%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC185+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 : n011.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 20:50:08 EDT 2023 % Result : Theorem 23.30s 3.85s % Output : Proof 45.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC185+1 : TPTP v8.1.2. Released v2.4.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n011.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Mon Aug 28 14:58:40 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.77/1.49 Prover 1: Preprocessing ... % 5.91/1.50 Prover 4: Preprocessing ... % 6.03/1.52 Prover 3: Preprocessing ... % 6.03/1.52 Prover 5: Preprocessing ... % 6.03/1.52 Prover 2: Preprocessing ... % 6.03/1.52 Prover 6: Preprocessing ... % 6.03/1.52 Prover 0: Preprocessing ... % 14.27/2.75 Prover 5: Constructing countermodel ... % 14.27/2.76 Prover 2: Proving ... % 14.27/2.79 Prover 1: Constructing countermodel ... % 15.78/2.86 Prover 6: Proving ... % 15.78/2.90 Prover 3: Constructing countermodel ... % 21.00/3.59 Prover 4: Constructing countermodel ... % 23.05/3.84 Prover 3: proved (3225ms) % 23.05/3.84 % 23.30/3.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.30/3.85 % 23.30/3.85 Prover 6: stopped % 23.30/3.86 Prover 2: stopped % 23.30/3.86 Prover 0: Proving ... % 23.30/3.86 Prover 0: stopped % 23.30/3.87 Prover 5: stopped % 23.30/3.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.30/3.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.30/3.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.30/3.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.30/3.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.23/4.13 Prover 8: Preprocessing ... % 25.11/4.15 Prover 13: Preprocessing ... % 25.11/4.15 Prover 7: Preprocessing ... % 25.51/4.18 Prover 10: Preprocessing ... % 25.51/4.19 Prover 11: Preprocessing ... % 27.87/4.46 Prover 7: Constructing countermodel ... % 28.49/4.56 Prover 13: Constructing countermodel ... % 28.49/4.57 Prover 10: Constructing countermodel ... % 29.21/4.70 Prover 8: Warning: ignoring some quantifiers % 29.21/4.71 Prover 8: Constructing countermodel ... % 36.35/5.59 Prover 11: Constructing countermodel ... % 44.29/6.74 Prover 1: Found proof (size 218) % 44.29/6.74 Prover 1: proved (6125ms) % 44.29/6.74 Prover 4: stopped % 44.29/6.74 Prover 11: stopped % 44.29/6.74 Prover 8: stopped % 44.29/6.74 Prover 7: stopped % 44.29/6.74 Prover 13: stopped % 44.29/6.74 Prover 10: stopped % 44.29/6.74 % 44.29/6.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 44.29/6.74 % 45.50/6.76 % SZS output start Proof for theBenchmark % 45.50/6.77 Assumptions after simplification: % 45.50/6.77 --------------------------------- % 45.50/6.77 % 45.50/6.77 (ax13) % 45.50/6.80 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 45.50/6.80 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 45.50/6.80 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 45.50/6.80 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 45.50/6.80 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 45.50/6.80 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 45.50/6.80 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 45.50/6.80 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 45.50/6.80 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 45.50/6.80 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 45.50/6.80 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 45.50/6.80 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 45.50/6.80 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 45.50/6.80 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 45.50/6.80 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 45.50/6.80 % 45.50/6.80 (ax16) % 45.50/6.80 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 45.50/6.80 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 45.50/6.80 (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 45.50/6.80 % 45.50/6.80 (ax17) % 45.50/6.80 ssList(nil) = 0 & $i(nil) % 45.50/6.80 % 45.50/6.80 (ax23) % 45.50/6.80 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 45.50/6.80 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 45.50/6.80 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 45.50/6.80 % 45.50/6.80 (ax25) % 45.50/6.80 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 45.50/6.80 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 45.50/6.80 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 45.50/6.80 % 45.50/6.80 (ax26) % 45.50/6.80 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 45.50/6.80 ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 45.50/6.80 (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 45.50/6.80 % 45.50/6.80 (ax59) % 45.50/6.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 45.50/6.81 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 45.50/6.81 (v2 = 0) | v3 = 0))) % 45.50/6.81 % 45.50/6.81 (ax61) % 45.50/6.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 45.72/6.81 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 45.72/6.81 (v2 = 0) | v3 = 0))) % 45.72/6.81 % 45.72/6.81 (ax63) % 45.72/6.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 45.72/6.81 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 45.72/6.81 (v2 = 0) | v3 = 0))) % 45.72/6.81 % 45.72/6.81 (ax65) % 45.72/6.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 45.72/6.81 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 45.72/6.81 (v2 = 0) | v3 = 0))) % 45.72/6.81 % 45.72/6.81 (ax68) % 45.72/6.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 45.72/6.81 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 45.72/6.81 ~ (v2 = 0) | v3 = 0))) % 45.72/6.81 % 45.72/6.81 (ax71) % 45.72/6.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 45.72/6.81 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 45.72/6.81 ~ (v2 = 0) | v3 = 0))) % 45.72/6.81 % 45.72/6.81 (ax72) % 45.72/6.81 duplicatefreeP(nil) = 0 & $i(nil) % 45.72/6.81 % 45.72/6.81 (ax73) % 45.72/6.81 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 45.72/6.81 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 45.72/6.81 (v2 = 0) | v3 = 0))) % 45.72/6.81 % 45.72/6.81 (ax82) % 45.72/6.81 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 45.72/6.81 ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 45.72/6.81 ssList(v1) = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ (app(v2, v3) = v4) | % 45.72/6.81 ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : (ssList(v3) = v5 & % 45.72/6.81 app(v1, v3) = v6 & app(v0, v6) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | % 45.72/6.81 v7 = v4))))) % 45.72/6.81 % 45.72/6.81 (co1) % 45.72/6.82 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 45.72/6.82 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ % 45.72/6.82 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : % 45.72/6.82 ! [v5: $i] : ( ~ (app(v4, v3) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: % 45.72/6.82 any] : (memberP(v4, v2) = v7 & ssList(v4) = v6 & ( ~ (v6 = 0) | ! % 45.72/6.82 [v8: $i] : ( ~ (app(v5, v8) = v0) | ~ $i(v8) | ? [v9: any] : ? % 45.72/6.82 [v10: any] : (memberP(v8, v2) = v10 & ssList(v8) = v9 & ( ~ (v9 % 45.72/6.82 = 0) | ( ~ (v10 = 0) & ~ (v7 = 0))))))))) & ? [v2: $i] : % 45.72/6.82 ? [v3: $i] : (cons(v2, nil) = v3 & ssItem(v2) = 0 & $i(v3) & $i(v2) & ? % 45.72/6.82 [v4: $i] : ? [v5: $i] : ? [v6: any] : (memberP(v4, v2) = v6 & % 45.72/6.82 ssList(v4) = 0 & app(v4, v3) = v5 & $i(v5) & $i(v4) & ? [v7: $i] : ? % 45.72/6.82 [v8: any] : (memberP(v7, v2) = v8 & ssList(v7) = 0 & app(v5, v7) = v0 % 45.72/6.82 & $i(v7) & (v8 = 0 | v6 = 0)))))) % 45.72/6.82 % 45.72/6.82 (function-axioms) % 45.72/6.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 45.72/6.82 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 45.72/6.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 45.72/6.82 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 45.72/6.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 45.72/6.82 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 45.72/6.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 45.72/6.82 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 45.72/6.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 45.72/6.82 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 45.72/6.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 45.72/6.82 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 45.72/6.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 45.72/6.82 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 45.72/6.82 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 45.72/6.82 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 45.72/6.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 45.72/6.82 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 45.72/6.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 45.72/6.82 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 45.72/6.82 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 45.72/6.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 45.72/6.82 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 45.72/6.82 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 45.72/6.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 45.72/6.82 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.72/6.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 45.72/6.83 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.72/6.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 45.72/6.83 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.72/6.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 45.72/6.83 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.72/6.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 45.72/6.83 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.72/6.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 45.72/6.83 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.72/6.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 45.72/6.83 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.72/6.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 45.72/6.83 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 45.72/6.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 45.72/6.83 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 45.72/6.83 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 45.72/6.83 % 45.72/6.83 Further assumptions not needed in the proof: % 45.72/6.83 -------------------------------------------- % 45.72/6.83 ax1, ax10, ax11, ax12, ax14, ax15, ax18, ax19, ax2, ax20, ax21, ax22, ax24, % 45.72/6.83 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, % 45.72/6.83 ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, % 45.72/6.83 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, % 45.72/6.83 ax66, ax67, ax69, ax7, ax70, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, % 45.72/6.83 ax81, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 45.72/6.83 ax94, ax95 % 45.72/6.83 % 45.72/6.83 Those formulas are unsatisfiable: % 45.72/6.83 --------------------------------- % 45.72/6.83 % 45.72/6.83 Begin of proof % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax17) implies: % 45.72/6.83 | (1) ssList(nil) = 0 % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax59) implies: % 45.72/6.83 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.72/6.83 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 45.72/6.83 | ~ (v2 = 0) | v3 = 0))) % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax61) implies: % 45.72/6.83 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.72/6.83 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 45.72/6.83 | ( ~ (v2 = 0) | v3 = 0))) % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax63) implies: % 45.72/6.83 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.72/6.83 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 45.72/6.83 | ( ~ (v2 = 0) | v3 = 0))) % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax65) implies: % 45.72/6.83 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.72/6.83 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 45.72/6.83 | & ( ~ (v2 = 0) | v3 = 0))) % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax68) implies: % 45.72/6.83 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.72/6.83 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 45.72/6.83 | & ( ~ (v2 = 0) | v3 = 0))) % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax71) implies: % 45.72/6.83 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.72/6.83 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 45.72/6.83 | & ( ~ (v2 = 0) | v3 = 0))) % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax72) implies: % 45.72/6.83 | (8) duplicatefreeP(nil) = 0 % 45.72/6.83 | % 45.72/6.83 | ALPHA: (ax73) implies: % 45.72/6.83 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.72/6.83 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 45.72/6.83 | ( ~ (v2 = 0) | v3 = 0))) % 45.72/6.83 | % 45.72/6.83 | ALPHA: (co1) implies: % 45.72/6.84 | (10) $i(nil) % 45.72/6.84 | (11) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 45.72/6.84 | & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | % 45.72/6.84 | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! % 45.72/6.84 | [v4: $i] : ! [v5: $i] : ( ~ (app(v4, v3) = v5) | ~ $i(v4) | ? % 45.72/6.84 | [v6: any] : ? [v7: any] : (memberP(v4, v2) = v7 & ssList(v4) % 45.72/6.84 | = v6 & ( ~ (v6 = 0) | ! [v8: $i] : ( ~ (app(v5, v8) = v0) | % 45.72/6.84 | ~ $i(v8) | ? [v9: any] : ? [v10: any] : (memberP(v8, % 45.72/6.84 | v2) = v10 & ssList(v8) = v9 & ( ~ (v9 = 0) | ( ~ % 45.72/6.84 | (v10 = 0) & ~ (v7 = 0))))))))) & ? [v2: $i] : ? % 45.72/6.84 | [v3: $i] : (cons(v2, nil) = v3 & ssItem(v2) = 0 & $i(v3) & $i(v2) % 45.72/6.84 | & ? [v4: $i] : ? [v5: $i] : ? [v6: any] : (memberP(v4, v2) = % 45.72/6.84 | v6 & ssList(v4) = 0 & app(v4, v3) = v5 & $i(v5) & $i(v4) & ? % 45.72/6.84 | [v7: $i] : ? [v8: any] : (memberP(v7, v2) = v8 & ssList(v7) = % 45.72/6.84 | 0 & app(v5, v7) = v0 & $i(v7) & (v8 = 0 | v6 = 0)))))) % 45.72/6.84 | % 45.72/6.84 | ALPHA: (function-axioms) implies: % 45.72/6.84 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 45.72/6.84 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 45.72/6.84 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 45.72/6.84 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 45.72/6.84 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 45.72/6.84 | : ! [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, % 45.72/6.84 | v2) = v0)) % 45.72/6.84 | % 45.72/6.84 | DELTA: instantiating (11) with fresh symbol all_93_0 gives: % 45.91/6.84 | (15) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 45.91/6.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~ % 45.91/6.84 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: % 45.91/6.85 | $i] : ! [v4: $i] : ( ~ (app(v3, v2) = v4) | ~ $i(v3) | ? [v5: % 45.91/6.85 | any] : ? [v6: any] : (memberP(v3, v1) = v6 & ssList(v3) = v5 % 45.91/6.85 | & ( ~ (v5 = 0) | ! [v7: $i] : ( ~ (app(v4, v7) = all_93_0) | % 45.91/6.85 | ~ $i(v7) | ? [v8: any] : ? [v9: any] : (memberP(v7, v1) % 45.91/6.85 | = v9 & ssList(v7) = v8 & ( ~ (v8 = 0) | ( ~ (v9 = 0) & % 45.91/6.85 | ~ (v6 = 0))))))))) & ? [v1: $i] : ? [v2: $i] : % 45.91/6.85 | (cons(v1, nil) = v2 & ssItem(v1) = 0 & $i(v2) & $i(v1) & ? [v3: $i] % 45.91/6.85 | : ? [v4: $i] : ? [v5: any] : (memberP(v3, v1) = v5 & ssList(v3) % 45.91/6.85 | = 0 & app(v3, v2) = v4 & $i(v4) & $i(v3) & ? [v6: $i] : ? [v7: % 45.91/6.85 | any] : (memberP(v6, v1) = v7 & ssList(v6) = 0 & app(v4, v6) = % 45.91/6.85 | all_93_0 & $i(v6) & (v7 = 0 | v5 = 0))))) % 45.91/6.85 | % 45.91/6.85 | ALPHA: (15) implies: % 45.91/6.85 | (16) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 45.91/6.85 | ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 45.91/6.85 | ssItem(v1) = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ (app(v3, v2) % 45.91/6.85 | = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (memberP(v3, % 45.91/6.85 | v1) = v6 & ssList(v3) = v5 & ( ~ (v5 = 0) | ! [v7: $i] : ( % 45.91/6.85 | ~ (app(v4, v7) = all_93_0) | ~ $i(v7) | ? [v8: any] : ? % 45.91/6.85 | [v9: any] : (memberP(v7, v1) = v9 & ssList(v7) = v8 & ( ~ % 45.91/6.85 | (v8 = 0) | ( ~ (v9 = 0) & ~ (v6 = 0))))))))) & ? % 45.91/6.85 | [v1: $i] : ? [v2: $i] : (cons(v1, nil) = v2 & ssItem(v1) = 0 & % 45.91/6.85 | $i(v2) & $i(v1) & ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 45.91/6.85 | (memberP(v3, v1) = v5 & ssList(v3) = 0 & app(v3, v2) = v4 & $i(v4) % 45.91/6.85 | & $i(v3) & ? [v6: $i] : ? [v7: any] : (memberP(v6, v1) = v7 & % 45.91/6.85 | ssList(v6) = 0 & app(v4, v6) = all_93_0 & $i(v6) & (v7 = 0 | % 45.91/6.85 | v5 = 0))))) % 45.91/6.85 | % 45.91/6.85 | DELTA: instantiating (16) with fresh symbol all_97_0 gives: % 45.91/6.85 | (17) ssList(all_97_0) = 0 & $i(all_97_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 45.91/6.85 | (cons(v0, nil) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 45.91/6.85 | ssItem(v0) = v2) | ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v1) = % 45.91/6.85 | v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (memberP(v2, v0) % 45.91/6.85 | = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | ! [v6: $i] : ( ~ % 45.91/6.85 | (app(v3, v6) = all_93_0) | ~ $i(v6) | ? [v7: any] : ? % 45.91/6.85 | [v8: any] : (memberP(v6, v0) = v8 & ssList(v6) = v7 & ( ~ % 45.91/6.85 | (v7 = 0) | ( ~ (v8 = 0) & ~ (v5 = 0))))))))) & ? [v0: % 45.91/6.85 | $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & $i(v1) & % 45.91/6.85 | $i(v0) & ? [v2: $i] : ? [v3: $i] : ? [v4: any] : (memberP(v2, v0) % 45.91/6.85 | = v4 & ssList(v2) = 0 & app(v2, v1) = v3 & $i(v3) & $i(v2) & ? % 45.91/6.85 | [v5: $i] : ? [v6: any] : (memberP(v5, v0) = v6 & ssList(v5) = 0 & % 45.91/6.85 | app(v3, v5) = all_93_0 & $i(v5) & (v6 = 0 | v4 = 0)))) % 45.91/6.85 | % 45.91/6.85 | ALPHA: (17) implies: % 45.91/6.85 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.91/6.85 | [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | ! [v2: $i] : ! [v3: % 45.91/6.85 | $i] : ( ~ (app(v2, v1) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 45.91/6.85 | any] : (memberP(v2, v0) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | % 45.91/6.85 | ! [v6: $i] : ( ~ (app(v3, v6) = all_93_0) | ~ $i(v6) | ? % 45.91/6.85 | [v7: any] : ? [v8: any] : (memberP(v6, v0) = v8 & % 45.91/6.85 | ssList(v6) = v7 & ( ~ (v7 = 0) | ( ~ (v8 = 0) & ~ (v5 = % 45.91/6.85 | 0))))))))) % 45.91/6.85 | (19) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & % 45.91/6.85 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : ? [v4: any] : % 45.91/6.85 | (memberP(v2, v0) = v4 & ssList(v2) = 0 & app(v2, v1) = v3 & $i(v3) & % 45.91/6.86 | $i(v2) & ? [v5: $i] : ? [v6: any] : (memberP(v5, v0) = v6 & % 45.91/6.86 | ssList(v5) = 0 & app(v3, v5) = all_93_0 & $i(v5) & (v6 = 0 | v4 % 45.91/6.86 | = 0)))) % 45.91/6.86 | % 45.91/6.86 | DELTA: instantiating (19) with fresh symbols all_100_0, all_100_1 gives: % 45.91/6.86 | (20) cons(all_100_1, nil) = all_100_0 & ssItem(all_100_1) = 0 & % 45.91/6.86 | $i(all_100_0) & $i(all_100_1) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 45.91/6.86 | any] : (memberP(v0, all_100_1) = v2 & ssList(v0) = 0 & app(v0, % 45.91/6.86 | all_100_0) = v1 & $i(v1) & $i(v0) & ? [v3: $i] : ? [v4: any] : % 45.91/6.86 | (memberP(v3, all_100_1) = v4 & ssList(v3) = 0 & app(v1, v3) = % 45.91/6.86 | all_93_0 & $i(v3) & (v4 = 0 | v2 = 0))) % 45.91/6.86 | % 45.91/6.86 | ALPHA: (20) implies: % 45.91/6.86 | (21) $i(all_100_1) % 45.91/6.86 | (22) $i(all_100_0) % 45.91/6.86 | (23) ssItem(all_100_1) = 0 % 45.91/6.86 | (24) cons(all_100_1, nil) = all_100_0 % 45.91/6.86 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (memberP(v0, all_100_1) = % 45.91/6.86 | v2 & ssList(v0) = 0 & app(v0, all_100_0) = v1 & $i(v1) & $i(v0) & ? % 45.91/6.86 | [v3: $i] : ? [v4: any] : (memberP(v3, all_100_1) = v4 & ssList(v3) % 45.91/6.86 | = 0 & app(v1, v3) = all_93_0 & $i(v3) & (v4 = 0 | v2 = 0))) % 45.91/6.86 | % 45.91/6.86 | DELTA: instantiating (25) with fresh symbols all_102_0, all_102_1, all_102_2 % 45.91/6.86 | gives: % 45.91/6.86 | (26) memberP(all_102_2, all_100_1) = all_102_0 & ssList(all_102_2) = 0 & % 45.91/6.86 | app(all_102_2, all_100_0) = all_102_1 & $i(all_102_1) & $i(all_102_2) % 45.91/6.86 | & ? [v0: $i] : ? [v1: any] : (memberP(v0, all_100_1) = v1 & % 45.91/6.86 | ssList(v0) = 0 & app(all_102_1, v0) = all_93_0 & $i(v0) & (v1 = 0 | % 45.91/6.86 | all_102_0 = 0)) % 45.91/6.86 | % 45.91/6.86 | ALPHA: (26) implies: % 45.91/6.86 | (27) $i(all_102_2) % 45.91/6.86 | (28) app(all_102_2, all_100_0) = all_102_1 % 45.91/6.86 | (29) ssList(all_102_2) = 0 % 45.91/6.86 | (30) memberP(all_102_2, all_100_1) = all_102_0 % 45.91/6.86 | (31) ? [v0: $i] : ? [v1: any] : (memberP(v0, all_100_1) = v1 & ssList(v0) % 45.91/6.86 | = 0 & app(all_102_1, v0) = all_93_0 & $i(v0) & (v1 = 0 | all_102_0 = % 45.91/6.86 | 0)) % 45.91/6.86 | % 45.91/6.86 | DELTA: instantiating (31) with fresh symbols all_104_0, all_104_1 gives: % 45.91/6.86 | (32) memberP(all_104_1, all_100_1) = all_104_0 & ssList(all_104_1) = 0 & % 45.91/6.86 | app(all_102_1, all_104_1) = all_93_0 & $i(all_104_1) & (all_104_0 = 0 % 45.91/6.86 | | all_102_0 = 0) % 45.91/6.86 | % 45.91/6.86 | ALPHA: (32) implies: % 45.91/6.86 | (33) $i(all_104_1) % 45.91/6.86 | (34) app(all_102_1, all_104_1) = all_93_0 % 45.91/6.86 | (35) ssList(all_104_1) = 0 % 45.91/6.86 | (36) memberP(all_104_1, all_100_1) = all_104_0 % 45.91/6.86 | (37) all_104_0 = 0 | all_102_0 = 0 % 45.91/6.86 | % 45.91/6.86 | GROUND_INST: instantiating (9) with all_100_1, all_100_0, simplifying with % 45.91/6.86 | (21), (24) gives: % 45.91/6.86 | (38) ? [v0: any] : ? [v1: any] : (equalelemsP(all_100_0) = v1 & % 45.91/6.86 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.86 | % 45.91/6.86 | GROUND_INST: instantiating (7) with all_100_1, all_100_0, simplifying with % 45.91/6.86 | (21), (24) gives: % 45.91/6.86 | (39) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_100_0) = v1 & % 45.91/6.86 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.86 | % 45.91/6.86 | GROUND_INST: instantiating (6) with all_100_1, all_100_0, simplifying with % 45.91/6.86 | (21), (24) gives: % 45.91/6.86 | (40) ? [v0: any] : ? [v1: any] : (strictorderedP(all_100_0) = v1 & % 45.91/6.86 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.86 | % 45.91/6.86 | GROUND_INST: instantiating (5) with all_100_1, all_100_0, simplifying with % 45.91/6.86 | (21), (24) gives: % 45.91/6.86 | (41) ? [v0: any] : ? [v1: any] : (totalorderedP(all_100_0) = v1 & % 45.91/6.86 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.86 | % 45.91/6.86 | GROUND_INST: instantiating (4) with all_100_1, all_100_0, simplifying with % 45.91/6.86 | (21), (24) gives: % 45.91/6.87 | (42) ? [v0: any] : ? [v1: any] : (strictorderP(all_100_0) = v1 & % 45.91/6.87 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (3) with all_100_1, all_100_0, simplifying with % 45.91/6.87 | (21), (24) gives: % 45.91/6.87 | (43) ? [v0: any] : ? [v1: any] : (totalorderP(all_100_0) = v1 & % 45.91/6.87 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (2) with all_100_1, all_100_0, simplifying with % 45.91/6.87 | (21), (24) gives: % 45.91/6.87 | (44) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_100_0) = v1 & % 45.91/6.87 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (18) with all_100_1, all_100_0, simplifying with % 45.91/6.87 | (21), (24) gives: % 45.91/6.87 | (45) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_100_1) = v0) | ! [v0: $i] : % 45.91/6.87 | ! [v1: $i] : ( ~ (app(v0, all_100_0) = v1) | ~ $i(v0) | ? [v2: any] % 45.91/6.87 | : ? [v3: any] : (memberP(v0, all_100_1) = v3 & ssList(v0) = v2 & ( % 45.91/6.87 | ~ (v2 = 0) | ! [v4: $i] : ( ~ (app(v1, v4) = all_93_0) | ~ % 45.91/6.87 | $i(v4) | ? [v5: any] : ? [v6: any] : (memberP(v4, all_100_1) % 45.91/6.87 | = v6 & ssList(v4) = v5 & ( ~ (v5 = 0) | ( ~ (v6 = 0) & ~ % 45.91/6.87 | (v3 = 0)))))))) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (10) gives: % 45.91/6.87 | (46) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.91/6.87 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 45.91/6.87 | ( ~ (v2 = 0) | v3 = nil))) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (10) gives: % 45.91/6.87 | (47) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.91/6.87 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 45.91/6.87 | ( ~ (v2 = 0) | v3 = v0))) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (ax16) with nil, simplifying with (1), (10) gives: % 45.91/6.87 | (48) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 45.91/6.87 | [v2: any] : ? [v3: any] : (ssList(v1) = v3 & ssItem(v0) = v2 & ( ~ % 45.91/6.87 | (v2 = 0) | v3 = 0))) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (ax26) with all_102_2, simplifying with (27), (29) % 45.91/6.87 | gives: % 45.91/6.87 | (49) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_102_2, v0) = v1) | ~ $i(v0) % 45.91/6.87 | | ? [v2: any] : ? [v3: any] : (ssList(v1) = v3 & ssList(v0) = v2 & % 45.91/6.87 | ( ~ (v2 = 0) | v3 = 0))) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (ax82) with all_102_2, simplifying with (27), (29) % 45.91/6.87 | gives: % 45.91/6.87 | (50) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_102_2, v0) = v1) | ~ $i(v0) % 45.91/6.87 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ! % 45.91/6.87 | [v3: $i] : ( ~ (app(v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 45.91/6.87 | [v5: $i] : ? [v6: $i] : (ssList(v2) = v4 & app(v0, v2) = v5 & % 45.91/6.87 | app(all_102_2, v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 45.91/6.87 | v3)))) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (8), (10) % 45.91/6.87 | gives: % 45.91/6.87 | (51) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 45.91/6.87 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 45.91/6.87 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 45.91/6.87 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 45.91/6.87 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 45.91/6.87 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 45.91/6.87 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 45.91/6.87 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 45.91/6.87 | v8)))))) % 45.91/6.87 | % 45.91/6.87 | GROUND_INST: instantiating (48) with all_100_1, all_100_0, simplifying with % 45.91/6.87 | (21), (24) gives: % 45.91/6.87 | (52) ? [v0: any] : ? [v1: any] : (ssList(all_100_0) = v1 & % 45.91/6.87 | ssItem(all_100_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.87 | % 45.91/6.88 | GROUND_INST: instantiating (47) with all_100_1, all_100_0, simplifying with % 45.91/6.88 | (21), (24) gives: % 45.91/6.88 | (53) ? [v0: any] : ? [v1: $i] : (hd(all_100_0) = v1 & ssItem(all_100_1) = % 45.91/6.88 | v0 & $i(v1) & ( ~ (v0 = 0) | v1 = all_100_1)) % 45.91/6.88 | % 45.91/6.88 | GROUND_INST: instantiating (46) with all_100_1, all_100_0, simplifying with % 45.91/6.88 | (21), (24) gives: % 45.91/6.88 | (54) ? [v0: any] : ? [v1: $i] : (tl(all_100_0) = v1 & ssItem(all_100_1) = % 45.91/6.88 | v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 45.91/6.88 | % 45.91/6.88 | GROUND_INST: instantiating (50) with all_100_0, all_102_1, simplifying with % 45.91/6.88 | (22), (28) gives: % 45.91/6.88 | (55) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_100_0) = v0) | ! [v0: $i] : % 45.91/6.88 | ! [v1: $i] : ( ~ (app(all_102_1, v0) = v1) | ~ $i(v0) | ? [v2: any] % 45.91/6.88 | : ? [v3: $i] : ? [v4: $i] : (ssList(v0) = v2 & app(all_102_2, v3) % 45.91/6.88 | = v4 & app(all_100_0, v0) = v3 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | % 45.91/6.88 | v4 = v1))) % 45.91/6.88 | % 45.91/6.88 | GROUND_INST: instantiating (49) with all_100_0, all_102_1, simplifying with % 45.91/6.88 | (22), (28) gives: % 45.91/6.88 | (56) ? [v0: any] : ? [v1: any] : (ssList(all_102_1) = v1 & % 45.91/6.88 | ssList(all_100_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (43) with fresh symbols all_345_0, all_345_1 gives: % 45.91/6.88 | (57) totalorderP(all_100_0) = all_345_0 & ssItem(all_100_1) = all_345_1 & ( % 45.91/6.88 | ~ (all_345_1 = 0) | all_345_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (57) implies: % 45.91/6.88 | (58) ssItem(all_100_1) = all_345_1 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (42) with fresh symbols all_347_0, all_347_1 gives: % 45.91/6.88 | (59) strictorderP(all_100_0) = all_347_0 & ssItem(all_100_1) = all_347_1 & % 45.91/6.88 | ( ~ (all_347_1 = 0) | all_347_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (59) implies: % 45.91/6.88 | (60) ssItem(all_100_1) = all_347_1 % 45.91/6.88 | (61) ~ (all_347_1 = 0) | all_347_0 = 0 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (41) with fresh symbols all_349_0, all_349_1 gives: % 45.91/6.88 | (62) totalorderedP(all_100_0) = all_349_0 & ssItem(all_100_1) = all_349_1 & % 45.91/6.88 | ( ~ (all_349_1 = 0) | all_349_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (62) implies: % 45.91/6.88 | (63) ssItem(all_100_1) = all_349_1 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (40) with fresh symbols all_351_0, all_351_1 gives: % 45.91/6.88 | (64) strictorderedP(all_100_0) = all_351_0 & ssItem(all_100_1) = all_351_1 % 45.91/6.88 | & ( ~ (all_351_1 = 0) | all_351_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (64) implies: % 45.91/6.88 | (65) ssItem(all_100_1) = all_351_1 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (39) with fresh symbols all_353_0, all_353_1 gives: % 45.91/6.88 | (66) duplicatefreeP(all_100_0) = all_353_0 & ssItem(all_100_1) = all_353_1 % 45.91/6.88 | & ( ~ (all_353_1 = 0) | all_353_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (66) implies: % 45.91/6.88 | (67) ssItem(all_100_1) = all_353_1 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (44) with fresh symbols all_355_0, all_355_1 gives: % 45.91/6.88 | (68) cyclefreeP(all_100_0) = all_355_0 & ssItem(all_100_1) = all_355_1 & ( % 45.91/6.88 | ~ (all_355_1 = 0) | all_355_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (68) implies: % 45.91/6.88 | (69) ssItem(all_100_1) = all_355_1 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (38) with fresh symbols all_357_0, all_357_1 gives: % 45.91/6.88 | (70) equalelemsP(all_100_0) = all_357_0 & ssItem(all_100_1) = all_357_1 & ( % 45.91/6.88 | ~ (all_357_1 = 0) | all_357_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (70) implies: % 45.91/6.88 | (71) ssItem(all_100_1) = all_357_1 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (52) with fresh symbols all_359_0, all_359_1 gives: % 45.91/6.88 | (72) ssList(all_100_0) = all_359_0 & ssItem(all_100_1) = all_359_1 & ( ~ % 45.91/6.88 | (all_359_1 = 0) | all_359_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (72) implies: % 45.91/6.88 | (73) ssItem(all_100_1) = all_359_1 % 45.91/6.88 | (74) ssList(all_100_0) = all_359_0 % 45.91/6.88 | (75) ~ (all_359_1 = 0) | all_359_0 = 0 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (53) with fresh symbols all_361_0, all_361_1 gives: % 45.91/6.88 | (76) hd(all_100_0) = all_361_0 & ssItem(all_100_1) = all_361_1 & % 45.91/6.88 | $i(all_361_0) & ( ~ (all_361_1 = 0) | all_361_0 = all_100_1) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (76) implies: % 45.91/6.88 | (77) ssItem(all_100_1) = all_361_1 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (54) with fresh symbols all_363_0, all_363_1 gives: % 45.91/6.88 | (78) tl(all_100_0) = all_363_0 & ssItem(all_100_1) = all_363_1 & % 45.91/6.88 | $i(all_363_0) & ( ~ (all_363_1 = 0) | all_363_0 = nil) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (78) implies: % 45.91/6.88 | (79) ssItem(all_100_1) = all_363_1 % 45.91/6.88 | % 45.91/6.88 | DELTA: instantiating (56) with fresh symbols all_365_0, all_365_1 gives: % 45.91/6.88 | (80) ssList(all_102_1) = all_365_0 & ssList(all_100_0) = all_365_1 & ( ~ % 45.91/6.88 | (all_365_1 = 0) | all_365_0 = 0) % 45.91/6.88 | % 45.91/6.88 | ALPHA: (80) implies: % 45.91/6.88 | (81) ssList(all_100_0) = all_365_1 % 45.91/6.88 | (82) ~ (all_365_1 = 0) | all_365_0 = 0 % 45.91/6.88 | % 45.91/6.88 | BETA: splitting (51) gives: % 45.91/6.88 | % 45.91/6.88 | Case 1: % 45.91/6.88 | | % 45.91/6.88 | | (83) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 45.91/6.89 | | % 45.91/6.89 | | REF_CLOSE: (1), (13), (83) are inconsistent by sub-proof #1. % 45.91/6.89 | | % 45.91/6.89 | Case 2: % 45.91/6.89 | | % 45.91/6.89 | | (84) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 45.91/6.89 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 45.91/6.89 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 45.91/6.89 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 45.91/6.89 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 45.91/6.89 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 45.91/6.89 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 45.91/6.89 | | 0) & ssList(v6) = v8)))))) % 45.91/6.89 | | % 45.91/6.89 | | GROUND_INST: instantiating (84) with all_100_1, simplifying with (21), (23) % 45.91/6.89 | | gives: % 45.91/6.89 | | (85) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 45.91/6.89 | | (ssList(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ! % 45.91/6.89 | | [v4: $i] : ( ~ (cons(all_100_1, v2) = v3) | ~ (app(v1, v3) = % 45.91/6.89 | | v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v2) = % 45.91/6.89 | | v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (v0 = all_100_1) | ~ % 45.91/6.89 | | (cons(all_100_1, v5) = v6) | ~ (app(v4, v6) = nil) | ~ % 45.91/6.89 | | $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & ssList(v5) = v7))))) % 45.91/6.89 | | % 45.91/6.89 | | GROUND_INST: instantiating (85) with all_100_1, simplifying with (21), (23) % 45.91/6.89 | | gives: % 45.91/6.89 | | (86) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 45.91/6.89 | | [v2: $i] : ! [v3: $i] : ( ~ (cons(all_100_1, v1) = v2) | ~ % 45.91/6.89 | | (app(v0, v2) = v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 45.91/6.89 | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : ( ~ % 45.91/6.89 | | (cons(all_100_1, v4) = v5) | ~ (app(v3, v5) = nil) | ~ % 45.91/6.89 | | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v4) = v6)))) % 45.91/6.89 | | % 45.91/6.89 | | GROUND_INST: instantiating (86) with all_102_2, simplifying with (27), (29) % 45.91/6.89 | | gives: % 45.91/6.89 | | (87) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(all_100_1, v0) = % 45.91/6.89 | | v1) | ~ (app(all_102_2, v1) = v2) | ~ $i(v0) | ? [v3: int] : % 45.91/6.89 | | ( ~ (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 45.91/6.89 | | (cons(all_100_1, v3) = v4) | ~ (app(v2, v4) = nil) | ~ $i(v3) % 45.91/6.89 | | | ? [v5: int] : ( ~ (v5 = 0) & ssList(v3) = v5))) % 45.91/6.89 | | % 45.91/6.89 | | GROUND_INST: instantiating (87) with nil, all_100_0, all_102_1, simplifying % 45.91/6.89 | | with (10), (24), (28) gives: % 45.91/6.89 | | (88) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ! % 45.91/6.89 | | [v1: $i] : ( ~ (cons(all_100_1, v0) = v1) | ~ (app(all_102_1, v1) = % 45.91/6.89 | | nil) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = % 45.91/6.89 | | v2)) % 45.91/6.89 | | % 45.91/6.89 | | BETA: splitting (88) gives: % 45.91/6.89 | | % 45.91/6.89 | | Case 1: % 45.91/6.89 | | | % 45.91/6.89 | | | (89) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 45.91/6.89 | | | % 45.91/6.89 | | | REF_CLOSE: (1), (13), (89) are inconsistent by sub-proof #1. % 45.91/6.89 | | | % 45.91/6.89 | | Case 2: % 45.91/6.89 | | | % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_347_1, all_349_1, all_100_1, % 45.91/6.89 | | | simplifying with (60), (63) gives: % 45.91/6.89 | | | (90) all_349_1 = all_347_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_349_1, all_351_1, all_100_1, % 45.91/6.89 | | | simplifying with (63), (65) gives: % 45.91/6.89 | | | (91) all_351_1 = all_349_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with 0, all_353_1, all_100_1, simplifying % 45.91/6.89 | | | with (23), (67) gives: % 45.91/6.89 | | | (92) all_353_1 = 0 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_347_1, all_353_1, all_100_1, % 45.91/6.89 | | | simplifying with (60), (67) gives: % 45.91/6.89 | | | (93) all_353_1 = all_347_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_351_1, all_355_1, all_100_1, % 45.91/6.89 | | | simplifying with (65), (69) gives: % 45.91/6.89 | | | (94) all_355_1 = all_351_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_355_1, all_357_1, all_100_1, % 45.91/6.89 | | | simplifying with (69), (71) gives: % 45.91/6.89 | | | (95) all_357_1 = all_355_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_359_1, all_361_1, all_100_1, % 45.91/6.89 | | | simplifying with (73), (77) gives: % 45.91/6.89 | | | (96) all_361_1 = all_359_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_357_1, all_361_1, all_100_1, % 45.91/6.89 | | | simplifying with (71), (77) gives: % 45.91/6.89 | | | (97) all_361_1 = all_357_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_361_1, all_363_1, all_100_1, % 45.91/6.89 | | | simplifying with (77), (79) gives: % 45.91/6.89 | | | (98) all_363_1 = all_361_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (12) with all_345_1, all_363_1, all_100_1, % 45.91/6.89 | | | simplifying with (58), (79) gives: % 45.91/6.89 | | | (99) all_363_1 = all_345_1 % 45.91/6.89 | | | % 45.91/6.89 | | | GROUND_INST: instantiating (13) with all_359_0, all_365_1, all_100_0, % 45.91/6.89 | | | simplifying with (74), (81) gives: % 45.91/6.89 | | | (100) all_365_1 = all_359_0 % 45.91/6.89 | | | % 45.91/6.89 | | | COMBINE_EQS: (98), (99) imply: % 45.91/6.89 | | | (101) all_361_1 = all_345_1 % 45.91/6.89 | | | % 45.91/6.89 | | | SIMP: (101) implies: % 45.91/6.89 | | | (102) all_361_1 = all_345_1 % 45.91/6.89 | | | % 45.91/6.90 | | | COMBINE_EQS: (96), (97) imply: % 45.91/6.90 | | | (103) all_359_1 = all_357_1 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (96), (102) imply: % 45.91/6.90 | | | (104) all_359_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (103), (104) imply: % 45.91/6.90 | | | (105) all_357_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | SIMP: (105) implies: % 45.91/6.90 | | | (106) all_357_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (95), (106) imply: % 45.91/6.90 | | | (107) all_355_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | SIMP: (107) implies: % 45.91/6.90 | | | (108) all_355_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (94), (108) imply: % 45.91/6.90 | | | (109) all_351_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | SIMP: (109) implies: % 45.91/6.90 | | | (110) all_351_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (92), (93) imply: % 45.91/6.90 | | | (111) all_347_1 = 0 % 45.91/6.90 | | | % 45.91/6.90 | | | SIMP: (111) implies: % 45.91/6.90 | | | (112) all_347_1 = 0 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (91), (110) imply: % 45.91/6.90 | | | (113) all_349_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | SIMP: (113) implies: % 45.91/6.90 | | | (114) all_349_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (90), (114) imply: % 45.91/6.90 | | | (115) all_347_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | SIMP: (115) implies: % 45.91/6.90 | | | (116) all_347_1 = all_345_1 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (112), (116) imply: % 45.91/6.90 | | | (117) all_345_1 = 0 % 45.91/6.90 | | | % 45.91/6.90 | | | COMBINE_EQS: (104), (117) imply: % 45.91/6.90 | | | (118) all_359_1 = 0 % 45.91/6.90 | | | % 45.91/6.90 | | | BETA: splitting (45) gives: % 45.91/6.90 | | | % 45.91/6.90 | | | Case 1: % 45.91/6.90 | | | | % 45.91/6.90 | | | | (119) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_100_1) = v0) % 45.91/6.90 | | | | % 45.91/6.90 | | | | DELTA: instantiating (119) with fresh symbol all_519_0 gives: % 45.91/6.90 | | | | (120) ~ (all_519_0 = 0) & ssItem(all_100_1) = all_519_0 % 45.91/6.90 | | | | % 45.91/6.90 | | | | ALPHA: (120) implies: % 45.91/6.90 | | | | (121) ~ (all_519_0 = 0) % 45.91/6.90 | | | | (122) ssItem(all_100_1) = all_519_0 % 45.91/6.90 | | | | % 45.91/6.90 | | | | DELTA: instantiating (119) with fresh symbol all_527_0 gives: % 45.91/6.90 | | | | (123) ~ (all_527_0 = 0) & ssItem(all_100_1) = all_527_0 % 45.91/6.90 | | | | % 45.91/6.90 | | | | ALPHA: (123) implies: % 45.91/6.90 | | | | (124) ssItem(all_100_1) = all_527_0 % 45.91/6.90 | | | | % 45.91/6.90 | | | | BETA: splitting (75) gives: % 45.91/6.90 | | | | % 45.91/6.90 | | | | Case 1: % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | (125) ~ (all_359_1 = 0) % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | REDUCE: (118), (125) imply: % 45.91/6.90 | | | | | (126) $false % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | CLOSE: (126) is inconsistent. % 45.91/6.90 | | | | | % 45.91/6.90 | | | | Case 2: % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | (127) all_359_0 = 0 % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | COMBINE_EQS: (100), (127) imply: % 45.91/6.90 | | | | | (128) all_365_1 = 0 % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | BETA: splitting (82) gives: % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | Case 1: % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | (129) ~ (all_365_1 = 0) % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | REDUCE: (128), (129) imply: % 45.91/6.90 | | | | | | (130) $false % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | CLOSE: (130) is inconsistent. % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | Case 2: % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | DELTA: instantiating (119) with fresh symbol all_551_0 gives: % 45.91/6.90 | | | | | | (131) ~ (all_551_0 = 0) & ssItem(all_100_1) = all_551_0 % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | ALPHA: (131) implies: % 45.91/6.90 | | | | | | (132) ssItem(all_100_1) = all_551_0 % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | GROUND_INST: instantiating (12) with 0, all_527_0, all_100_1, % 45.91/6.90 | | | | | | simplifying with (23), (124) gives: % 45.91/6.90 | | | | | | (133) all_527_0 = 0 % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | GROUND_INST: instantiating (12) with all_527_0, all_551_0, % 45.91/6.90 | | | | | | all_100_1, simplifying with (124), (132) gives: % 45.91/6.90 | | | | | | (134) all_551_0 = all_527_0 % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | GROUND_INST: instantiating (12) with all_519_0, all_551_0, % 45.91/6.90 | | | | | | all_100_1, simplifying with (122), (132) gives: % 45.91/6.90 | | | | | | (135) all_551_0 = all_519_0 % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | COMBINE_EQS: (134), (135) imply: % 45.91/6.90 | | | | | | (136) all_527_0 = all_519_0 % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | SIMP: (136) implies: % 45.91/6.90 | | | | | | (137) all_527_0 = all_519_0 % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | COMBINE_EQS: (133), (137) imply: % 45.91/6.90 | | | | | | (138) all_519_0 = 0 % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | REDUCE: (121), (138) imply: % 45.91/6.90 | | | | | | (139) $false % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | CLOSE: (139) is inconsistent. % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | End of split % 45.91/6.90 | | | | | % 45.91/6.90 | | | | End of split % 45.91/6.90 | | | | % 45.91/6.90 | | | Case 2: % 45.91/6.90 | | | | % 45.91/6.90 | | | | (140) ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_100_0) = v1) | ~ % 45.91/6.90 | | | | $i(v0) | ? [v2: any] : ? [v3: any] : (memberP(v0, % 45.91/6.90 | | | | all_100_1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | ! % 45.91/6.90 | | | | [v4: $i] : ( ~ (app(v1, v4) = all_93_0) | ~ $i(v4) | ? % 45.91/6.90 | | | | [v5: any] : ? [v6: any] : (memberP(v4, all_100_1) = v6 % 45.91/6.90 | | | | & ssList(v4) = v5 & ( ~ (v5 = 0) | ( ~ (v6 = 0) & ~ % 45.91/6.90 | | | | (v3 = 0)))))))) % 45.91/6.90 | | | | % 45.91/6.90 | | | | GROUND_INST: instantiating (140) with all_102_2, all_102_1, simplifying % 45.91/6.90 | | | | with (27), (28) gives: % 45.91/6.90 | | | | (141) ? [v0: any] : ? [v1: any] : (memberP(all_102_2, all_100_1) = % 45.91/6.90 | | | | v1 & ssList(all_102_2) = v0 & ( ~ (v0 = 0) | ! [v2: $i] : ( % 45.91/6.90 | | | | ~ (app(all_102_1, v2) = all_93_0) | ~ $i(v2) | ? [v3: % 45.91/6.90 | | | | any] : ? [v4: any] : (memberP(v2, all_100_1) = v4 & % 45.91/6.90 | | | | ssList(v2) = v3 & ( ~ (v3 = 0) | ( ~ (v4 = 0) & ~ (v1 % 45.91/6.90 | | | | = 0))))))) % 45.91/6.90 | | | | % 45.91/6.90 | | | | DELTA: instantiating (141) with fresh symbols all_520_0, all_520_1 % 45.91/6.90 | | | | gives: % 45.91/6.90 | | | | (142) memberP(all_102_2, all_100_1) = all_520_0 & ssList(all_102_2) = % 45.91/6.90 | | | | all_520_1 & ( ~ (all_520_1 = 0) | ! [v0: $i] : ( ~ % 45.91/6.90 | | | | (app(all_102_1, v0) = all_93_0) | ~ $i(v0) | ? [v1: any] % 45.91/6.90 | | | | : ? [v2: any] : (memberP(v0, all_100_1) = v2 & ssList(v0) % 45.91/6.90 | | | | = v1 & ( ~ (v1 = 0) | ( ~ (v2 = 0) & ~ (all_520_0 = % 45.91/6.90 | | | | 0)))))) % 45.91/6.90 | | | | % 45.91/6.90 | | | | ALPHA: (142) implies: % 45.91/6.90 | | | | (143) ssList(all_102_2) = all_520_1 % 45.91/6.90 | | | | (144) memberP(all_102_2, all_100_1) = all_520_0 % 45.91/6.90 | | | | (145) ~ (all_520_1 = 0) | ! [v0: $i] : ( ~ (app(all_102_1, v0) = % 45.91/6.90 | | | | all_93_0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 45.91/6.90 | | | | (memberP(v0, all_100_1) = v2 & ssList(v0) = v1 & ( ~ (v1 = 0) % 45.91/6.90 | | | | | ( ~ (v2 = 0) & ~ (all_520_0 = 0))))) % 45.91/6.90 | | | | % 45.91/6.90 | | | | BETA: splitting (75) gives: % 45.91/6.90 | | | | % 45.91/6.90 | | | | Case 1: % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | (146) ~ (all_359_1 = 0) % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | REDUCE: (118), (146) imply: % 45.91/6.90 | | | | | (147) $false % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | CLOSE: (147) is inconsistent. % 45.91/6.90 | | | | | % 45.91/6.90 | | | | Case 2: % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | (148) all_359_0 = 0 % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | REDUCE: (74), (148) imply: % 45.91/6.90 | | | | | (149) ssList(all_100_0) = 0 % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | BETA: splitting (55) gives: % 45.91/6.90 | | | | | % 45.91/6.90 | | | | | Case 1: % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | (150) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_100_0) = v0) % 45.91/6.90 | | | | | | % 45.91/6.90 | | | | | | DELTA: instantiating (150) with fresh symbol all_552_0 gives: % 45.91/6.91 | | | | | | (151) ~ (all_552_0 = 0) & ssList(all_100_0) = all_552_0 % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | ALPHA: (151) implies: % 45.91/6.91 | | | | | | (152) ~ (all_552_0 = 0) % 45.91/6.91 | | | | | | (153) ssList(all_100_0) = all_552_0 % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | GROUND_INST: instantiating (13) with 0, all_552_0, all_100_0, % 45.91/6.91 | | | | | | simplifying with (149), (153) gives: % 45.91/6.91 | | | | | | (154) all_552_0 = 0 % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | REDUCE: (152), (154) imply: % 45.91/6.91 | | | | | | (155) $false % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | CLOSE: (155) is inconsistent. % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | Case 2: % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | (156) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_102_1, v0) = v1) | % 45.91/6.91 | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 45.91/6.91 | | | | | | (ssList(v0) = v2 & app(all_102_2, v3) = v4 & % 45.91/6.91 | | | | | | app(all_100_0, v0) = v3 & $i(v4) & $i(v3) & ( ~ (v2 = % 45.91/6.91 | | | | | | 0) | v4 = v1))) % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | GROUND_INST: instantiating (156) with all_104_1, all_93_0, % 45.91/6.91 | | | | | | simplifying with (33), (34) gives: % 45.91/6.91 | | | | | | (157) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 45.91/6.91 | | | | | | (ssList(all_104_1) = v0 & app(all_102_2, v1) = v2 & % 45.91/6.91 | | | | | | app(all_100_0, all_104_1) = v1 & $i(v2) & $i(v1) & ( ~ % 45.91/6.91 | | | | | | (v0 = 0) | v2 = all_93_0)) % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | DELTA: instantiating (157) with fresh symbols all_553_0, all_553_1, % 45.91/6.91 | | | | | | all_553_2 gives: % 45.91/6.91 | | | | | | (158) ssList(all_104_1) = all_553_2 & app(all_102_2, all_553_1) = % 45.91/6.91 | | | | | | all_553_0 & app(all_100_0, all_104_1) = all_553_1 & % 45.91/6.91 | | | | | | $i(all_553_0) & $i(all_553_1) & ( ~ (all_553_2 = 0) | % 45.91/6.91 | | | | | | all_553_0 = all_93_0) % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | ALPHA: (158) implies: % 45.91/6.91 | | | | | | (159) ssList(all_104_1) = all_553_2 % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | BETA: splitting (61) gives: % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | | Case 1: % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | (160) ~ (all_347_1 = 0) % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | REDUCE: (112), (160) imply: % 45.91/6.91 | | | | | | | (161) $false % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | CLOSE: (161) is inconsistent. % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | Case 2: % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | GROUND_INST: instantiating (13) with 0, all_520_1, all_102_2, % 45.91/6.91 | | | | | | | simplifying with (29), (143) gives: % 45.91/6.91 | | | | | | | (162) all_520_1 = 0 % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | GROUND_INST: instantiating (13) with 0, all_553_2, all_104_1, % 45.91/6.91 | | | | | | | simplifying with (35), (159) gives: % 45.91/6.91 | | | | | | | (163) all_553_2 = 0 % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | GROUND_INST: instantiating (14) with all_102_0, all_520_0, % 45.91/6.91 | | | | | | | all_100_1, all_102_2, simplifying with (30), (144) % 45.91/6.91 | | | | | | | gives: % 45.91/6.91 | | | | | | | (164) all_520_0 = all_102_0 % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | BETA: splitting (145) gives: % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | | Case 1: % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | (165) ~ (all_520_1 = 0) % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | REDUCE: (162), (165) imply: % 45.91/6.91 | | | | | | | | (166) $false % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | CLOSE: (166) is inconsistent. % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | Case 2: % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | (167) ! [v0: $i] : ( ~ (app(all_102_1, v0) = all_93_0) | ~ % 45.91/6.91 | | | | | | | | $i(v0) | ? [v1: any] : ? [v2: any] : (memberP(v0, % 45.91/6.91 | | | | | | | | all_100_1) = v2 & ssList(v0) = v1 & ( ~ (v1 = 0) % 45.91/6.91 | | | | | | | | | ( ~ (v2 = 0) & ~ (all_520_0 = 0))))) % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | GROUND_INST: instantiating (167) with all_104_1, simplifying % 45.91/6.91 | | | | | | | | with (33), (34) gives: % 45.91/6.91 | | | | | | | | (168) ? [v0: any] : ? [v1: any] : (memberP(all_104_1, % 45.91/6.91 | | | | | | | | all_100_1) = v1 & ssList(all_104_1) = v0 & ( ~ (v0 % 45.91/6.91 | | | | | | | | = 0) | ( ~ (v1 = 0) & ~ (all_520_0 = 0)))) % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | DELTA: instantiating (168) with fresh symbols all_589_0, % 45.91/6.91 | | | | | | | | all_589_1 gives: % 45.91/6.91 | | | | | | | | (169) memberP(all_104_1, all_100_1) = all_589_0 & % 45.91/6.91 | | | | | | | | ssList(all_104_1) = all_589_1 & ( ~ (all_589_1 = 0) | ( % 45.91/6.91 | | | | | | | | ~ (all_589_0 = 0) & ~ (all_520_0 = 0))) % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | ALPHA: (169) implies: % 45.91/6.91 | | | | | | | | (170) ssList(all_104_1) = all_589_1 % 45.91/6.91 | | | | | | | | (171) memberP(all_104_1, all_100_1) = all_589_0 % 45.91/6.91 | | | | | | | | (172) ~ (all_589_1 = 0) | ( ~ (all_589_0 = 0) & ~ % 45.91/6.91 | | | | | | | | (all_520_0 = 0)) % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | GROUND_INST: instantiating (13) with 0, all_589_1, all_104_1, % 45.91/6.91 | | | | | | | | simplifying with (35), (170) gives: % 45.91/6.91 | | | | | | | | (173) all_589_1 = 0 % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | GROUND_INST: instantiating (14) with all_104_0, all_589_0, % 45.91/6.91 | | | | | | | | all_100_1, all_104_1, simplifying with (36), (171) % 45.91/6.91 | | | | | | | | gives: % 45.91/6.91 | | | | | | | | (174) all_589_0 = all_104_0 % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | BETA: splitting (172) gives: % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | | Case 1: % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | (175) ~ (all_589_1 = 0) % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | REDUCE: (173), (175) imply: % 45.91/6.91 | | | | | | | | | (176) $false % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | CLOSE: (176) is inconsistent. % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | Case 2: % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | (177) ~ (all_589_0 = 0) & ~ (all_520_0 = 0) % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | ALPHA: (177) implies: % 45.91/6.91 | | | | | | | | | (178) ~ (all_520_0 = 0) % 45.91/6.91 | | | | | | | | | (179) ~ (all_589_0 = 0) % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | REDUCE: (174), (179) imply: % 45.91/6.91 | | | | | | | | | (180) ~ (all_104_0 = 0) % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | REDUCE: (164), (178) imply: % 45.91/6.91 | | | | | | | | | (181) ~ (all_102_0 = 0) % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | BETA: splitting (37) gives: % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | | Case 1: % 45.91/6.91 | | | | | | | | | | % 45.91/6.91 | | | | | | | | | | (182) all_104_0 = 0 % 45.91/6.91 | | | | | | | | | | % 45.91/6.91 | | | | | | | | | | REDUCE: (180), (182) imply: % 45.91/6.91 | | | | | | | | | | (183) $false % 45.91/6.91 | | | | | | | | | | % 45.91/6.91 | | | | | | | | | | CLOSE: (183) is inconsistent. % 45.91/6.91 | | | | | | | | | | % 45.91/6.91 | | | | | | | | | Case 2: % 45.91/6.91 | | | | | | | | | | % 45.91/6.91 | | | | | | | | | | (184) all_102_0 = 0 % 45.91/6.91 | | | | | | | | | | % 45.91/6.91 | | | | | | | | | | REDUCE: (181), (184) imply: % 45.91/6.91 | | | | | | | | | | (185) $false % 45.91/6.91 | | | | | | | | | | % 45.91/6.91 | | | | | | | | | | CLOSE: (185) is inconsistent. % 45.91/6.91 | | | | | | | | | | % 45.91/6.91 | | | | | | | | | End of split % 45.91/6.91 | | | | | | | | | % 45.91/6.91 | | | | | | | | End of split % 45.91/6.91 | | | | | | | | % 45.91/6.91 | | | | | | | End of split % 45.91/6.91 | | | | | | | % 45.91/6.91 | | | | | | End of split % 45.91/6.91 | | | | | | % 45.91/6.91 | | | | | End of split % 45.91/6.91 | | | | | % 45.91/6.91 | | | | End of split % 45.91/6.91 | | | | % 45.91/6.91 | | | End of split % 45.91/6.91 | | | % 45.91/6.91 | | End of split % 45.91/6.91 | | % 45.91/6.91 | End of split % 45.91/6.91 | % 45.91/6.91 End of proof % 45.91/6.91 % 45.91/6.91 Sub-proof #1 shows that the following formulas are inconsistent: % 45.91/6.91 ---------------------------------------------------------------- % 45.91/6.91 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 45.91/6.91 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 45.91/6.91 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 45.91/6.91 (3) ssList(nil) = 0 % 45.91/6.91 % 45.91/6.91 Begin of proof % 45.91/6.91 | % 45.91/6.91 | DELTA: instantiating (1) with fresh symbol all_484_0 gives: % 45.91/6.91 | (4) ~ (all_484_0 = 0) & ssList(nil) = all_484_0 % 45.91/6.91 | % 45.91/6.91 | ALPHA: (4) implies: % 45.91/6.91 | (5) ~ (all_484_0 = 0) % 45.91/6.91 | (6) ssList(nil) = all_484_0 % 45.91/6.91 | % 45.91/6.91 | DELTA: instantiating (1) with fresh symbol all_486_0 gives: % 45.91/6.92 | (7) ~ (all_486_0 = 0) & ssList(nil) = all_486_0 % 45.91/6.92 | % 45.91/6.92 | ALPHA: (7) implies: % 45.91/6.92 | (8) ssList(nil) = all_486_0 % 45.91/6.92 | % 45.91/6.92 | DELTA: instantiating (1) with fresh symbol all_488_0 gives: % 45.91/6.92 | (9) ~ (all_488_0 = 0) & ssList(nil) = all_488_0 % 45.91/6.92 | % 45.91/6.92 | ALPHA: (9) implies: % 45.91/6.92 | (10) ssList(nil) = all_488_0 % 45.91/6.92 | % 45.91/6.92 | DELTA: instantiating (1) with fresh symbol all_490_0 gives: % 45.91/6.92 | (11) ~ (all_490_0 = 0) & ssList(nil) = all_490_0 % 45.91/6.92 | % 45.91/6.92 | ALPHA: (11) implies: % 45.91/6.92 | (12) ssList(nil) = all_490_0 % 45.91/6.92 | % 45.91/6.92 | GROUND_INST: instantiating (2) with 0, all_488_0, nil, simplifying with (3), % 45.91/6.92 | (10) gives: % 45.91/6.92 | (13) all_488_0 = 0 % 45.91/6.92 | % 45.91/6.92 | GROUND_INST: instantiating (2) with all_488_0, all_490_0, nil, simplifying % 45.91/6.92 | with (10), (12) gives: % 45.91/6.92 | (14) all_490_0 = all_488_0 % 45.91/6.92 | % 45.91/6.92 | GROUND_INST: instantiating (2) with all_486_0, all_490_0, nil, simplifying % 45.91/6.92 | with (8), (12) gives: % 45.91/6.92 | (15) all_490_0 = all_486_0 % 45.91/6.92 | % 45.91/6.92 | GROUND_INST: instantiating (2) with all_484_0, all_490_0, nil, simplifying % 45.91/6.92 | with (6), (12) gives: % 45.91/6.92 | (16) all_490_0 = all_484_0 % 45.91/6.92 | % 45.91/6.92 | COMBINE_EQS: (15), (16) imply: % 45.91/6.92 | (17) all_486_0 = all_484_0 % 45.91/6.92 | % 45.91/6.92 | COMBINE_EQS: (14), (15) imply: % 45.91/6.92 | (18) all_488_0 = all_486_0 % 45.91/6.92 | % 45.91/6.92 | SIMP: (18) implies: % 45.91/6.92 | (19) all_488_0 = all_486_0 % 45.91/6.92 | % 45.91/6.92 | COMBINE_EQS: (13), (19) imply: % 45.91/6.92 | (20) all_486_0 = 0 % 45.91/6.92 | % 45.91/6.92 | SIMP: (20) implies: % 45.91/6.92 | (21) all_486_0 = 0 % 45.91/6.92 | % 45.91/6.92 | COMBINE_EQS: (17), (21) imply: % 45.91/6.92 | (22) all_484_0 = 0 % 45.91/6.92 | % 45.91/6.92 | SIMP: (22) implies: % 45.91/6.92 | (23) all_484_0 = 0 % 45.91/6.92 | % 45.91/6.92 | REDUCE: (5), (23) imply: % 45.91/6.92 | (24) $false % 45.91/6.92 | % 45.91/6.92 | CLOSE: (24) is inconsistent. % 45.91/6.92 | % 45.91/6.92 End of proof % 45.91/6.92 % SZS output end Proof for theBenchmark % 45.91/6.92 % 45.91/6.92 6322ms %------------------------------------------------------------------------------