermodel ... % 15.66/2.94 Prover 8: stopped % 15.66/2.94 % 15.66/2.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.66/2.94 % 15.78/2.95 % SZS output start Proof for theBenchmark % 15.78/2.96 Assumptions after simplification: % 15.78/2.96 --------------------------------- % 15.78/2.96 % 15.78/2.96 (equal_set) % 15.78/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 15.78/2.98 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 15.78/2.98 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 15.78/2.98 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 15.78/2.98 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 15.78/2.98 % 15.78/2.98 (image3) % 15.78/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.78/2.98 int] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = v5) | % 15.78/2.98 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & % 15.78/2.98 member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v6, v3) = 0) | ~ % 15.78/2.98 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) & ! [v0: % 15.78/2.98 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.78/2.98 (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2) % 15.78/2.98 | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] : (apply(v0, v5, % 15.78/2.98 v3) = 0 & member(v5, v1) = 0 & $i(v5)))) % 15.78/2.98 % 15.78/2.98 (injective) % 15.78/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.78/2.99 (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 15.78/2.99 $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & % 15.78/2.99 apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & % 15.78/2.99 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: % 15.78/2.99 $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) % 15.78/2.99 | ~ $i(v0) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 15.78/2.99 (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ % 15.78/2.99 $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 15.78/2.99 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 % 15.78/2.99 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))) % 15.78/2.99 % 15.78/2.99 (intersection) % 15.78/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.78/2.99 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 15.78/2.99 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 15.78/2.99 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 15.78/2.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 15.78/2.99 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 15.78/2.99 0 & member(v0, v1) = 0)) % 15.78/2.99 % 15.78/2.99 (subset) % 15.78/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 15.78/2.99 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 15.78/2.99 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 15.78/2.99 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 15.78/2.99 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 15.78/2.99 % 15.78/2.99 (thIIa11) % 15.78/2.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.78/2.99 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 15.78/2.99 : ( ~ (v10 = 0) & image3(v0, v5, v2) = v6 & image3(v0, v4, v2) = v8 & % 15.78/2.99 image3(v0, v3, v2) = v7 & injective(v0, v1, v2) = 0 & maps(v0, v1, v2) = 0 & % 15.78/2.99 intersection(v7, v8) = v9 & intersection(v3, v4) = v5 & equal_set(v6, v9) = % 15.78/2.99 v10 & subset(v4, v1) = 0 & subset(v3, v1) = 0 & $i(v9) & $i(v8) & $i(v7) & % 15.78/2.99 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.78/2.99 % 15.78/2.99 (function-axioms) % 15.78/3.00 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.78/3.00 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 15.78/3.00 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 15.78/3.00 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.78/3.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.78/3.00 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 15.78/3.00 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.78/3.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.78/3.00 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 15.78/3.00 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.78/3.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.78/3.00 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 15.78/3.00 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 15.78/3.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 15.78/3.00 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 15.78/3.00 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 15.78/3.00 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.78/3.00 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 15.78/3.00 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.78/3.00 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.78/3.00 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 15.78/3.00 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.78/3.00 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 15.78/3.00 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.78/3.00 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 15.78/3.00 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.78/3.00 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 15.78/3.00 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.78/3.00 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 15.78/3.00 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 15.78/3.00 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.78/3.00 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 15.78/3.00 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.78/3.00 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.78/3.00 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 15.78/3.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.78/3.00 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 15.78/3.00 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.78/3.00 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 15.78/3.00 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.78/3.00 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 15.78/3.00 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.78/3.00 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 15.78/3.00 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.78/3.00 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 15.78/3.00 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.78/3.00 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 15.78/3.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.78/3.00 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 15.78/3.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 15.78/3.00 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.78/3.00 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 15.78/3.00 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.78/3.00 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 15.78/3.00 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.78/3.00 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 15.78/3.00 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.78/3.00 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.78/3.00 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 15.78/3.00 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 15.78/3.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 15.78/3.00 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.78/3.00 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 15.78/3.00 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 15.78/3.00 (power_set(v2) = v0)) % 15.78/3.00 % 15.78/3.00 Further assumptions not needed in the proof: % 15.78/3.00 -------------------------------------------- % 15.78/3.00 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 15.78/3.00 equal_maps, identity, image2, increasing_function, inverse_function, % 15.78/3.00 inverse_image2, inverse_image3, inverse_predicate, isomorphism, maps, % 15.78/3.00 one_to_one, power_set, product, singleton, sum, surjective, union, % 15.78/3.00 unordered_pair % 15.78/3.00 % 15.78/3.00 Those formulas are unsatisfiable: % 15.78/3.00 --------------------------------- % 15.78/3.00 % 15.78/3.00 Begin of proof % 15.78/3.01 | % 15.78/3.01 | ALPHA: (subset) implies: % 15.78/3.01 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 15.78/3.01 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 15.78/3.01 | member(v2, v1) = 0)) % 15.78/3.01 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.78/3.01 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 15.78/3.01 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 15.78/3.01 | % 15.78/3.01 | ALPHA: (equal_set) implies: % 15.78/3.01 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 15.78/3.01 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 15.78/3.01 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 15.78/3.01 | 0)))) % 15.78/3.01 | % 15.78/3.01 | ALPHA: (intersection) implies: % 15.78/3.01 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.78/3.01 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 15.78/3.01 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 15.78/3.01 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.78/3.01 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 15.78/3.01 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 15.78/3.01 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 15.78/3.01 | 0)))) % 15.78/3.01 | % 15.78/3.01 | ALPHA: (injective) implies: % 15.78/3.01 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = % 15.78/3.01 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: $i] % 15.78/3.01 | : ! [v5: $i] : (v4 = v3 | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, % 15.78/3.01 | v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: any] % 15.78/3.01 | : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, % 15.78/3.01 | v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | % 15.78/3.01 | ~ (v6 = 0))))) % 15.78/3.01 | % 15.78/3.01 | ALPHA: (image3) implies: % 15.78/3.01 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 15.78/3.01 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | % 15.78/3.01 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] % 15.78/3.01 | : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0 & $i(v5)))) % 15.78/3.02 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.78/3.02 | ! [v5: int] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, % 15.78/3.02 | v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 15.78/3.02 | [v6: int] : ( ~ (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : ( ~ % 15.78/3.02 | (apply(v0, v6, v3) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & % 15.78/3.02 | member(v6, v1) = v7))) % 15.78/3.02 | % 15.78/3.02 | ALPHA: (function-axioms) implies: % 15.78/3.02 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.78/3.02 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 15.78/3.02 | = v0)) % 15.78/3.02 | % 15.78/3.02 | DELTA: instantiating (thIIa11) with fresh symbols all_32_0, all_32_1, % 15.78/3.02 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8, % 15.78/3.02 | all_32_9, all_32_10 gives: % 15.78/3.02 | (10) ~ (all_32_0 = 0) & image3(all_32_10, all_32_5, all_32_8) = all_32_4 & % 15.78/3.02 | image3(all_32_10, all_32_6, all_32_8) = all_32_2 & image3(all_32_10, % 15.78/3.02 | all_32_7, all_32_8) = all_32_3 & injective(all_32_10, all_32_9, % 15.78/3.02 | all_32_8) = 0 & maps(all_32_10, all_32_9, all_32_8) = 0 & % 15.78/3.02 | intersection(all_32_3, all_32_2) = all_32_1 & intersection(all_32_7, % 16.13/3.02 | all_32_6) = all_32_5 & equal_set(all_32_4, all_32_1) = all_32_0 & % 16.13/3.02 | subset(all_32_6, all_32_9) = 0 & subset(all_32_7, all_32_9) = 0 & % 16.13/3.02 | $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & % 16.13/3.02 | $i(all_32_5) & $i(all_32_6) & $i(all_32_7) & $i(all_32_8) & % 16.13/3.02 | $i(all_32_9) & $i(all_32_10) % 16.13/3.02 | % 16.13/3.02 | ALPHA: (10) implies: % 16.13/3.02 | (11) ~ (all_32_0 = 0) % 16.13/3.02 | (12) $i(all_32_10) % 16.13/3.02 | (13) $i(all_32_9) % 16.13/3.02 | (14) $i(all_32_8) % 16.13/3.02 | (15) $i(all_32_7) % 16.13/3.02 | (16) $i(all_32_6) % 16.13/3.02 | (17) $i(all_32_5) % 16.13/3.02 | (18) $i(all_32_4) % 16.13/3.02 | (19) $i(all_32_3) % 16.13/3.02 | (20) $i(all_32_2) % 16.13/3.02 | (21) $i(all_32_1) % 16.13/3.02 | (22) subset(all_32_7, all_32_9) = 0 % 16.13/3.02 | (23) subset(all_32_6, all_32_9) = 0 % 16.13/3.02 | (24) equal_set(all_32_4, all_32_1) = all_32_0 % 16.13/3.02 | (25) intersection(all_32_7, all_32_6) = all_32_5 % 16.13/3.02 | (26) intersection(all_32_3, all_32_2) = all_32_1 % 16.13/3.02 | (27) injective(all_32_10, all_32_9, all_32_8) = 0 % 16.13/3.02 | (28) image3(all_32_10, all_32_7, all_32_8) = all_32_3 % 16.13/3.02 | (29) image3(all_32_10, all_32_6, all_32_8) = all_32_2 % 16.13/3.02 | (30) image3(all_32_10, all_32_5, all_32_8) = all_32_4 % 16.13/3.02 | % 16.13/3.02 | GROUND_INST: instantiating (1) with all_32_7, all_32_9, simplifying with (13), % 16.13/3.02 | (15), (22) gives: % 16.13/3.02 | (31) ! [v0: $i] : ( ~ (member(v0, all_32_7) = 0) | ~ $i(v0) | member(v0, % 16.13/3.02 | all_32_9) = 0) % 16.13/3.02 | % 16.13/3.02 | GROUND_INST: instantiating (1) with all_32_6, all_32_9, simplifying with (13), % 16.13/3.02 | (16), (23) gives: % 16.13/3.03 | (32) ! [v0: $i] : ( ~ (member(v0, all_32_6) = 0) | ~ $i(v0) | member(v0, % 16.13/3.03 | all_32_9) = 0) % 16.13/3.03 | % 16.13/3.03 | GROUND_INST: instantiating (3) with all_32_4, all_32_1, all_32_0, simplifying % 16.13/3.03 | with (18), (21), (24) gives: % 16.13/3.03 | (33) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_32_1, % 16.13/3.03 | all_32_4) = v1 & subset(all_32_4, all_32_1) = v0 & ( ~ (v1 = 0) | % 16.13/3.03 | ~ (v0 = 0))) % 16.13/3.03 | % 16.13/3.03 | GROUND_INST: instantiating (6) with all_32_10, all_32_9, all_32_8, simplifying % 16.13/3.03 | with (12), (13), (14), (27) gives: % 16.13/3.03 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.13/3.03 | (apply(all_32_10, v1, v2) = 0) | ~ (apply(all_32_10, v0, v2) = 0) | % 16.13/3.03 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 16.13/3.03 | [v5: any] : (member(v2, all_32_8) = v5 & member(v1, all_32_9) = v4 & % 16.13/3.03 | member(v0, all_32_9) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 16.13/3.03 | 0)))) % 16.13/3.03 | % 16.13/3.03 | BETA: splitting (33) gives: % 16.13/3.03 | % 16.13/3.03 | Case 1: % 16.13/3.03 | | % 16.13/3.03 | | (35) all_32_0 = 0 % 16.13/3.03 | | % 16.13/3.03 | | REDUCE: (11), (35) imply: % 16.13/3.03 | | (36) $false % 16.13/3.03 | | % 16.13/3.03 | | CLOSE: (36) is inconsistent. % 16.13/3.03 | | % 16.13/3.03 | Case 2: % 16.13/3.03 | | % 16.13/3.03 | | (37) ? [v0: any] : ? [v1: any] : (subset(all_32_1, all_32_4) = v1 & % 16.13/3.03 | | subset(all_32_4, all_32_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.13/3.03 | | % 16.13/3.03 | | DELTA: instantiating (37) with fresh symbols all_46_0, all_46_1 gives: % 16.13/3.03 | | (38) subset(all_32_1, all_32_4) = all_46_0 & subset(all_32_4, all_32_1) = % 16.13/3.03 | | all_46_1 & ( ~ (all_46_0 = 0) | ~ (all_46_1 = 0)) % 16.13/3.03 | | % 16.13/3.03 | | ALPHA: (38) implies: % 16.13/3.03 | | (39) subset(all_32_4, all_32_1) = all_46_1 % 16.13/3.03 | | (40) subset(all_32_1, all_32_4) = all_46_0 % 16.13/3.03 | | (41) ~ (all_46_0 = 0) | ~ (all_46_1 = 0) % 16.13/3.03 | | % 16.13/3.03 | | GROUND_INST: instantiating (2) with all_32_4, all_32_1, all_46_1, % 16.13/3.03 | | simplifying with (18), (21), (39) gives: % 16.13/3.03 | | (42) all_46_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.13/3.03 | | member(v0, all_32_1) = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 16.13/3.03 | | % 16.13/3.03 | | GROUND_INST: instantiating (2) with all_32_1, all_32_4, all_46_0, % 16.13/3.03 | | simplifying with (18), (21), (40) gives: % 16.13/3.03 | | (43) all_46_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.13/3.03 | | member(v0, all_32_1) = 0 & member(v0, all_32_4) = v1 & $i(v0)) % 16.13/3.03 | | % 16.13/3.03 | | BETA: splitting (41) gives: % 16.13/3.03 | | % 16.13/3.03 | | Case 1: % 16.13/3.03 | | | % 16.13/3.03 | | | (44) ~ (all_46_0 = 0) % 16.13/3.03 | | | % 16.13/3.03 | | | BETA: splitting (43) gives: % 16.13/3.03 | | | % 16.13/3.03 | | | Case 1: % 16.13/3.03 | | | | % 16.13/3.03 | | | | (45) all_46_0 = 0 % 16.13/3.03 | | | | % 16.13/3.03 | | | | REDUCE: (44), (45) imply: % 16.13/3.03 | | | | (46) $false % 16.13/3.03 | | | | % 16.13/3.03 | | | | CLOSE: (46) is inconsistent. % 16.13/3.03 | | | | % 16.13/3.03 | | | Case 2: % 16.13/3.03 | | | | % 16.13/3.04 | | | | (47) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) % 16.13/3.04 | | | | = 0 & member(v0, all_32_4) = v1 & $i(v0)) % 16.13/3.04 | | | | % 16.13/3.04 | | | | DELTA: instantiating (47) with fresh symbols all_59_0, all_59_1 gives: % 16.13/3.04 | | | | (48) ~ (all_59_0 = 0) & member(all_59_1, all_32_1) = 0 & % 16.13/3.04 | | | | member(all_59_1, all_32_4) = all_59_0 & $i(all_59_1) % 16.13/3.04 | | | | % 16.13/3.04 | | | | ALPHA: (48) implies: % 16.13/3.04 | | | | (49) ~ (all_59_0 = 0) % 16.13/3.04 | | | | (50) $i(all_59_1) % 16.13/3.04 | | | | (51) member(all_59_1, all_32_4) = all_59_0 % 16.13/3.04 | | | | (52) member(all_59_1, all_32_1) = 0 % 16.13/3.04 | | | | % 16.13/3.04 | | | | GROUND_INST: instantiating (8) with all_32_10, all_32_5, all_32_8, % 16.13/3.04 | | | | all_59_1, all_32_4, all_59_0, simplifying with (12), (14), % 16.13/3.04 | | | | (17), (30), (50), (51) gives: % 16.13/3.04 | | | | (53) all_59_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, % 16.13/3.04 | | | | all_32_8) = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, v0, % 16.13/3.04 | | | | all_59_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 16.13/3.04 | | | | member(v0, all_32_5) = v1)) % 16.13/3.04 | | | | % 16.13/3.04 | | | | GROUND_INST: instantiating (4) with all_59_1, all_32_3, all_32_2, % 16.13/3.04 | | | | all_32_1, simplifying with (19), (20), (26), (50), (52) % 16.13/3.04 | | | | gives: % 16.13/3.04 | | | | (54) member(all_59_1, all_32_2) = 0 & member(all_59_1, all_32_3) = 0 % 16.13/3.04 | | | | % 16.13/3.04 | | | | ALPHA: (54) implies: % 16.13/3.04 | | | | (55) member(all_59_1, all_32_3) = 0 % 16.13/3.04 | | | | (56) member(all_59_1, all_32_2) = 0 % 16.13/3.04 | | | | % 16.13/3.04 | | | | GROUND_INST: instantiating (7) with all_32_10, all_32_7, all_32_8, % 16.13/3.04 | | | | all_59_1, all_32_3, simplifying with (12), (14), (15), % 16.13/3.04 | | | | (28), (50), (55) gives: % 16.13/3.04 | | | | (57) member(all_59_1, all_32_8) = 0 & ? [v0: $i] : (apply(all_32_10, % 16.13/3.04 | | | | v0, all_59_1) = 0 & member(v0, all_32_7) = 0 & $i(v0)) % 16.13/3.04 | | | | % 16.13/3.04 | | | | ALPHA: (57) implies: % 16.13/3.04 | | | | (58) ? [v0: $i] : (apply(all_32_10, v0, all_59_1) = 0 & member(v0, % 16.13/3.04 | | | | all_32_7) = 0 & $i(v0)) % 16.13/3.04 | | | | % 16.13/3.04 | | | | GROUND_INST: instantiating (7) with all_32_10, all_32_6, all_32_8, % 16.13/3.04 | | | | all_59_1, all_32_2, simplifying with (12), (14), (16), % 16.13/3.04 | | | | (29), (50), (56) gives: % 16.13/3.04 | | | | (59) member(all_59_1, all_32_8) = 0 & ? [v0: $i] : (apply(all_32_10, % 16.13/3.04 | | | | v0, all_59_1) = 0 & member(v0, all_32_6) = 0 & $i(v0)) % 16.13/3.04 | | | | % 16.13/3.04 | | | | ALPHA: (59) implies: % 16.13/3.04 | | | | (60) member(all_59_1, all_32_8) = 0 % 16.13/3.04 | | | | (61) ? [v0: $i] : (apply(all_32_10, v0, all_59_1) = 0 & member(v0, % 16.13/3.04 | | | | all_32_6) = 0 & $i(v0)) % 16.13/3.04 | | | | % 16.13/3.04 | | | | DELTA: instantiating (58) with fresh symbol all_73_0 gives: % 16.13/3.04 | | | | (62) apply(all_32_10, all_73_0, all_59_1) = 0 & member(all_73_0, % 16.13/3.04 | | | | all_32_7) = 0 & $i(all_73_0) % 16.13/3.04 | | | | % 16.13/3.04 | | | | ALPHA: (62) implies: % 16.13/3.04 | | | | (63) $i(all_73_0) % 16.13/3.05 | | | | (64) member(all_73_0, all_32_7) = 0 % 16.13/3.05 | | | | (65) apply(all_32_10, all_73_0, all_59_1) = 0 % 16.13/3.05 | | | | % 16.13/3.05 | | | | DELTA: instantiating (61) with fresh symbol all_75_0 gives: % 16.13/3.05 | | | | (66) apply(all_32_10, all_75_0, all_59_1) = 0 & member(all_75_0, % 16.13/3.05 | | | | all_32_6) = 0 & $i(all_75_0) % 16.13/3.05 | | | | % 16.13/3.05 | | | | ALPHA: (66) implies: % 16.13/3.05 | | | | (67) $i(all_75_0) % 16.13/3.05 | | | | (68) member(all_75_0, all_32_6) = 0 % 16.13/3.05 | | | | (69) apply(all_32_10, all_75_0, all_59_1) = 0 % 16.13/3.05 | | | | % 16.13/3.05 | | | | BETA: splitting (53) gives: % 16.13/3.05 | | | | % 16.13/3.05 | | | | Case 1: % 16.13/3.05 | | | | | % 16.13/3.05 | | | | | (70) all_59_0 = 0 % 16.13/3.05 | | | | | % 16.13/3.05 | | | | | REDUCE: (49), (70) imply: % 16.13/3.05 | | | | | (71) $false % 16.13/3.05 | | | | | % 16.13/3.05 | | | | | CLOSE: (71) is inconsistent. % 16.13/3.05 | | | | | % 16.13/3.05 | | | | Case 2: % 16.13/3.05 | | | | | % 16.13/3.05 | | | | | (72) ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, all_32_8) = v0) % 16.13/3.05 | | | | | | ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_59_1) = 0) | ~ % 16.13/3.05 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_5) % 16.13/3.05 | | | | | = v1)) % 16.13/3.05 | | | | | % 16.13/3.05 | | | | | BETA: splitting (72) gives: % 16.13/3.05 | | | | | % 16.13/3.05 | | | | | Case 1: % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, all_32_8) = % 16.13/3.05 | | | | | | v0) % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | DELTA: instantiating (73) with fresh symbol all_84_0 gives: % 16.13/3.05 | | | | | | (74) ~ (all_84_0 = 0) & member(all_59_1, all_32_8) = all_84_0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | ALPHA: (74) implies: % 16.13/3.05 | | | | | | (75) ~ (all_84_0 = 0) % 16.13/3.05 | | | | | | (76) member(all_59_1, all_32_8) = all_84_0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | GROUND_INST: instantiating (9) with 0, all_84_0, all_32_8, all_59_1, % 16.13/3.05 | | | | | | simplifying with (60), (76) gives: % 16.13/3.05 | | | | | | (77) all_84_0 = 0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | REDUCE: (75), (77) imply: % 16.13/3.05 | | | | | | (78) $false % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | CLOSE: (78) is inconsistent. % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | Case 2: % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | (79) ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_59_1) = 0) | ~ % 16.13/3.05 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 16.13/3.05 | | | | | | all_32_5) = v1)) % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | GROUND_INST: instantiating (31) with all_73_0, simplifying with % 16.13/3.05 | | | | | | (63), (64) gives: % 16.13/3.05 | | | | | | (80) member(all_73_0, all_32_9) = 0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | GROUND_INST: instantiating (32) with all_75_0, simplifying with % 16.13/3.05 | | | | | | (67), (68) gives: % 16.13/3.05 | | | | | | (81) member(all_75_0, all_32_9) = 0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | GROUND_INST: instantiating (79) with all_73_0, simplifying with % 16.13/3.05 | | | | | | (63), (65) gives: % 16.13/3.05 | | | | | | (82) ? [v0: int] : ( ~ (v0 = 0) & member(all_73_0, all_32_5) = % 16.13/3.05 | | | | | | v0) % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | GROUND_INST: instantiating (34) with all_75_0, all_73_0, all_59_1, % 16.13/3.05 | | | | | | simplifying with (50), (63), (65), (67), (69) gives: % 16.13/3.05 | | | | | | (83) all_75_0 = all_73_0 | ? [v0: any] : ? [v1: any] : ? [v2: % 16.13/3.05 | | | | | | any] : (member(all_75_0, all_32_9) = v0 & member(all_73_0, % 16.13/3.05 | | | | | | all_32_9) = v1 & member(all_59_1, all_32_8) = v2 & ( ~ % 16.13/3.05 | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | GROUND_INST: instantiating (79) with all_75_0, simplifying with % 16.13/3.05 | | | | | | (67), (69) gives: % 16.13/3.05 | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & member(all_75_0, all_32_5) = % 16.13/3.05 | | | | | | v0) % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | DELTA: instantiating (84) with fresh symbol all_90_0 gives: % 16.13/3.05 | | | | | | (85) ~ (all_90_0 = 0) & member(all_75_0, all_32_5) = all_90_0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | ALPHA: (85) implies: % 16.13/3.05 | | | | | | (86) member(all_75_0, all_32_5) = all_90_0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | DELTA: instantiating (82) with fresh symbol all_92_0 gives: % 16.13/3.05 | | | | | | (87) ~ (all_92_0 = 0) & member(all_73_0, all_32_5) = all_92_0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | ALPHA: (87) implies: % 16.13/3.05 | | | | | | (88) ~ (all_92_0 = 0) % 16.13/3.05 | | | | | | (89) member(all_73_0, all_32_5) = all_92_0 % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | BETA: splitting (83) gives: % 16.13/3.05 | | | | | | % 16.13/3.05 | | | | | | Case 1: % 16.13/3.05 | | | | | | | % 16.13/3.05 | | | | | | | (90) all_75_0 = all_73_0 % 16.13/3.05 | | | | | | | % 16.13/3.05 | | | | | | | REDUCE: (86), (90) imply: % 16.13/3.05 | | | | | | | (91) member(all_73_0, all_32_5) = all_90_0 % 16.13/3.05 | | | | | | | % 16.13/3.05 | | | | | | | REDUCE: (68), (90) imply: % 16.13/3.05 | | | | | | | (92) member(all_73_0, all_32_6) = 0 % 16.13/3.05 | | | | | | | % 16.13/3.05 | | | | | | | GROUND_INST: instantiating (9) with all_90_0, all_92_0, all_32_5, % 16.13/3.05 | | | | | | | all_73_0, simplifying with (89), (91) gives: % 16.13/3.05 | | | | | | | (93) all_92_0 = all_90_0 % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | REDUCE: (88), (93) imply: % 16.13/3.06 | | | | | | | (94) ~ (all_90_0 = 0) % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | GROUND_INST: instantiating (5) with all_73_0, all_32_7, all_32_6, % 16.13/3.06 | | | | | | | all_32_5, all_90_0, simplifying with (15), (16), % 16.13/3.06 | | | | | | | (25), (63), (91) gives: % 16.13/3.06 | | | | | | | (95) all_90_0 = 0 | ? [v0: any] : ? [v1: any] : % 16.13/3.06 | | | | | | | (member(all_73_0, all_32_6) = v1 & member(all_73_0, % 16.13/3.06 | | | | | | | all_32_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | BETA: splitting (95) gives: % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | Case 1: % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | (96) all_90_0 = 0 % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | REDUCE: (94), (96) imply: % 16.13/3.06 | | | | | | | | (97) $false % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | CLOSE: (97) is inconsistent. % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | Case 2: % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | (98) ? [v0: any] : ? [v1: any] : (member(all_73_0, % 16.13/3.06 | | | | | | | | all_32_6) = v1 & member(all_73_0, all_32_7) = v0 & ( % 16.13/3.06 | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | DELTA: instantiating (98) with fresh symbols all_113_0, % 16.13/3.06 | | | | | | | | all_113_1 gives: % 16.13/3.06 | | | | | | | | (99) member(all_73_0, all_32_6) = all_113_0 & % 16.13/3.06 | | | | | | | | member(all_73_0, all_32_7) = all_113_1 & ( ~ (all_113_0 % 16.13/3.06 | | | | | | | | = 0) | ~ (all_113_1 = 0)) % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | ALPHA: (99) implies: % 16.13/3.06 | | | | | | | | (100) member(all_73_0, all_32_7) = all_113_1 % 16.13/3.06 | | | | | | | | (101) member(all_73_0, all_32_6) = all_113_0 % 16.13/3.06 | | | | | | | | (102) ~ (all_113_0 = 0) | ~ (all_113_1 = 0) % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_113_1, all_32_7, % 16.13/3.06 | | | | | | | | all_73_0, simplifying with (64), (100) gives: % 16.13/3.06 | | | | | | | | (103) all_113_1 = 0 % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_113_0, all_32_6, % 16.13/3.06 | | | | | | | | all_73_0, simplifying with (92), (101) gives: % 16.13/3.06 | | | | | | | | (104) all_113_0 = 0 % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | BETA: splitting (102) gives: % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | Case 1: % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | (105) ~ (all_113_0 = 0) % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | REDUCE: (104), (105) imply: % 16.13/3.06 | | | | | | | | | (106) $false % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | CLOSE: (106) is inconsistent. % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | Case 2: % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | (107) ~ (all_113_1 = 0) % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | REDUCE: (103), (107) imply: % 16.13/3.06 | | | | | | | | | (108) $false % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | CLOSE: (108) is inconsistent. % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | End of split % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | End of split % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | Case 2: % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | (109) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 16.13/3.06 | | | | | | | (member(all_75_0, all_32_9) = v0 & member(all_73_0, % 16.13/3.06 | | | | | | | all_32_9) = v1 & member(all_59_1, all_32_8) = v2 & ( % 16.13/3.06 | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | DELTA: instantiating (109) with fresh symbols all_98_0, all_98_1, % 16.13/3.06 | | | | | | | all_98_2 gives: % 16.13/3.06 | | | | | | | (110) member(all_75_0, all_32_9) = all_98_2 & member(all_73_0, % 16.13/3.06 | | | | | | | all_32_9) = all_98_1 & member(all_59_1, all_32_8) = % 16.13/3.06 | | | | | | | all_98_0 & ( ~ (all_98_0 = 0) | ~ (all_98_1 = 0) | ~ % 16.13/3.06 | | | | | | | (all_98_2 = 0)) % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | ALPHA: (110) implies: % 16.13/3.06 | | | | | | | (111) member(all_59_1, all_32_8) = all_98_0 % 16.13/3.06 | | | | | | | (112) member(all_73_0, all_32_9) = all_98_1 % 16.13/3.06 | | | | | | | (113) member(all_75_0, all_32_9) = all_98_2 % 16.13/3.06 | | | | | | | (114) ~ (all_98_0 = 0) | ~ (all_98_1 = 0) | ~ (all_98_2 = 0) % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | GROUND_INST: instantiating (9) with 0, all_98_0, all_32_8, % 16.13/3.06 | | | | | | | all_59_1, simplifying with (60), (111) gives: % 16.13/3.06 | | | | | | | (115) all_98_0 = 0 % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | GROUND_INST: instantiating (9) with 0, all_98_1, all_32_9, % 16.13/3.06 | | | | | | | all_73_0, simplifying with (80), (112) gives: % 16.13/3.06 | | | | | | | (116) all_98_1 = 0 % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | GROUND_INST: instantiating (9) with 0, all_98_2, all_32_9, % 16.13/3.06 | | | | | | | all_75_0, simplifying with (81), (113) gives: % 16.13/3.06 | | | | | | | (117) all_98_2 = 0 % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | BETA: splitting (114) gives: % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | | Case 1: % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | (118) ~ (all_98_0 = 0) % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | REDUCE: (115), (118) imply: % 16.13/3.06 | | | | | | | | (119) $false % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | CLOSE: (119) is inconsistent. % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | Case 2: % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | (120) ~ (all_98_1 = 0) | ~ (all_98_2 = 0) % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | BETA: splitting (120) gives: % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | | Case 1: % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | (121) ~ (all_98_1 = 0) % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | REDUCE: (116), (121) imply: % 16.13/3.06 | | | | | | | | | (122) $false % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | CLOSE: (122) is inconsistent. % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | Case 2: % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | (123) ~ (all_98_2 = 0) % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | REDUCE: (117), (123) imply: % 16.13/3.06 | | | | | | | | | (124) $false % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | | CLOSE: (124) is inconsistent. % 16.13/3.06 | | | | | | | | | % 16.13/3.06 | | | | | | | | End of split % 16.13/3.06 | | | | | | | | % 16.13/3.06 | | | | | | | End of split % 16.13/3.06 | | | | | | | % 16.13/3.06 | | | | | | End of split % 16.13/3.06 | | | | | | % 16.13/3.06 | | | | | End of split % 16.13/3.06 | | | | | % 16.13/3.06 | | | | End of split % 16.13/3.06 | | | | % 16.13/3.06 | | | End of split % 16.13/3.06 | | | % 16.13/3.06 | | Case 2: % 16.13/3.06 | | | % 16.13/3.06 | | | (125) ~ (all_46_1 = 0) % 16.13/3.06 | | | % 16.13/3.06 | | | BETA: splitting (42) gives: % 16.13/3.06 | | | % 16.13/3.06 | | | Case 1: % 16.13/3.06 | | | | % 16.13/3.06 | | | | (126) all_46_1 = 0 % 16.13/3.06 | | | | % 16.13/3.07 | | | | REDUCE: (125), (126) imply: % 16.13/3.07 | | | | (127) $false % 16.13/3.07 | | | | % 16.13/3.07 | | | | CLOSE: (127) is inconsistent. % 16.13/3.07 | | | | % 16.13/3.07 | | | Case 2: % 16.13/3.07 | | | | % 16.13/3.07 | | | | (128) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 16.13/3.07 | | | | all_32_1) = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 16.13/3.07 | | | | % 16.13/3.07 | | | | DELTA: instantiating (128) with fresh symbols all_59_0, all_59_1 gives: % 16.13/3.07 | | | | (129) ~ (all_59_0 = 0) & member(all_59_1, all_32_1) = all_59_0 & % 16.13/3.07 | | | | member(all_59_1, all_32_4) = 0 & $i(all_59_1) % 16.13/3.07 | | | | % 16.13/3.07 | | | | ALPHA: (129) implies: % 16.13/3.07 | | | | (130) ~ (all_59_0 = 0) % 16.13/3.07 | | | | (131) $i(all_59_1) % 16.13/3.07 | | | | (132) member(all_59_1, all_32_4) = 0 % 16.13/3.07 | | | | (133) member(all_59_1, all_32_1) = all_59_0 % 16.13/3.07 | | | | % 16.13/3.07 | | | | GROUND_INST: instantiating (7) with all_32_10, all_32_5, all_32_8, % 16.13/3.07 | | | | all_59_1, all_32_4, simplifying with (12), (14), (17), % 16.13/3.07 | | | | (30), (131), (132) gives: % 16.13/3.07 | | | | (134) member(all_59_1, all_32_8) = 0 & ? [v0: $i] : % 16.13/3.07 | | | | (apply(all_32_10, v0, all_59_1) = 0 & member(v0, all_32_5) = 0 % 16.13/3.07 | | | | & $i(v0)) % 16.13/3.07 | | | | % 16.13/3.07 | | | | ALPHA: (134) implies: % 16.13/3.07 | | | | (135) member(all_59_1, all_32_8) = 0 % 16.13/3.07 | | | | (136) ? [v0: $i] : (apply(all_32_10, v0, all_59_1) = 0 & member(v0, % 16.13/3.07 | | | | all_32_5) = 0 & $i(v0)) % 16.13/3.07 | | | | % 16.37/3.07 | | | | GROUND_INST: instantiating (5) with all_59_1, all_32_3, all_32_2, % 16.37/3.07 | | | | all_32_1, all_59_0, simplifying with (19), (20), (26), % 16.37/3.07 | | | | (131), (133) gives: % 16.37/3.07 | | | | (137) all_59_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_59_1, % 16.37/3.07 | | | | all_32_2) = v1 & member(all_59_1, all_32_3) = v0 & ( ~ (v1 % 16.37/3.07 | | | | = 0) | ~ (v0 = 0))) % 16.37/3.07 | | | | % 16.37/3.07 | | | | DELTA: instantiating (136) with fresh symbol all_68_0 gives: % 16.37/3.07 | | | | (138) apply(all_32_10, all_68_0, all_59_1) = 0 & member(all_68_0, % 16.37/3.07 | | | | all_32_5) = 0 & $i(all_68_0) % 16.37/3.07 | | | | % 16.37/3.07 | | | | ALPHA: (138) implies: % 16.37/3.07 | | | | (139) $i(all_68_0) % 16.37/3.07 | | | | (140) member(all_68_0, all_32_5) = 0 % 16.37/3.07 | | | | (141) apply(all_32_10, all_68_0, all_59_1) = 0 % 16.37/3.07 | | | | % 16.37/3.07 | | | | BETA: splitting (137) gives: % 16.37/3.07 | | | | % 16.37/3.07 | | | | Case 1: % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | (142) all_59_0 = 0 % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | REDUCE: (130), (142) imply: % 16.37/3.07 | | | | | (143) $false % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | CLOSE: (143) is inconsistent. % 16.37/3.07 | | | | | % 16.37/3.07 | | | | Case 2: % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | (144) ? [v0: any] : ? [v1: any] : (member(all_59_1, all_32_2) = % 16.37/3.07 | | | | | v1 & member(all_59_1, all_32_3) = v0 & ( ~ (v1 = 0) | ~ % 16.37/3.07 | | | | | (v0 = 0))) % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | DELTA: instantiating (144) with fresh symbols all_74_0, all_74_1 % 16.37/3.07 | | | | | gives: % 16.37/3.07 | | | | | (145) member(all_59_1, all_32_2) = all_74_0 & member(all_59_1, % 16.37/3.07 | | | | | all_32_3) = all_74_1 & ( ~ (all_74_0 = 0) | ~ (all_74_1 = % 16.37/3.07 | | | | | 0)) % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | ALPHA: (145) implies: % 16.37/3.07 | | | | | (146) member(all_59_1, all_32_3) = all_74_1 % 16.37/3.07 | | | | | (147) member(all_59_1, all_32_2) = all_74_0 % 16.37/3.07 | | | | | (148) ~ (all_74_0 = 0) | ~ (all_74_1 = 0) % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | GROUND_INST: instantiating (8) with all_32_10, all_32_7, all_32_8, % 16.37/3.07 | | | | | all_59_1, all_32_3, all_74_1, simplifying with (12), % 16.37/3.07 | | | | | (14), (15), (28), (131), (146) gives: % 16.37/3.07 | | | | | (149) all_74_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, % 16.37/3.07 | | | | | all_32_8) = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, v0, % 16.37/3.07 | | | | | all_59_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 16.37/3.07 | | | | | 0) & member(v0, all_32_7) = v1)) % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | GROUND_INST: instantiating (8) with all_32_10, all_32_6, all_32_8, % 16.37/3.07 | | | | | all_59_1, all_32_2, all_74_0, simplifying with (12), % 16.37/3.07 | | | | | (14), (16), (29), (131), (147) gives: % 16.37/3.07 | | | | | (150) all_74_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, % 16.37/3.07 | | | | | all_32_8) = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, v0, % 16.37/3.07 | | | | | all_59_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 16.37/3.07 | | | | | 0) & member(v0, all_32_6) = v1)) % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | GROUND_INST: instantiating (4) with all_68_0, all_32_7, all_32_6, % 16.37/3.07 | | | | | all_32_5, simplifying with (15), (16), (25), (139), (140) % 16.37/3.07 | | | | | gives: % 16.37/3.07 | | | | | (151) member(all_68_0, all_32_6) = 0 & member(all_68_0, all_32_7) = % 16.37/3.07 | | | | | 0 % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | ALPHA: (151) implies: % 16.37/3.07 | | | | | (152) member(all_68_0, all_32_7) = 0 % 16.37/3.07 | | | | | (153) member(all_68_0, all_32_6) = 0 % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | BETA: splitting (148) gives: % 16.37/3.07 | | | | | % 16.37/3.07 | | | | | Case 1: % 16.37/3.07 | | | | | | % 16.37/3.07 | | | | | | (154) ~ (all_74_0 = 0) % 16.37/3.07 | | | | | | % 16.37/3.07 | | | | | | BETA: splitting (150) gives: % 16.37/3.07 | | | | | | % 16.37/3.07 | | | | | | Case 1: % 16.37/3.07 | | | | | | | % 16.37/3.07 | | | | | | | (155) all_74_0 = 0 % 16.37/3.07 | | | | | | | % 16.37/3.08 | | | | | | | REDUCE: (154), (155) imply: % 16.37/3.08 | | | | | | | (156) $false % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | CLOSE: (156) is inconsistent. % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | Case 2: % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | (157) ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, all_32_8) % 16.37/3.08 | | | | | | | = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, v0, % 16.37/3.08 | | | | | | | all_59_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 16.37/3.08 | | | | | | | = 0) & member(v0, all_32_6) = v1)) % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | BETA: splitting (157) gives: % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | Case 1: % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | (158) ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, % 16.37/3.08 | | | | | | | | all_32_8) = v0) % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | DELTA: instantiating (158) with fresh symbol all_113_0 gives: % 16.37/3.08 | | | | | | | | (159) ~ (all_113_0 = 0) & member(all_59_1, all_32_8) = % 16.37/3.08 | | | | | | | | all_113_0 % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | REF_CLOSE: (9), (135), (159) are inconsistent by sub-proof #1. % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | Case 2: % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | (160) ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_59_1) = 0) % 16.37/3.08 | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 16.37/3.08 | | | | | | | | member(v0, all_32_6) = v1)) % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | GROUND_INST: instantiating (160) with all_68_0, simplifying with % 16.37/3.08 | | | | | | | | (139), (141) gives: % 16.37/3.08 | | | | | | | | (161) ? [v0: int] : ( ~ (v0 = 0) & member(all_68_0, % 16.37/3.08 | | | | | | | | all_32_6) = v0) % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | DELTA: instantiating (161) with fresh symbol all_113_0 gives: % 16.37/3.08 | | | | | | | | (162) ~ (all_113_0 = 0) & member(all_68_0, all_32_6) = % 16.37/3.08 | | | | | | | | all_113_0 % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | ALPHA: (162) implies: % 16.37/3.08 | | | | | | | | (163) ~ (all_113_0 = 0) % 16.37/3.08 | | | | | | | | (164) member(all_68_0, all_32_6) = all_113_0 % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_113_0, all_32_6, % 16.37/3.08 | | | | | | | | all_68_0, simplifying with (153), (164) gives: % 16.37/3.08 | | | | | | | | (165) all_113_0 = 0 % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | REDUCE: (163), (165) imply: % 16.37/3.08 | | | | | | | | (166) $false % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | CLOSE: (166) is inconsistent. % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | End of split % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | End of split % 16.37/3.08 | | | | | | % 16.37/3.08 | | | | | Case 2: % 16.37/3.08 | | | | | | % 16.37/3.08 | | | | | | (167) ~ (all_74_1 = 0) % 16.37/3.08 | | | | | | % 16.37/3.08 | | | | | | BETA: splitting (149) gives: % 16.37/3.08 | | | | | | % 16.37/3.08 | | | | | | Case 1: % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | (168) all_74_1 = 0 % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | REDUCE: (167), (168) imply: % 16.37/3.08 | | | | | | | (169) $false % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | CLOSE: (169) is inconsistent. % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | Case 2: % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | (170) ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, all_32_8) % 16.37/3.08 | | | | | | | = v0) | ! [v0: $i] : ( ~ (apply(all_32_10, v0, % 16.37/3.08 | | | | | | | all_59_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 16.37/3.08 | | | | | | | = 0) & member(v0, all_32_7) = v1)) % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | BETA: splitting (170) gives: % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | | Case 1: % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | (171) ? [v0: int] : ( ~ (v0 = 0) & member(all_59_1, % 16.37/3.08 | | | | | | | | all_32_8) = v0) % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | DELTA: instantiating (171) with fresh symbol all_113_0 gives: % 16.37/3.08 | | | | | | | | (172) ~ (all_113_0 = 0) & member(all_59_1, all_32_8) = % 16.37/3.08 | | | | | | | | all_113_0 % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | REF_CLOSE: (9), (135), (172) are inconsistent by sub-proof #1. % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | Case 2: % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | (173) ! [v0: $i] : ( ~ (apply(all_32_10, v0, all_59_1) = 0) % 16.37/3.08 | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 16.37/3.08 | | | | | | | | member(v0, all_32_7) = v1)) % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | GROUND_INST: instantiating (173) with all_68_0, simplifying with % 16.37/3.08 | | | | | | | | (139), (141) gives: % 16.37/3.08 | | | | | | | | (174) ? [v0: int] : ( ~ (v0 = 0) & member(all_68_0, % 16.37/3.08 | | | | | | | | all_32_7) = v0) % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | DELTA: instantiating (174) with fresh symbol all_114_0 gives: % 16.37/3.08 | | | | | | | | (175) ~ (all_114_0 = 0) & member(all_68_0, all_32_7) = % 16.37/3.08 | | | | | | | | all_114_0 % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | ALPHA: (175) implies: % 16.37/3.08 | | | | | | | | (176) ~ (all_114_0 = 0) % 16.37/3.08 | | | | | | | | (177) member(all_68_0, all_32_7) = all_114_0 % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_114_0, all_32_7, % 16.37/3.08 | | | | | | | | all_68_0, simplifying with (152), (177) gives: % 16.37/3.08 | | | | | | | | (178) all_114_0 = 0 % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | REDUCE: (176), (178) imply: % 16.37/3.08 | | | | | | | | (179) $false % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | | CLOSE: (179) is inconsistent. % 16.37/3.08 | | | | | | | | % 16.37/3.08 | | | | | | | End of split % 16.37/3.08 | | | | | | | % 16.37/3.08 | | | | | | End of split % 16.37/3.08 | | | | | | % 16.37/3.08 | | | | | End of split % 16.37/3.08 | | | | | % 16.37/3.08 | | | | End of split % 16.37/3.08 | | | | % 16.37/3.08 | | | End of split % 16.37/3.08 | | | % 16.37/3.08 | | End of split % 16.37/3.08 | | % 16.37/3.08 | End of split % 16.37/3.08 | % 16.37/3.08 End of proof % 16.37/3.08 % 16.37/3.08 Sub-proof #1 shows that the following formulas are inconsistent: % 16.37/3.08 ---------------------------------------------------------------- % 16.37/3.08 (1) ~ (all_113_0 = 0) & member(all_59_1, all_32_8) = all_113_0 % 16.37/3.08 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.37/3.08 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 16.37/3.08 v0)) % 16.37/3.08 (3) member(all_59_1, all_32_8) = 0 % 16.37/3.08 % 16.37/3.08 Begin of proof % 16.37/3.08 | % 16.37/3.08 | ALPHA: (1) implies: % 16.37/3.08 | (4) ~ (all_113_0 = 0) % 16.37/3.08 | (5) member(all_59_1, all_32_8) = all_113_0 % 16.37/3.08 | % 16.37/3.08 | GROUND_INST: instantiating (2) with 0, all_113_0, all_32_8, all_59_1, % 16.37/3.08 | simplifying with (3), (5) gives: % 16.37/3.08 | (6) all_113_0 = 0 % 16.37/3.08 | % 16.37/3.08 | REDUCE: (4), (6) imply: % 16.37/3.08 | (7) $false % 16.37/3.08 | % 16.37/3.08 | CLOSE: (7) is inconsistent. % 16.37/3.08 | % 16.37/3.08 End of proof % 16.37/3.08 % SZS output end Proof for theBenchmark % 16.37/3.08 % 16.37/3.08 2450ms %------------------------------------------------------------------------------