%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC029+1 : TPTP v8.1.2. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 20:49:16 EDT 2023 % Result : Theorem 27.04s 4.38s % Output : Proof 50.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWC029+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n012.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 : Mon Aug 28 18:40:24 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 4.56/1.36 Prover 1: Preprocessing ... % 4.56/1.37 Prover 4: Preprocessing ... % 4.56/1.41 Prover 3: Preprocessing ... % 4.56/1.41 Prover 2: Preprocessing ... % 4.56/1.41 Prover 0: Preprocessing ... % 4.56/1.41 Prover 5: Preprocessing ... % 4.56/1.42 Prover 6: Preprocessing ... % 14.75/2.73 Prover 2: Proving ... % 15.02/2.79 Prover 1: Constructing countermodel ... % 15.02/2.80 Prover 5: Constructing countermodel ... % 15.02/2.82 Prover 3: Constructing countermodel ... % 15.02/2.84 Prover 6: Proving ... % 20.53/3.55 Prover 0: Proving ... % 20.53/3.55 Prover 4: Constructing countermodel ... % 27.04/4.38 Prover 3: proved (3757ms) % 27.04/4.38 % 27.04/4.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 27.04/4.38 % 27.04/4.39 Prover 2: stopped % 27.04/4.39 Prover 6: stopped % 27.04/4.39 Prover 5: stopped % 27.04/4.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 27.04/4.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 27.04/4.39 Prover 0: stopped % 27.04/4.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 27.04/4.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 27.04/4.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 28.74/4.61 Prover 13: Preprocessing ... % 28.74/4.64 Prover 7: Preprocessing ... % 28.74/4.65 Prover 10: Preprocessing ... % 29.54/4.70 Prover 11: Preprocessing ... % 29.54/4.71 Prover 8: Preprocessing ... % 30.55/4.85 Prover 7: Constructing countermodel ... % 30.55/4.90 Prover 10: Constructing countermodel ... % 31.79/5.03 Prover 13: Constructing countermodel ... % 31.79/5.08 Prover 8: Warning: ignoring some quantifiers % 32.44/5.10 Prover 8: Constructing countermodel ... % 37.45/5.81 Prover 11: Constructing countermodel ... % 49.43/7.39 Prover 1: Found proof (size 161) % 49.43/7.39 Prover 1: proved (6772ms) % 49.43/7.39 Prover 10: stopped % 49.43/7.39 Prover 7: stopped % 49.43/7.39 Prover 8: stopped % 49.43/7.39 Prover 13: stopped % 49.43/7.39 Prover 11: stopped % 49.43/7.39 Prover 4: stopped % 49.43/7.39 % 49.43/7.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 49.43/7.39 % 50.07/7.41 % SZS output start Proof for theBenchmark % 50.07/7.42 Assumptions after simplification: % 50.07/7.42 --------------------------------- % 50.07/7.42 % 50.07/7.42 (ax15) % 50.07/7.45 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 50.07/7.45 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 50.07/7.45 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 50.07/7.45 % 50.07/7.45 (ax16) % 50.07/7.45 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 50.07/7.45 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 50.07/7.45 (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 50.07/7.45 % 50.07/7.45 (ax17) % 50.07/7.45 ssList(nil) = 0 & $i(nil) % 50.07/7.45 % 50.07/7.45 (ax23) % 50.07/7.45 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 50.07/7.45 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 50.07/7.45 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 50.07/7.45 % 50.07/7.45 (ax25) % 50.07/7.45 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 50.07/7.45 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 50.07/7.45 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 50.07/7.45 % 50.07/7.45 (ax26) % 50.07/7.46 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 50.07/7.46 ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 50.07/7.46 (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 50.07/7.46 % 50.07/7.46 (ax59) % 50.07/7.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 50.07/7.46 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 50.07/7.46 (v2 = 0) | v3 = 0))) % 50.07/7.46 % 50.07/7.46 (ax61) % 50.07/7.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 50.07/7.46 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 50.07/7.46 (v2 = 0) | v3 = 0))) % 50.07/7.46 % 50.07/7.46 (ax63) % 50.07/7.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 50.07/7.46 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 50.07/7.46 (v2 = 0) | v3 = 0))) % 50.07/7.46 % 50.07/7.46 (ax65) % 50.07/7.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 50.07/7.46 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 50.07/7.46 (v2 = 0) | v3 = 0))) % 50.07/7.46 % 50.07/7.46 (ax68) % 50.07/7.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 50.07/7.46 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 50.07/7.46 ~ (v2 = 0) | v3 = 0))) % 50.07/7.46 % 50.07/7.46 (ax71) % 50.07/7.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 50.07/7.46 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 50.07/7.46 ~ (v2 = 0) | v3 = 0))) % 50.07/7.46 % 50.07/7.46 (ax73) % 50.07/7.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 50.07/7.46 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 50.07/7.46 (v2 = 0) | v3 = 0))) % 50.07/7.46 % 50.07/7.46 (ax81) % 50.07/7.46 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 50.07/7.46 [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | % 50.07/7.46 ~ $i(v1) | ? [v4: any] : ? [v5: $i] : (cons(v1, v0) = v5 & ssItem(v1) = % 50.07/7.46 v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3)))) % 50.07/7.46 % 50.07/7.46 (ax83) % 50.07/7.46 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 50.07/7.46 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 50.07/7.46 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1 % 50.07/7.46 = nil) | ~ (v0 = nil) | v2 = nil)))) % 50.07/7.46 % 50.07/7.46 (co1) % 50.07/7.47 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 50.07/7.47 0 & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: any] : (v2 = % 50.07/7.47 v0 & neq(v1, nil) = v3 & ( ~ (v3 = 0) | ? [v4: $i] : ? [v5: $i] : % 50.07/7.47 (cons(v4, nil) = v5 & ssItem(v4) = 0 & $i(v5) & $i(v4) & ? [v6: $i] % 50.07/7.47 : (ssList(v6) = 0 & app(v6, v5) = v0 & app(v5, v6) = v1 & % 50.07/7.47 $i(v6)))) & ( ~ (v1 = nil) | v0 = nil) & ((v1 = nil & ~ (v0 = % 50.07/7.47 nil)) | (v0 = nil & ~ (v1 = nil))))))) % 50.07/7.47 % 50.07/7.47 (function-axioms) % 50.07/7.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 50.07/7.47 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 50.07/7.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 50.07/7.47 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 50.07/7.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 50.07/7.47 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 50.07/7.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 50.07/7.47 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 50.07/7.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 50.07/7.47 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 50.07/7.47 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 50.07/7.47 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 50.07/7.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 50.07/7.47 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 50.07/7.47 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 50.07/7.47 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 50.07/7.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.07/7.47 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 50.07/7.47 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 50.07/7.47 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 50.07/7.47 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 50.07/7.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 50.07/7.47 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 50.07/7.47 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 50.07/7.47 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 50.07/7.47 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.07/7.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 50.07/7.47 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.07/7.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 50.07/7.47 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.07/7.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 50.07/7.47 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.07/7.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 50.07/7.47 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.07/7.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 50.07/7.47 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.07/7.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 50.07/7.47 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.07/7.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 50.07/7.47 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.07/7.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 50.07/7.47 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 50.07/7.47 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 50.07/7.47 % 50.07/7.47 Further assumptions not needed in the proof: % 50.07/7.47 -------------------------------------------- % 50.07/7.48 ax1, ax10, ax11, ax12, ax13, ax14, ax18, ax19, ax2, ax20, ax21, ax22, ax24, % 50.07/7.48 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, % 50.07/7.48 ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, % 50.07/7.48 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, % 50.07/7.48 ax66, ax67, ax69, ax7, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax8, % 50.07/7.48 ax80, ax82, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 50.07/7.48 ax94, ax95 % 50.07/7.48 % 50.07/7.48 Those formulas are unsatisfiable: % 50.07/7.48 --------------------------------- % 50.07/7.48 % 50.07/7.48 Begin of proof % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax17) implies: % 50.07/7.48 | (1) ssList(nil) = 0 % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax59) implies: % 50.07/7.48 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.07/7.48 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 50.07/7.48 | ~ (v2 = 0) | v3 = 0))) % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax61) implies: % 50.07/7.48 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.07/7.48 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 50.07/7.48 | ( ~ (v2 = 0) | v3 = 0))) % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax63) implies: % 50.07/7.48 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.07/7.48 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 50.07/7.48 | ( ~ (v2 = 0) | v3 = 0))) % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax65) implies: % 50.07/7.48 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.07/7.48 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 50.07/7.48 | & ( ~ (v2 = 0) | v3 = 0))) % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax68) implies: % 50.07/7.48 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.07/7.48 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 50.07/7.48 | & ( ~ (v2 = 0) | v3 = 0))) % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax71) implies: % 50.07/7.48 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.07/7.48 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 50.07/7.48 | & ( ~ (v2 = 0) | v3 = 0))) % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax73) implies: % 50.07/7.48 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.07/7.48 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 50.07/7.48 | ( ~ (v2 = 0) | v3 = 0))) % 50.07/7.48 | % 50.07/7.48 | ALPHA: (ax81) implies: % 50.42/7.48 | (9) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 50.42/7.48 | $i] : ! [v3: $i] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = % 50.42/7.48 | v3) | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : (cons(v1, v0) = v5 % 50.42/7.48 | & ssItem(v1) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3)))) % 50.42/7.48 | % 50.42/7.48 | ALPHA: (ax83) implies: % 50.42/7.49 | (10) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 50.42/7.49 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 % 50.42/7.49 | = 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = % 50.42/7.49 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil)))) % 50.42/7.49 | % 50.42/7.49 | ALPHA: (co1) implies: % 50.42/7.49 | (11) $i(nil) % 50.42/7.49 | (12) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 50.42/7.49 | & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: any] : % 50.42/7.49 | (v2 = v0 & neq(v1, nil) = v3 & ( ~ (v3 = 0) | ? [v4: $i] : ? % 50.42/7.49 | [v5: $i] : (cons(v4, nil) = v5 & ssItem(v4) = 0 & $i(v5) & % 50.42/7.49 | $i(v4) & ? [v6: $i] : (ssList(v6) = 0 & app(v6, v5) = v0 % 50.42/7.49 | & app(v5, v6) = v1 & $i(v6)))) & ( ~ (v1 = nil) | v0 = % 50.42/7.49 | nil) & ((v1 = nil & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = % 50.42/7.49 | nil))))))) % 50.42/7.49 | % 50.42/7.49 | ALPHA: (function-axioms) implies: % 50.42/7.49 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 50.42/7.49 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 50.42/7.49 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 50.42/7.49 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 50.42/7.49 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.42/7.49 | (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 50.42/7.49 | % 50.42/7.49 | DELTA: instantiating (12) with fresh symbol all_93_0 gives: % 50.42/7.49 | (16) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 50.42/7.49 | $i(v0) & ? [v1: $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: any] : (v1 % 50.42/7.49 | = all_93_0 & neq(v0, nil) = v2 & ( ~ (v2 = 0) | ? [v3: $i] : ? % 50.42/7.49 | [v4: $i] : (cons(v3, nil) = v4 & ssItem(v3) = 0 & $i(v4) & % 50.42/7.49 | $i(v3) & ? [v5: $i] : (ssList(v5) = 0 & app(v5, v4) = % 50.42/7.49 | all_93_0 & app(v4, v5) = v0 & $i(v5)))) & ( ~ (v0 = nil) | % 50.42/7.49 | all_93_0 = nil) & ((v0 = nil & ~ (all_93_0 = nil)) | % 50.42/7.49 | (all_93_0 = nil & ~ (v0 = nil)))))) % 50.42/7.49 | % 50.42/7.49 | ALPHA: (16) implies: % 50.42/7.50 | (17) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 50.42/7.50 | & $i(v1) & ? [v2: any] : (v1 = all_93_0 & neq(v0, nil) = v2 & ( ~ % 50.42/7.50 | (v2 = 0) | ? [v3: $i] : ? [v4: $i] : (cons(v3, nil) = v4 & % 50.42/7.50 | ssItem(v3) = 0 & $i(v4) & $i(v3) & ? [v5: $i] : (ssList(v5) % 50.42/7.50 | = 0 & app(v5, v4) = all_93_0 & app(v4, v5) = v0 & % 50.42/7.50 | $i(v5)))) & ( ~ (v0 = nil) | all_93_0 = nil) & ((v0 = nil % 50.42/7.50 | & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ (v0 = % 50.42/7.50 | nil)))))) % 50.42/7.50 | % 50.42/7.50 | DELTA: instantiating (17) with fresh symbol all_97_0 gives: % 50.42/7.50 | (18) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: $i] : (ssList(v0) = 0 & % 50.42/7.50 | $i(v0) & ? [v1: any] : (v0 = all_93_0 & neq(all_97_0, nil) = v1 & ( % 50.42/7.50 | ~ (v1 = 0) | ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) = v3 & % 50.42/7.50 | ssItem(v2) = 0 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = % 50.42/7.50 | 0 & app(v4, v3) = all_93_0 & app(v3, v4) = all_97_0 & % 50.42/7.50 | $i(v4)))) & ( ~ (all_97_0 = nil) | all_93_0 = nil) & % 50.42/7.50 | ((all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 50.42/7.50 | (all_97_0 = nil))))) % 50.42/7.50 | % 50.42/7.50 | ALPHA: (18) implies: % 50.42/7.50 | (19) $i(all_97_0) % 50.42/7.50 | (20) ssList(all_97_0) = 0 % 50.42/7.50 | (21) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: any] : (v0 = all_93_0 % 50.42/7.50 | & neq(all_97_0, nil) = v1 & ( ~ (v1 = 0) | ? [v2: $i] : ? [v3: % 50.42/7.50 | $i] : (cons(v2, nil) = v3 & ssItem(v2) = 0 & $i(v3) & $i(v2) & % 50.42/7.50 | ? [v4: $i] : (ssList(v4) = 0 & app(v4, v3) = all_93_0 & % 50.42/7.50 | app(v3, v4) = all_97_0 & $i(v4)))) & ( ~ (all_97_0 = nil) | % 50.42/7.50 | all_93_0 = nil) & ((all_97_0 = nil & ~ (all_93_0 = nil)) | % 50.42/7.50 | (all_93_0 = nil & ~ (all_97_0 = nil))))) % 50.42/7.50 | % 50.42/7.50 | DELTA: instantiating (21) with fresh symbol all_99_0 gives: % 50.42/7.50 | (22) ssList(all_99_0) = 0 & $i(all_99_0) & ? [v0: any] : (all_99_0 = % 50.42/7.50 | all_93_0 & neq(all_97_0, nil) = v0 & ( ~ (v0 = 0) | ? [v1: $i] : ? % 50.42/7.50 | [v2: $i] : (cons(v1, nil) = v2 & ssItem(v1) = 0 & $i(v2) & $i(v1) % 50.42/7.50 | & ? [v3: $i] : (ssList(v3) = 0 & app(v3, v2) = all_93_0 & % 50.42/7.50 | app(v2, v3) = all_97_0 & $i(v3)))) & ( ~ (all_97_0 = nil) | % 50.42/7.50 | all_93_0 = nil) & ((all_97_0 = nil & ~ (all_93_0 = nil)) | % 50.42/7.50 | (all_93_0 = nil & ~ (all_97_0 = nil)))) % 50.42/7.50 | % 50.42/7.50 | ALPHA: (22) implies: % 50.42/7.50 | (23) ssList(all_99_0) = 0 % 50.42/7.50 | (24) ? [v0: any] : (all_99_0 = all_93_0 & neq(all_97_0, nil) = v0 & ( ~ % 50.42/7.50 | (v0 = 0) | ? [v1: $i] : ? [v2: $i] : (cons(v1, nil) = v2 & % 50.42/7.50 | ssItem(v1) = 0 & $i(v2) & $i(v1) & ? [v3: $i] : (ssList(v3) = 0 % 50.42/7.50 | & app(v3, v2) = all_93_0 & app(v2, v3) = all_97_0 & $i(v3)))) % 50.42/7.50 | & ( ~ (all_97_0 = nil) | all_93_0 = nil) & ((all_97_0 = nil & ~ % 50.42/7.50 | (all_93_0 = nil)) | (all_93_0 = nil & ~ (all_97_0 = nil)))) % 50.42/7.50 | % 50.42/7.50 | DELTA: instantiating (24) with fresh symbol all_101_0 gives: % 50.42/7.51 | (25) all_99_0 = all_93_0 & neq(all_97_0, nil) = all_101_0 & ( ~ (all_101_0 % 50.42/7.51 | = 0) | ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & % 50.42/7.51 | ssItem(v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & % 50.42/7.51 | app(v2, v1) = all_93_0 & app(v1, v2) = all_97_0 & $i(v2)))) & ( % 50.42/7.51 | ~ (all_97_0 = nil) | all_93_0 = nil) & ((all_97_0 = nil & ~ % 50.42/7.51 | (all_93_0 = nil)) | (all_93_0 = nil & ~ (all_97_0 = nil))) % 50.42/7.51 | % 50.42/7.51 | ALPHA: (25) implies: % 50.42/7.51 | (26) all_99_0 = all_93_0 % 50.42/7.51 | (27) neq(all_97_0, nil) = all_101_0 % 50.42/7.51 | (28) (all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 50.42/7.51 | (all_97_0 = nil)) % 50.42/7.51 | (29) ~ (all_97_0 = nil) | all_93_0 = nil % 50.42/7.51 | (30) ~ (all_101_0 = 0) | ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & % 50.42/7.51 | ssItem(v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & % 50.42/7.51 | app(v2, v1) = all_93_0 & app(v1, v2) = all_97_0 & $i(v2))) % 50.42/7.51 | % 50.42/7.51 | REDUCE: (23), (26) imply: % 50.42/7.51 | (31) ssList(all_93_0) = 0 % 50.42/7.51 | % 50.42/7.51 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (11) gives: % 50.42/7.51 | (32) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.42/7.51 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 50.42/7.51 | ( ~ (v2 = 0) | v3 = nil))) % 50.42/7.51 | % 50.42/7.51 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (11) gives: % 50.42/7.51 | (33) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.42/7.51 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 50.42/7.51 | ( ~ (v2 = 0) | v3 = v0))) % 50.42/7.51 | % 50.42/7.51 | GROUND_INST: instantiating (ax16) with nil, simplifying with (1), (11) gives: % 50.42/7.51 | (34) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 50.42/7.51 | [v2: any] : ? [v3: any] : (ssList(v1) = v3 & ssItem(v0) = v2 & ( ~ % 50.42/7.51 | (v2 = 0) | v3 = 0))) % 50.42/7.51 | % 50.42/7.51 | GROUND_INST: instantiating (ax15) with all_97_0, simplifying with (19), (20) % 50.42/7.51 | gives: % 50.42/7.51 | (35) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_0, v0) = v1) | ~ $i(v0) % 50.42/7.51 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 50.42/7.51 | ~ (v0 = all_97_0)) & (v1 = 0 | v0 = all_97_0))) % 50.42/7.51 | % 50.42/7.51 | GROUND_INST: instantiating (35) with nil, all_101_0, simplifying with (11), % 50.42/7.51 | (27) gives: % 50.42/7.51 | (36) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_101_0 = 0) % 50.42/7.51 | | ~ (all_97_0 = nil)) & (all_101_0 = 0 | all_97_0 = nil)) % 50.42/7.51 | % 50.42/7.51 | BETA: splitting (28) gives: % 50.42/7.51 | % 50.42/7.51 | Case 1: % 50.42/7.51 | | % 50.42/7.51 | | (37) all_97_0 = nil & ~ (all_93_0 = nil) % 50.42/7.51 | | % 50.42/7.51 | | ALPHA: (37) implies: % 50.42/7.51 | | (38) all_97_0 = nil % 50.42/7.51 | | (39) ~ (all_93_0 = nil) % 50.42/7.51 | | % 50.42/7.51 | | BETA: splitting (29) gives: % 50.42/7.51 | | % 50.42/7.51 | | Case 1: % 50.42/7.51 | | | % 50.42/7.51 | | | (40) ~ (all_97_0 = nil) % 50.42/7.51 | | | % 50.42/7.51 | | | REDUCE: (38), (40) imply: % 50.42/7.51 | | | (41) $false % 50.42/7.51 | | | % 50.42/7.51 | | | CLOSE: (41) is inconsistent. % 50.42/7.51 | | | % 50.42/7.51 | | Case 2: % 50.42/7.51 | | | % 50.42/7.51 | | | (42) all_93_0 = nil % 50.42/7.51 | | | % 50.42/7.51 | | | REDUCE: (39), (42) imply: % 50.42/7.51 | | | (43) $false % 50.42/7.51 | | | % 50.42/7.51 | | | CLOSE: (43) is inconsistent. % 50.42/7.51 | | | % 50.42/7.51 | | End of split % 50.42/7.51 | | % 50.42/7.52 | Case 2: % 50.42/7.52 | | % 50.42/7.52 | | (44) all_93_0 = nil & ~ (all_97_0 = nil) % 50.42/7.52 | | % 50.42/7.52 | | ALPHA: (44) implies: % 50.42/7.52 | | (45) all_93_0 = nil % 50.42/7.52 | | (46) ~ (all_97_0 = nil) % 50.42/7.52 | | % 50.42/7.52 | | BETA: splitting (36) gives: % 50.42/7.52 | | % 50.42/7.52 | | Case 1: % 50.42/7.52 | | | % 50.42/7.52 | | | (47) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 50.42/7.52 | | | % 50.42/7.52 | | | DELTA: instantiating (47) with fresh symbol all_278_0 gives: % 50.42/7.52 | | | (48) ~ (all_278_0 = 0) & ssList(nil) = all_278_0 % 50.42/7.52 | | | % 50.42/7.52 | | | ALPHA: (48) implies: % 50.42/7.52 | | | (49) ~ (all_278_0 = 0) % 50.42/7.52 | | | (50) ssList(nil) = all_278_0 % 50.42/7.52 | | | % 50.42/7.52 | | | DELTA: instantiating (47) with fresh symbol all_280_0 gives: % 50.42/7.52 | | | (51) ~ (all_280_0 = 0) & ssList(nil) = all_280_0 % 50.42/7.52 | | | % 50.42/7.52 | | | ALPHA: (51) implies: % 50.42/7.52 | | | (52) ssList(nil) = all_280_0 % 50.42/7.52 | | | % 50.42/7.52 | | | GROUND_INST: instantiating (14) with 0, all_280_0, nil, simplifying with % 50.42/7.52 | | | (1), (52) gives: % 50.42/7.52 | | | (53) all_280_0 = 0 % 50.42/7.52 | | | % 50.42/7.52 | | | GROUND_INST: instantiating (14) with all_278_0, all_280_0, nil, % 50.42/7.52 | | | simplifying with (50), (52) gives: % 50.42/7.52 | | | (54) all_280_0 = all_278_0 % 50.42/7.52 | | | % 50.42/7.52 | | | COMBINE_EQS: (53), (54) imply: % 50.42/7.52 | | | (55) all_278_0 = 0 % 50.42/7.52 | | | % 50.42/7.52 | | | REDUCE: (49), (55) imply: % 50.42/7.52 | | | (56) $false % 50.42/7.52 | | | % 50.42/7.52 | | | CLOSE: (56) is inconsistent. % 50.42/7.52 | | | % 50.42/7.52 | | Case 2: % 50.42/7.52 | | | % 50.42/7.52 | | | (57) ( ~ (all_101_0 = 0) | ~ (all_97_0 = nil)) & (all_101_0 = 0 | % 50.42/7.52 | | | all_97_0 = nil) % 50.42/7.52 | | | % 50.42/7.52 | | | ALPHA: (57) implies: % 50.42/7.52 | | | (58) all_101_0 = 0 | all_97_0 = nil % 50.42/7.52 | | | % 50.42/7.52 | | | BETA: splitting (58) gives: % 50.42/7.52 | | | % 50.42/7.52 | | | Case 1: % 50.42/7.52 | | | | % 50.42/7.52 | | | | (59) all_97_0 = nil % 50.42/7.52 | | | | % 50.42/7.52 | | | | REDUCE: (46), (59) imply: % 50.42/7.52 | | | | (60) $false % 50.42/7.52 | | | | % 50.42/7.52 | | | | CLOSE: (60) is inconsistent. % 50.42/7.52 | | | | % 50.42/7.52 | | | Case 2: % 50.42/7.52 | | | | % 50.42/7.52 | | | | (61) all_101_0 = 0 % 50.42/7.52 | | | | % 50.42/7.52 | | | | BETA: splitting (30) gives: % 50.42/7.52 | | | | % 50.42/7.52 | | | | Case 1: % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | (62) ~ (all_101_0 = 0) % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | REDUCE: (61), (62) imply: % 50.42/7.52 | | | | | (63) $false % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | CLOSE: (63) is inconsistent. % 50.42/7.52 | | | | | % 50.42/7.52 | | | | Case 2: % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | (64) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = % 50.42/7.52 | | | | | 0 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & % 50.42/7.52 | | | | | app(v2, v1) = all_93_0 & app(v1, v2) = all_97_0 & $i(v2))) % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | DELTA: instantiating (64) with fresh symbols all_316_0, all_316_1 % 50.42/7.52 | | | | | gives: % 50.42/7.52 | | | | | (65) cons(all_316_1, nil) = all_316_0 & ssItem(all_316_1) = 0 & % 50.42/7.52 | | | | | $i(all_316_0) & $i(all_316_1) & ? [v0: $i] : (ssList(v0) = 0 % 50.42/7.52 | | | | | & app(v0, all_316_0) = all_93_0 & app(all_316_0, v0) = % 50.42/7.52 | | | | | all_97_0 & $i(v0)) % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | ALPHA: (65) implies: % 50.42/7.52 | | | | | (66) $i(all_316_1) % 50.42/7.52 | | | | | (67) $i(all_316_0) % 50.42/7.52 | | | | | (68) ssItem(all_316_1) = 0 % 50.42/7.52 | | | | | (69) cons(all_316_1, nil) = all_316_0 % 50.42/7.52 | | | | | (70) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_316_0) = all_93_0 % 50.42/7.52 | | | | | & app(all_316_0, v0) = all_97_0 & $i(v0)) % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | DELTA: instantiating (70) with fresh symbol all_318_0 gives: % 50.42/7.52 | | | | | (71) ssList(all_318_0) = 0 & app(all_318_0, all_316_0) = all_93_0 & % 50.42/7.52 | | | | | app(all_316_0, all_318_0) = all_97_0 & $i(all_318_0) % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | ALPHA: (71) implies: % 50.42/7.52 | | | | | (72) $i(all_318_0) % 50.42/7.52 | | | | | (73) app(all_316_0, all_318_0) = all_97_0 % 50.42/7.52 | | | | | (74) app(all_318_0, all_316_0) = all_93_0 % 50.42/7.52 | | | | | (75) ssList(all_318_0) = 0 % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | REDUCE: (45), (74) imply: % 50.42/7.52 | | | | | (76) app(all_318_0, all_316_0) = nil % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | GROUND_INST: instantiating (32) with all_316_1, all_316_0, simplifying % 50.42/7.52 | | | | | with (66), (69) gives: % 50.42/7.52 | | | | | (77) ? [v0: any] : ? [v1: $i] : (tl(all_316_0) = v1 & % 50.42/7.52 | | | | | ssItem(all_316_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | GROUND_INST: instantiating (33) with all_316_1, all_316_0, simplifying % 50.42/7.52 | | | | | with (66), (69) gives: % 50.42/7.52 | | | | | (78) ? [v0: any] : ? [v1: $i] : (hd(all_316_0) = v1 & % 50.42/7.52 | | | | | ssItem(all_316_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 50.42/7.52 | | | | | all_316_1)) % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | GROUND_INST: instantiating (8) with all_316_1, all_316_0, simplifying % 50.42/7.52 | | | | | with (66), (69) gives: % 50.42/7.52 | | | | | (79) ? [v0: any] : ? [v1: any] : (equalelemsP(all_316_0) = v1 & % 50.42/7.52 | | | | | ssItem(all_316_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.52 | | | | | % 50.42/7.52 | | | | | GROUND_INST: instantiating (7) with all_316_1, all_316_0, simplifying % 50.42/7.52 | | | | | with (66), (69) gives: % 50.42/7.53 | | | | | (80) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_316_0) = v1 % 50.42/7.53 | | | | | & ssItem(all_316_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (6) with all_316_1, all_316_0, simplifying % 50.42/7.53 | | | | | with (66), (69) gives: % 50.42/7.53 | | | | | (81) ? [v0: any] : ? [v1: any] : (strictorderedP(all_316_0) = v1 % 50.42/7.53 | | | | | & ssItem(all_316_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (5) with all_316_1, all_316_0, simplifying % 50.42/7.53 | | | | | with (66), (69) gives: % 50.42/7.53 | | | | | (82) ? [v0: any] : ? [v1: any] : (totalorderedP(all_316_0) = v1 & % 50.42/7.53 | | | | | ssItem(all_316_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (4) with all_316_1, all_316_0, simplifying % 50.42/7.53 | | | | | with (66), (69) gives: % 50.42/7.53 | | | | | (83) ? [v0: any] : ? [v1: any] : (strictorderP(all_316_0) = v1 & % 50.42/7.53 | | | | | ssItem(all_316_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (3) with all_316_1, all_316_0, simplifying % 50.42/7.53 | | | | | with (66), (69) gives: % 50.42/7.53 | | | | | (84) ? [v0: any] : ? [v1: any] : (totalorderP(all_316_0) = v1 & % 50.42/7.53 | | | | | ssItem(all_316_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (2) with all_316_1, all_316_0, simplifying % 50.42/7.53 | | | | | with (66), (69) gives: % 50.42/7.53 | | | | | (85) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_316_0) = v1 & % 50.42/7.53 | | | | | ssItem(all_316_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (34) with all_316_1, all_316_0, simplifying % 50.42/7.53 | | | | | with (66), (69) gives: % 50.42/7.53 | | | | | (86) ? [v0: any] : ? [v1: any] : (ssList(all_316_0) = v1 & % 50.42/7.53 | | | | | ssItem(all_316_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (9) with all_318_0, simplifying with (72), % 50.42/7.53 | | | | | (75) gives: % 50.42/7.53 | | | | | (87) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, nil) = % 50.42/7.53 | | | | | v1) | ~ (app(v1, all_318_0) = v2) | ~ $i(v0) | ? [v3: % 50.42/7.53 | | | | | any] : ? [v4: $i] : (cons(v0, all_318_0) = v4 & % 50.42/7.53 | | | | | ssItem(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (ax26) with all_318_0, simplifying with % 50.42/7.53 | | | | | (72), (75) gives: % 50.42/7.53 | | | | | (88) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_318_0, v0) = v1) | ~ % 50.42/7.53 | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : (ssList(v1) = v3 & % 50.42/7.53 | | | | | ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (10) with all_318_0, simplifying with (72), % 50.42/7.53 | | | | | (75) gives: % 50.42/7.53 | | | | | (89) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_318_0, v0) = v1) | ~ % 50.42/7.53 | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( % 50.42/7.53 | | | | | ~ (v1 = nil) | (v0 = nil & all_318_0 = nil)) & ( ~ (v0 = % 50.42/7.53 | | | | | nil) | ~ (all_318_0 = nil) | v1 = nil))) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (89) with all_316_0, nil, simplifying with % 50.42/7.53 | | | | | (67), (76) gives: % 50.42/7.53 | | | | | (90) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_316_0) = v0) | % 50.42/7.53 | | | | | (all_318_0 = nil & all_316_0 = nil) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (87) with all_316_1, all_316_0, all_97_0, % 50.42/7.53 | | | | | simplifying with (66), (69), (73) gives: % 50.42/7.53 | | | | | (91) ? [v0: any] : ? [v1: $i] : (cons(all_316_1, all_318_0) = v1 % 50.42/7.53 | | | | | & ssItem(all_316_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 50.42/7.53 | | | | | all_97_0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | GROUND_INST: instantiating (88) with all_316_0, nil, simplifying with % 50.42/7.53 | | | | | (67), (76) gives: % 50.42/7.53 | | | | | (92) ? [v0: any] : ? [v1: any] : (ssList(all_316_0) = v0 & % 50.42/7.53 | | | | | ssList(nil) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | DELTA: instantiating (86) with fresh symbols all_587_0, all_587_1 % 50.42/7.53 | | | | | gives: % 50.42/7.53 | | | | | (93) ssList(all_316_0) = all_587_0 & ssItem(all_316_1) = all_587_1 % 50.42/7.53 | | | | | & ( ~ (all_587_1 = 0) | all_587_0 = 0) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | ALPHA: (93) implies: % 50.42/7.53 | | | | | (94) ssItem(all_316_1) = all_587_1 % 50.42/7.53 | | | | | (95) ssList(all_316_0) = all_587_0 % 50.42/7.53 | | | | | (96) ~ (all_587_1 = 0) | all_587_0 = 0 % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | DELTA: instantiating (80) with fresh symbols all_589_0, all_589_1 % 50.42/7.53 | | | | | gives: % 50.42/7.53 | | | | | (97) duplicatefreeP(all_316_0) = all_589_0 & ssItem(all_316_1) = % 50.42/7.53 | | | | | all_589_1 & ( ~ (all_589_1 = 0) | all_589_0 = 0) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | ALPHA: (97) implies: % 50.42/7.53 | | | | | (98) ssItem(all_316_1) = all_589_1 % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | DELTA: instantiating (79) with fresh symbols all_591_0, all_591_1 % 50.42/7.53 | | | | | gives: % 50.42/7.53 | | | | | (99) equalelemsP(all_316_0) = all_591_0 & ssItem(all_316_1) = % 50.42/7.53 | | | | | all_591_1 & ( ~ (all_591_1 = 0) | all_591_0 = 0) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | ALPHA: (99) implies: % 50.42/7.53 | | | | | (100) ssItem(all_316_1) = all_591_1 % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | DELTA: instantiating (85) with fresh symbols all_593_0, all_593_1 % 50.42/7.53 | | | | | gives: % 50.42/7.53 | | | | | (101) cyclefreeP(all_316_0) = all_593_0 & ssItem(all_316_1) = % 50.42/7.53 | | | | | all_593_1 & ( ~ (all_593_1 = 0) | all_593_0 = 0) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | ALPHA: (101) implies: % 50.42/7.53 | | | | | (102) ssItem(all_316_1) = all_593_1 % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | DELTA: instantiating (84) with fresh symbols all_595_0, all_595_1 % 50.42/7.53 | | | | | gives: % 50.42/7.53 | | | | | (103) totalorderP(all_316_0) = all_595_0 & ssItem(all_316_1) = % 50.42/7.53 | | | | | all_595_1 & ( ~ (all_595_1 = 0) | all_595_0 = 0) % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | ALPHA: (103) implies: % 50.42/7.53 | | | | | (104) ssItem(all_316_1) = all_595_1 % 50.42/7.53 | | | | | % 50.42/7.53 | | | | | DELTA: instantiating (83) with fresh symbols all_597_0, all_597_1 % 50.42/7.53 | | | | | gives: % 50.42/7.54 | | | | | (105) strictorderP(all_316_0) = all_597_0 & ssItem(all_316_1) = % 50.42/7.54 | | | | | all_597_1 & ( ~ (all_597_1 = 0) | all_597_0 = 0) % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | ALPHA: (105) implies: % 50.42/7.54 | | | | | (106) ssItem(all_316_1) = all_597_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | DELTA: instantiating (82) with fresh symbols all_599_0, all_599_1 % 50.42/7.54 | | | | | gives: % 50.42/7.54 | | | | | (107) totalorderedP(all_316_0) = all_599_0 & ssItem(all_316_1) = % 50.42/7.54 | | | | | all_599_1 & ( ~ (all_599_1 = 0) | all_599_0 = 0) % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | ALPHA: (107) implies: % 50.42/7.54 | | | | | (108) ssItem(all_316_1) = all_599_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | DELTA: instantiating (81) with fresh symbols all_601_0, all_601_1 % 50.42/7.54 | | | | | gives: % 50.42/7.54 | | | | | (109) strictorderedP(all_316_0) = all_601_0 & ssItem(all_316_1) = % 50.42/7.54 | | | | | all_601_1 & ( ~ (all_601_1 = 0) | all_601_0 = 0) % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | ALPHA: (109) implies: % 50.42/7.54 | | | | | (110) ssItem(all_316_1) = all_601_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | DELTA: instantiating (78) with fresh symbols all_603_0, all_603_1 % 50.42/7.54 | | | | | gives: % 50.42/7.54 | | | | | (111) hd(all_316_0) = all_603_0 & ssItem(all_316_1) = all_603_1 & % 50.42/7.54 | | | | | $i(all_603_0) & ( ~ (all_603_1 = 0) | all_603_0 = all_316_1) % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | ALPHA: (111) implies: % 50.42/7.54 | | | | | (112) ssItem(all_316_1) = all_603_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | DELTA: instantiating (77) with fresh symbols all_605_0, all_605_1 % 50.42/7.54 | | | | | gives: % 50.42/7.54 | | | | | (113) tl(all_316_0) = all_605_0 & ssItem(all_316_1) = all_605_1 & % 50.42/7.54 | | | | | $i(all_605_0) & ( ~ (all_605_1 = 0) | all_605_0 = nil) % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | ALPHA: (113) implies: % 50.42/7.54 | | | | | (114) ssItem(all_316_1) = all_605_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | DELTA: instantiating (91) with fresh symbols all_607_0, all_607_1 % 50.42/7.54 | | | | | gives: % 50.42/7.54 | | | | | (115) cons(all_316_1, all_318_0) = all_607_0 & ssItem(all_316_1) = % 50.42/7.54 | | | | | all_607_1 & $i(all_607_0) & ( ~ (all_607_1 = 0) | all_607_0 = % 50.42/7.54 | | | | | all_97_0) % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | ALPHA: (115) implies: % 50.42/7.54 | | | | | (116) ssItem(all_316_1) = all_607_1 % 50.42/7.54 | | | | | (117) cons(all_316_1, all_318_0) = all_607_0 % 50.42/7.54 | | | | | (118) ~ (all_607_1 = 0) | all_607_0 = all_97_0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | DELTA: instantiating (92) with fresh symbols all_609_0, all_609_1 % 50.42/7.54 | | | | | gives: % 50.42/7.54 | | | | | (119) ssList(all_316_0) = all_609_1 & ssList(nil) = all_609_0 & ( ~ % 50.42/7.54 | | | | | (all_609_1 = 0) | all_609_0 = 0) % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | ALPHA: (119) implies: % 50.42/7.54 | | | | | (120) ssList(all_316_0) = all_609_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_591_1, all_593_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (100), (102) gives: % 50.42/7.54 | | | | | (121) all_593_1 = all_591_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_593_1, all_597_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (102), (106) gives: % 50.42/7.54 | | | | | (122) all_597_1 = all_593_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_597_1, all_599_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (106), (108) gives: % 50.42/7.54 | | | | | (123) all_599_1 = all_597_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_599_1, all_601_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (108), (110) gives: % 50.42/7.54 | | | | | (124) all_601_1 = all_599_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with 0, all_603_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (68), (112) gives: % 50.42/7.54 | | | | | (125) all_603_1 = 0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_595_1, all_603_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (104), (112) gives: % 50.42/7.54 | | | | | (126) all_603_1 = all_595_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_601_1, all_605_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (110), (114) gives: % 50.42/7.54 | | | | | (127) all_605_1 = all_601_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_587_1, all_605_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (94), (114) gives: % 50.42/7.54 | | | | | (128) all_605_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_595_1, all_607_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (104), (116) gives: % 50.42/7.54 | | | | | (129) all_607_1 = all_595_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_593_1, all_607_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (102), (116) gives: % 50.42/7.54 | | | | | (130) all_607_1 = all_593_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (13) with all_589_1, all_607_1, all_316_1, % 50.42/7.54 | | | | | simplifying with (98), (116) gives: % 50.42/7.54 | | | | | (131) all_607_1 = all_589_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | GROUND_INST: instantiating (14) with all_587_0, all_609_1, all_316_0, % 50.42/7.54 | | | | | simplifying with (95), (120) gives: % 50.42/7.54 | | | | | (132) all_609_1 = all_587_0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (130), (131) imply: % 50.42/7.54 | | | | | (133) all_593_1 = all_589_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (133) implies: % 50.42/7.54 | | | | | (134) all_593_1 = all_589_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (129), (131) imply: % 50.42/7.54 | | | | | (135) all_595_1 = all_589_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (135) implies: % 50.42/7.54 | | | | | (136) all_595_1 = all_589_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (127), (128) imply: % 50.42/7.54 | | | | | (137) all_601_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (137) implies: % 50.42/7.54 | | | | | (138) all_601_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (125), (126) imply: % 50.42/7.54 | | | | | (139) all_595_1 = 0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (139) implies: % 50.42/7.54 | | | | | (140) all_595_1 = 0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (124), (138) imply: % 50.42/7.54 | | | | | (141) all_599_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (141) implies: % 50.42/7.54 | | | | | (142) all_599_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (123), (142) imply: % 50.42/7.54 | | | | | (143) all_597_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (143) implies: % 50.42/7.54 | | | | | (144) all_597_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (122), (144) imply: % 50.42/7.54 | | | | | (145) all_593_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (145) implies: % 50.42/7.54 | | | | | (146) all_593_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (136), (140) imply: % 50.42/7.54 | | | | | (147) all_589_1 = 0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (147) implies: % 50.42/7.54 | | | | | (148) all_589_1 = 0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (121), (134) imply: % 50.42/7.54 | | | | | (149) all_591_1 = all_589_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (121), (146) imply: % 50.42/7.54 | | | | | (150) all_591_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (149), (150) imply: % 50.42/7.54 | | | | | (151) all_589_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | SIMP: (151) implies: % 50.42/7.54 | | | | | (152) all_589_1 = all_587_1 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (148), (152) imply: % 50.42/7.54 | | | | | (153) all_587_1 = 0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | COMBINE_EQS: (131), (148) imply: % 50.42/7.54 | | | | | (154) all_607_1 = 0 % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | BETA: splitting (96) gives: % 50.42/7.54 | | | | | % 50.42/7.54 | | | | | Case 1: % 50.42/7.54 | | | | | | % 50.42/7.54 | | | | | | (155) ~ (all_587_1 = 0) % 50.42/7.54 | | | | | | % 50.42/7.54 | | | | | | REDUCE: (153), (155) imply: % 50.42/7.54 | | | | | | (156) $false % 50.42/7.54 | | | | | | % 50.42/7.54 | | | | | | CLOSE: (156) is inconsistent. % 50.42/7.54 | | | | | | % 50.42/7.54 | | | | | Case 2: % 50.42/7.54 | | | | | | % 50.42/7.54 | | | | | | (157) all_587_0 = 0 % 50.42/7.54 | | | | | | % 50.42/7.55 | | | | | | REDUCE: (95), (157) imply: % 50.42/7.55 | | | | | | (158) ssList(all_316_0) = 0 % 50.42/7.55 | | | | | | % 50.42/7.55 | | | | | | BETA: splitting (90) gives: % 50.42/7.55 | | | | | | % 50.42/7.55 | | | | | | Case 1: % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | (159) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_316_0) = v0) % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | DELTA: instantiating (159) with fresh symbol all_695_0 gives: % 50.42/7.55 | | | | | | | (160) ~ (all_695_0 = 0) & ssList(all_316_0) = all_695_0 % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | ALPHA: (160) implies: % 50.42/7.55 | | | | | | | (161) ~ (all_695_0 = 0) % 50.42/7.55 | | | | | | | (162) ssList(all_316_0) = all_695_0 % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | GROUND_INST: instantiating (14) with 0, all_695_0, all_316_0, % 50.42/7.55 | | | | | | | simplifying with (158), (162) gives: % 50.42/7.55 | | | | | | | (163) all_695_0 = 0 % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | REDUCE: (161), (163) imply: % 50.42/7.55 | | | | | | | (164) $false % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | CLOSE: (164) is inconsistent. % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | Case 2: % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | (165) all_318_0 = nil & all_316_0 = nil % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | ALPHA: (165) implies: % 50.42/7.55 | | | | | | | (166) all_316_0 = nil % 50.42/7.55 | | | | | | | (167) all_318_0 = nil % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | REDUCE: (117), (167) imply: % 50.42/7.55 | | | | | | | (168) cons(all_316_1, nil) = all_607_0 % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | REDUCE: (69), (166) imply: % 50.42/7.55 | | | | | | | (169) cons(all_316_1, nil) = nil % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | BETA: splitting (118) gives: % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | | Case 1: % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | | (170) ~ (all_607_1 = 0) % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | | REDUCE: (154), (170) imply: % 50.42/7.55 | | | | | | | | (171) $false % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | | CLOSE: (171) is inconsistent. % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | Case 2: % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | | (172) all_607_0 = all_97_0 % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | | REDUCE: (168), (172) imply: % 50.42/7.55 | | | | | | | | (173) cons(all_316_1, nil) = all_97_0 % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | | GROUND_INST: instantiating (15) with nil, all_97_0, nil, % 50.42/7.55 | | | | | | | | all_316_1, simplifying with (169), (173) gives: % 50.42/7.55 | | | | | | | | (174) all_97_0 = nil % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | | REDUCE: (46), (174) imply: % 50.42/7.55 | | | | | | | | (175) $false % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | | CLOSE: (175) is inconsistent. % 50.42/7.55 | | | | | | | | % 50.42/7.55 | | | | | | | End of split % 50.42/7.55 | | | | | | | % 50.42/7.55 | | | | | | End of split % 50.42/7.55 | | | | | | % 50.42/7.55 | | | | | End of split % 50.42/7.55 | | | | | % 50.42/7.55 | | | | End of split % 50.42/7.55 | | | | % 50.42/7.55 | | | End of split % 50.42/7.55 | | | % 50.42/7.55 | | End of split % 50.42/7.55 | | % 50.42/7.55 | End of split % 50.42/7.55 | % 50.42/7.55 End of proof % 50.42/7.55 % SZS output end Proof for theBenchmark % 50.42/7.55 % 50.42/7.55 6952ms %------------------------------------------------------------------------------