%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC275+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 : n021.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 20:50:35 EDT 2023 % Result : Theorem 51.79s 7.54s % Output : Proof 157.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWC275+1 : TPTP v8.1.2. Released v2.4.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 15:23:13 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.91/1.64 Prover 1: Preprocessing ... % 6.91/1.66 Prover 4: Preprocessing ... % 6.91/1.70 Prover 2: Preprocessing ... % 6.91/1.70 Prover 5: Preprocessing ... % 6.91/1.70 Prover 3: Preprocessing ... % 6.91/1.70 Prover 0: Preprocessing ... % 6.91/1.70 Prover 6: Preprocessing ... % 17.49/3.10 Prover 2: Proving ... % 17.87/3.16 Prover 5: Constructing countermodel ... % 18.24/3.19 Prover 1: Constructing countermodel ... % 18.48/3.23 Prover 6: Proving ... % 18.73/3.27 Prover 3: Constructing countermodel ... % 24.38/4.04 Prover 4: Constructing countermodel ... % 26.18/4.25 Prover 0: Proving ... % 51.79/7.54 Prover 3: proved (6899ms) % 51.79/7.54 % 51.79/7.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 51.79/7.54 % 51.79/7.54 Prover 5: stopped % 51.79/7.54 Prover 2: stopped % 51.79/7.55 Prover 6: stopped % 51.79/7.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 51.79/7.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 51.79/7.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 51.79/7.56 Prover 0: stopped % 51.79/7.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 51.79/7.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 53.72/7.77 Prover 13: Preprocessing ... % 53.72/7.78 Prover 8: Preprocessing ... % 53.72/7.78 Prover 7: Preprocessing ... % 53.72/7.79 Prover 10: Preprocessing ... % 53.88/7.81 Prover 11: Preprocessing ... % 54.72/7.98 Prover 7: Constructing countermodel ... % 54.72/8.01 Prover 10: Constructing countermodel ... % 56.48/8.14 Prover 13: Constructing countermodel ... % 56.48/8.14 Prover 8: Warning: ignoring some quantifiers % 56.48/8.16 Prover 8: Constructing countermodel ... % 62.78/8.98 Prover 11: Constructing countermodel ... % 86.81/12.09 Prover 13: stopped % 87.28/12.11 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 87.69/12.19 Prover 16: Preprocessing ... % 89.51/12.40 Prover 16: Constructing countermodel ... % 116.81/15.97 Prover 1: stopped % 116.81/15.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 118.09/16.12 Prover 19: Preprocessing ... % 121.39/16.59 Prover 19: Warning: ignoring some quantifiers % 121.39/16.65 Prover 19: Constructing countermodel ... % 128.21/17.41 Prover 16: stopped % 144.13/19.57 Prover 19: stopped % 156.25/21.66 Prover 8: Found proof (size 213) % 156.25/21.66 Prover 8: proved (14028ms) % 156.25/21.66 Prover 7: stopped % 156.25/21.67 Prover 11: stopped % 156.25/21.67 Prover 4: stopped % 156.25/21.73 Prover 10: stopped % 156.25/21.73 % 156.25/21.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 156.25/21.73 % 156.40/21.76 % SZS output start Proof for theBenchmark % 156.40/21.77 Assumptions after simplification: % 156.40/21.77 --------------------------------- % 156.40/21.77 % 156.40/21.77 (ax11) % 156.54/21.82 ! [v0: $i] : ! [v1: any] : ( ~ (totalorderedP(v0) = v1) | ~ $i(v0) | ? % 156.54/21.82 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 156.54/21.82 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~ % 156.54/21.82 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & % 156.54/21.82 ssItem(v3) = v5) | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5) % 156.54/21.82 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v6) = % 156.54/21.82 v7) | ~ (app(v5, v7) = v8) | ~ $i(v6) | ? [v9: int] : ( ~ % 156.54/21.82 (v9 = 0) & ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : (v4 % 156.54/21.82 = 0 | ~ (cons(v3, v9) = v10) | ~ (app(v8, v10) = v0) | ~ % 156.54/21.82 $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v9) = % 156.54/21.82 v11))))))) & (v1 = 0 | ? [v2: $i] : (ssItem(v2) = 0 & % 156.54/21.82 $i(v2) & ? [v3: $i] : ? [v4: any] : (leq(v2, v3) = v4 & ssItem(v3) = % 156.54/21.82 0 & $i(v3) & ? [v5: $i] : (ssList(v5) = 0 & $i(v5) & ? [v6: $i] : % 156.54/21.82 ? [v7: $i] : ? [v8: $i] : (ssList(v6) = 0 & cons(v2, v6) = v7 & % 156.54/21.82 app(v5, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ? [v9: $i] : ? % 156.54/21.82 [v10: $i] : ( ~ (v4 = 0) & ssList(v9) = 0 & cons(v3, v9) = v10 & % 156.54/21.82 app(v8, v10) = v0 & $i(v10) & $i(v9))))))))) % 156.54/21.82 % 156.54/21.82 (ax13) % 156.54/21.83 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 156.54/21.83 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 156.54/21.83 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 156.54/21.83 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 156.54/21.83 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 156.54/21.83 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 156.54/21.83 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 156.54/21.83 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 156.54/21.83 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 156.54/21.83 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 156.54/21.83 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 156.54/21.83 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 156.54/21.83 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 156.54/21.83 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 156.54/21.83 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 156.54/21.83 % 156.54/21.83 (ax15) % 156.54/21.83 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 156.54/21.83 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 156.54/21.83 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 156.54/21.83 % 156.54/21.83 (ax17) % 156.54/21.83 ssList(nil) = 0 & $i(nil) % 156.54/21.83 % 156.54/21.83 (ax2) % 156.80/21.83 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 156.80/21.84 ssItem(v1) = 0 & $i(v1))) % 156.80/21.84 % 156.80/21.84 (ax23) % 156.80/21.84 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 156.80/21.84 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 156.80/21.84 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 156.80/21.84 % 156.80/21.84 (ax25) % 156.80/21.84 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 156.80/21.84 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 156.80/21.84 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 156.80/21.84 % 156.80/21.84 (ax59) % 156.80/21.84 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 156.80/21.84 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 156.80/21.84 (v2 = 0) | v3 = 0))) % 156.80/21.84 % 156.80/21.84 (ax61) % 156.80/21.84 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 156.80/21.84 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 156.80/21.84 (v2 = 0) | v3 = 0))) % 156.80/21.84 % 156.80/21.84 (ax63) % 156.80/21.85 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 156.80/21.85 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 156.80/21.85 (v2 = 0) | v3 = 0))) % 156.80/21.85 % 156.80/21.85 (ax65) % 156.80/21.85 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 156.80/21.85 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 156.80/21.85 (v2 = 0) | v3 = 0))) % 156.80/21.85 % 156.80/21.85 (ax66) % 156.80/21.85 totalorderedP(nil) = 0 & $i(nil) % 156.80/21.85 % 156.80/21.85 (ax68) % 156.87/21.85 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 156.87/21.85 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 156.87/21.85 ~ (v2 = 0) | v3 = 0))) % 156.87/21.85 % 156.87/21.85 (ax71) % 156.87/21.85 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 156.87/21.85 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 156.87/21.85 ~ (v2 = 0) | v3 = 0))) % 156.87/21.85 % 156.87/21.85 (ax72) % 156.87/21.85 duplicatefreeP(nil) = 0 & $i(nil) % 156.87/21.85 % 156.87/21.85 (ax73) % 156.87/21.86 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 156.87/21.86 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 156.87/21.86 (v2 = 0) | v3 = 0))) % 156.87/21.86 % 156.87/21.86 (co1) % 156.87/21.86 $i(nil) & ? [v0: $i] : ? [v1: any] : (totalorderedP(v0) = v1 & ssList(v0) = % 156.87/21.86 0 & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : % 156.87/21.86 (ssList(v3) = 0 & $i(v3) & ? [v4: any] : (v3 = v0 & ~ (v1 = 0) & neq(v2, % 156.87/21.86 nil) = v4 & ( ~ (v4 = 0) | ? [v5: $i] : (memberP(v2, v5) = 0 & % 156.87/21.86 cons(v5, nil) = v0 & ssItem(v5) = 0 & $i(v5))) & ( ~ (v2 = nil) | % 156.87/21.86 v0 = nil))))) % 156.87/21.86 % 156.87/21.86 (function-axioms) % 156.87/21.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 156.87/21.88 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 156.87/21.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 156.87/21.88 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 156.87/21.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 156.87/21.88 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 156.87/21.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 156.87/21.88 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 156.87/21.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 156.87/21.88 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 156.87/21.88 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 156.87/21.88 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 156.87/21.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 156.87/21.88 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 156.87/21.88 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 156.87/21.88 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 156.87/21.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 156.87/21.88 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 156.87/21.88 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 156.87/21.88 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 156.87/21.88 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 156.87/21.88 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 156.87/21.88 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 156.87/21.88 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 156.87/21.88 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 156.87/21.88 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 156.87/21.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 156.87/21.88 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 156.87/21.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 156.87/21.88 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 156.87/21.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 156.87/21.88 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 156.87/21.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 156.87/21.88 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 156.87/21.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 156.87/21.88 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 156.87/21.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 156.87/21.88 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 156.87/21.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 156.87/21.88 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 156.87/21.88 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 156.87/21.88 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 156.87/21.88 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ? % 156.87/21.88 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ? % 156.87/21.88 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ? % 156.87/21.88 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ? % 156.87/21.88 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ? % 156.87/21.88 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2) % 156.87/21.88 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) = % 156.87/21.88 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 156.87/21.88 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 156.87/21.88 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 156.87/21.88 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 156.87/21.88 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 156.87/21.88 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 156.87/21.88 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 156.87/21.88 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 156.87/21.88 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 156.87/21.88 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 156.87/21.88 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 156.87/21.88 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 156.87/21.88 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 156.87/21.88 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0) % 156.87/21.88 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ? % 156.87/21.88 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 156.87/21.88 (hd(v0) = v1 & $i(v1)) % 156.87/21.88 % 156.87/21.88 Further assumptions not needed in the proof: % 156.87/21.88 -------------------------------------------- % 156.87/21.88 ax1, ax10, ax12, ax14, ax16, ax18, ax19, ax20, ax21, ax22, ax24, ax26, ax27, % 156.87/21.88 ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, % 156.87/21.88 ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, % 156.87/21.88 ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, ax67, % 156.87/21.88 ax69, ax7, ax70, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, % 156.87/21.88 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, % 156.87/21.88 ax95 % 156.87/21.88 % 156.87/21.88 Those formulas are unsatisfiable: % 156.87/21.88 --------------------------------- % 156.87/21.88 % 156.87/21.88 Begin of proof % 156.87/21.88 | % 156.87/21.88 | ALPHA: (ax17) implies: % 156.87/21.89 | (1) ssList(nil) = 0 % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax59) implies: % 156.87/21.89 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 156.87/21.89 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 156.87/21.89 | ~ (v2 = 0) | v3 = 0))) % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax61) implies: % 156.87/21.89 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 156.87/21.89 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 156.87/21.89 | ( ~ (v2 = 0) | v3 = 0))) % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax63) implies: % 156.87/21.89 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 156.87/21.89 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 156.87/21.89 | ( ~ (v2 = 0) | v3 = 0))) % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax65) implies: % 156.87/21.89 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 156.87/21.89 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 156.87/21.89 | & ( ~ (v2 = 0) | v3 = 0))) % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax66) implies: % 156.87/21.89 | (6) totalorderedP(nil) = 0 % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax68) implies: % 156.87/21.89 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 156.87/21.89 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 156.87/21.89 | & ( ~ (v2 = 0) | v3 = 0))) % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax71) implies: % 156.87/21.89 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 156.87/21.89 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 156.87/21.89 | & ( ~ (v2 = 0) | v3 = 0))) % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax72) implies: % 156.87/21.89 | (9) duplicatefreeP(nil) = 0 % 156.87/21.89 | % 156.87/21.89 | ALPHA: (ax73) implies: % 156.87/21.89 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 156.87/21.89 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 156.87/21.89 | ( ~ (v2 = 0) | v3 = 0))) % 156.87/21.89 | % 156.87/21.89 | ALPHA: (co1) implies: % 156.87/21.90 | (11) $i(nil) % 156.87/21.90 | (12) ? [v0: $i] : ? [v1: any] : (totalorderedP(v0) = v1 & ssList(v0) = 0 % 156.87/21.90 | & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : % 156.87/21.90 | (ssList(v3) = 0 & $i(v3) & ? [v4: any] : (v3 = v0 & ~ (v1 = 0) & % 156.87/21.90 | neq(v2, nil) = v4 & ( ~ (v4 = 0) | ? [v5: $i] : (memberP(v2, % 156.87/21.90 | v5) = 0 & cons(v5, nil) = v0 & ssItem(v5) = 0 & $i(v5))) % 156.87/21.90 | & ( ~ (v2 = nil) | v0 = nil))))) % 156.87/21.90 | % 156.87/21.90 | ALPHA: (function-axioms) implies: % 156.87/21.90 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 156.87/21.90 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 156.87/21.90 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 156.87/21.90 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 156.87/21.90 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 156.87/21.90 | : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = % 156.87/21.90 | v0)) % 156.87/21.90 | % 156.87/21.90 | DELTA: instantiating (ax2) with fresh symbol all_137_0 gives: % 156.87/21.90 | (16) ssItem(all_137_0) = 0 & $i(all_137_0) & ? [v0: any] : ( ~ (v0 = % 156.87/21.90 | all_137_0) & ssItem(v0) = 0 & $i(v0)) % 156.87/21.90 | % 156.87/21.90 | ALPHA: (16) implies: % 156.87/21.90 | (17) ? [v0: any] : ( ~ (v0 = all_137_0) & ssItem(v0) = 0 & $i(v0)) % 156.87/21.90 | % 156.87/21.90 | DELTA: instantiating (12) with fresh symbols all_139_0, all_139_1 gives: % 156.87/21.91 | (18) totalorderedP(all_139_1) = all_139_0 & ssList(all_139_1) = 0 & % 156.87/21.91 | $i(all_139_1) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 156.87/21.91 | (ssList(v1) = 0 & $i(v1) & ? [v2: any] : (v1 = all_139_1 & ~ % 156.87/21.91 | (all_139_0 = 0) & neq(v0, nil) = v2 & ( ~ (v2 = 0) | ? [v3: $i] % 156.87/21.91 | : (memberP(v0, v3) = 0 & cons(v3, nil) = all_139_1 & % 156.87/21.91 | ssItem(v3) = 0 & $i(v3))) & ( ~ (v0 = nil) | all_139_1 = % 156.87/21.91 | nil)))) % 156.87/21.91 | % 156.87/21.91 | ALPHA: (18) implies: % 156.87/21.91 | (19) totalorderedP(all_139_1) = all_139_0 % 156.87/21.91 | (20) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 156.87/21.91 | & $i(v1) & ? [v2: any] : (v1 = all_139_1 & ~ (all_139_0 = 0) & % 156.87/21.91 | neq(v0, nil) = v2 & ( ~ (v2 = 0) | ? [v3: $i] : (memberP(v0, % 156.87/21.91 | v3) = 0 & cons(v3, nil) = all_139_1 & ssItem(v3) = 0 & % 156.87/21.91 | $i(v3))) & ( ~ (v0 = nil) | all_139_1 = nil)))) % 156.87/21.91 | % 156.87/21.91 | DELTA: instantiating (17) with fresh symbol all_141_0 gives: % 156.87/21.91 | (21) ~ (all_141_0 = all_137_0) & ssItem(all_141_0) = 0 & $i(all_141_0) % 156.87/21.91 | % 156.87/21.91 | ALPHA: (21) implies: % 156.87/21.91 | (22) $i(all_141_0) % 156.87/21.91 | (23) ssItem(all_141_0) = 0 % 156.87/21.91 | % 156.87/21.91 | DELTA: instantiating (20) with fresh symbol all_143_0 gives: % 157.16/21.91 | (24) ssList(all_143_0) = 0 & $i(all_143_0) & ? [v0: $i] : (ssList(v0) = 0 % 157.16/21.91 | & $i(v0) & ? [v1: any] : (v0 = all_139_1 & ~ (all_139_0 = 0) & % 157.16/21.91 | neq(all_143_0, nil) = v1 & ( ~ (v1 = 0) | ? [v2: $i] : % 157.16/21.91 | (memberP(all_143_0, v2) = 0 & cons(v2, nil) = all_139_1 & % 157.16/21.91 | ssItem(v2) = 0 & $i(v2))) & ( ~ (all_143_0 = nil) | all_139_1 % 157.16/21.91 | = nil))) % 157.16/21.91 | % 157.16/21.91 | ALPHA: (24) implies: % 157.16/21.91 | (25) $i(all_143_0) % 157.16/21.91 | (26) ssList(all_143_0) = 0 % 157.16/21.92 | (27) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: any] : (v0 = % 157.16/21.92 | all_139_1 & ~ (all_139_0 = 0) & neq(all_143_0, nil) = v1 & ( ~ % 157.16/21.92 | (v1 = 0) | ? [v2: $i] : (memberP(all_143_0, v2) = 0 & cons(v2, % 157.16/21.92 | nil) = all_139_1 & ssItem(v2) = 0 & $i(v2))) & ( ~ % 157.16/21.92 | (all_143_0 = nil) | all_139_1 = nil))) % 157.16/21.92 | % 157.16/21.92 | DELTA: instantiating (27) with fresh symbol all_145_0 gives: % 157.16/21.92 | (28) ssList(all_145_0) = 0 & $i(all_145_0) & ? [v0: any] : (all_145_0 = % 157.16/21.92 | all_139_1 & ~ (all_139_0 = 0) & neq(all_143_0, nil) = v0 & ( ~ (v0 % 157.16/21.92 | = 0) | ? [v1: $i] : (memberP(all_143_0, v1) = 0 & cons(v1, nil) % 157.16/21.92 | = all_139_1 & ssItem(v1) = 0 & $i(v1))) & ( ~ (all_143_0 = nil) % 157.16/21.92 | | all_139_1 = nil)) % 157.16/21.92 | % 157.16/21.92 | ALPHA: (28) implies: % 157.16/21.92 | (29) $i(all_145_0) % 157.16/21.92 | (30) ssList(all_145_0) = 0 % 157.16/21.92 | (31) ? [v0: any] : (all_145_0 = all_139_1 & ~ (all_139_0 = 0) & % 157.16/21.92 | neq(all_143_0, nil) = v0 & ( ~ (v0 = 0) | ? [v1: $i] : % 157.16/21.92 | (memberP(all_143_0, v1) = 0 & cons(v1, nil) = all_139_1 & % 157.16/21.92 | ssItem(v1) = 0 & $i(v1))) & ( ~ (all_143_0 = nil) | all_139_1 = % 157.16/21.92 | nil)) % 157.16/21.92 | % 157.16/21.92 | DELTA: instantiating (31) with fresh symbol all_147_0 gives: % 157.16/21.92 | (32) all_145_0 = all_139_1 & ~ (all_139_0 = 0) & neq(all_143_0, nil) = % 157.16/21.92 | all_147_0 & ( ~ (all_147_0 = 0) | ? [v0: $i] : (memberP(all_143_0, % 157.16/21.92 | v0) = 0 & cons(v0, nil) = all_139_1 & ssItem(v0) = 0 & $i(v0))) % 157.16/21.92 | & ( ~ (all_143_0 = nil) | all_139_1 = nil) % 157.16/21.92 | % 157.16/21.92 | ALPHA: (32) implies: % 157.16/21.92 | (33) all_145_0 = all_139_1 % 157.16/21.92 | (34) ~ (all_139_0 = 0) % 157.16/21.92 | (35) neq(all_143_0, nil) = all_147_0 % 157.16/21.92 | (36) ~ (all_143_0 = nil) | all_139_1 = nil % 157.16/21.92 | (37) ~ (all_147_0 = 0) | ? [v0: $i] : (memberP(all_143_0, v0) = 0 & % 157.16/21.92 | cons(v0, nil) = all_139_1 & ssItem(v0) = 0 & $i(v0)) % 157.16/21.92 | % 157.16/21.92 | REDUCE: (30), (33) imply: % 157.16/21.92 | (38) ssList(all_139_1) = 0 % 157.16/21.92 | % 157.16/21.93 | REDUCE: (29), (33) imply: % 157.16/21.93 | (39) $i(all_139_1) % 157.16/21.93 | % 157.16/21.93 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (11) gives: % 157.16/21.93 | (40) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 157.16/21.93 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 157.16/21.93 | ( ~ (v2 = 0) | v3 = nil))) % 157.16/21.93 | % 157.16/21.93 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (11) gives: % 157.16/21.93 | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 157.16/21.93 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 157.16/21.93 | ( ~ (v2 = 0) | v3 = v0))) % 157.16/21.93 | % 157.16/21.93 | GROUND_INST: instantiating (ax15) with all_143_0, simplifying with (25), (26) % 157.16/21.93 | gives: % 157.16/21.93 | (42) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_143_0, v0) = v1) | ~ $i(v0) % 157.16/21.93 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 157.16/21.93 | ~ (v0 = all_143_0)) & (v1 = 0 | v0 = all_143_0))) % 157.16/21.93 | % 157.16/21.93 | GROUND_INST: instantiating (ax11) with all_139_1, all_139_0, simplifying with % 157.16/21.93 | (19), (39) gives: % 157.16/21.94 | (43) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) | (( ~ % 157.16/21.94 | (all_139_0 = 0) | ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | % 157.16/21.94 | ! [v1: $i] : ! [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1) % 157.16/21.94 | | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: $i] % 157.16/21.94 | : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: $i] % 157.16/21.94 | : ! [v6: $i] : ( ~ (cons(v0, v4) = v5) | ~ (app(v3, v5) = % 157.16/21.94 | v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & % 157.16/21.94 | ssList(v4) = v7) | ! [v7: $i] : ! [v8: $i] : (v2 = 0 | % 157.16/21.94 | ~ (cons(v1, v7) = v8) | ~ (app(v6, v8) = all_139_1) | % 157.16/21.94 | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v7) = % 157.16/21.94 | v9))))))) & (all_139_0 = 0 | ? [v0: $i] : (ssItem(v0) % 157.16/21.94 | = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : (leq(v0, v1) = v2 & % 157.16/21.94 | ssItem(v1) = 0 & $i(v1) & ? [v3: $i] : (ssList(v3) = 0 & % 157.16/21.94 | $i(v3) & ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 157.16/21.94 | (ssList(v4) = 0 & cons(v0, v4) = v5 & app(v3, v5) = v6 & % 157.16/21.94 | $i(v6) & $i(v5) & $i(v4) & ? [v7: $i] : ? [v8: $i] : ( ~ % 157.16/21.94 | (v2 = 0) & ssList(v7) = 0 & cons(v1, v7) = v8 & app(v6, % 157.16/21.94 | v8) = all_139_1 & $i(v8) & $i(v7)))))))) % 157.16/21.94 | % 157.16/21.94 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (9), (11) % 157.16/21.94 | gives: % 157.16/21.94 | (44) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 157.16/21.94 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 157.16/21.94 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 157.16/21.94 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 157.16/21.94 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 157.16/21.94 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 157.16/21.94 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 157.16/21.94 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 157.16/21.94 | v8)))))) % 157.16/21.94 | % 157.16/21.94 | GROUND_INST: instantiating (42) with nil, all_147_0, simplifying with (11), % 157.16/21.94 | (35) gives: % 157.16/21.94 | (45) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_147_0 = 0) % 157.16/21.94 | | ~ (all_143_0 = nil)) & (all_147_0 = 0 | all_143_0 = nil)) % 157.16/21.94 | % 157.16/21.94 | BETA: splitting (44) gives: % 157.16/21.94 | % 157.16/21.94 | Case 1: % 157.16/21.94 | | % 157.16/21.94 | | (46) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 157.16/21.95 | | % 157.16/21.95 | | DELTA: instantiating (46) with fresh symbol all_321_0 gives: % 157.16/21.95 | | (47) ~ (all_321_0 = 0) & ssList(nil) = all_321_0 % 157.16/21.95 | | % 157.16/21.95 | | ALPHA: (47) implies: % 157.16/21.95 | | (48) ~ (all_321_0 = 0) % 157.16/21.95 | | (49) ssList(nil) = all_321_0 % 157.16/21.95 | | % 157.16/21.95 | | DELTA: instantiating (46) with fresh symbol all_323_0 gives: % 157.16/21.95 | | (50) ~ (all_323_0 = 0) & ssList(nil) = all_323_0 % 157.16/21.95 | | % 157.16/21.95 | | ALPHA: (50) implies: % 157.16/21.95 | | (51) ssList(nil) = all_323_0 % 157.16/21.95 | | % 157.16/21.95 | | GROUND_INST: instantiating (14) with 0, all_323_0, nil, simplifying with % 157.16/21.95 | | (1), (51) gives: % 157.16/21.95 | | (52) all_323_0 = 0 % 157.16/21.95 | | % 157.16/21.95 | | GROUND_INST: instantiating (14) with all_321_0, all_323_0, nil, simplifying % 157.16/21.95 | | with (49), (51) gives: % 157.16/21.95 | | (53) all_323_0 = all_321_0 % 157.16/21.95 | | % 157.16/21.95 | | COMBINE_EQS: (52), (53) imply: % 157.16/21.95 | | (54) all_321_0 = 0 % 157.16/21.95 | | % 157.16/21.95 | | REDUCE: (48), (54) imply: % 157.16/21.95 | | (55) $false % 157.16/21.95 | | % 157.16/21.95 | | CLOSE: (55) is inconsistent. % 157.16/21.95 | | % 157.16/21.95 | Case 2: % 157.16/21.95 | | % 157.16/21.95 | | (56) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 157.16/21.95 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 157.16/21.95 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 157.16/21.95 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 157.16/21.95 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 157.16/21.95 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 157.16/21.95 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 157.16/21.95 | | 0) & ssList(v6) = v8)))))) % 157.16/21.95 | | % 157.16/21.95 | | BETA: splitting (43) gives: % 157.16/21.95 | | % 157.16/21.95 | | Case 1: % 157.16/21.95 | | | % 157.16/21.95 | | | (57) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 157.16/21.95 | | | % 157.16/21.95 | | | DELTA: instantiating (57) with fresh symbol all_336_0 gives: % 157.16/21.95 | | | (58) ~ (all_336_0 = 0) & ssList(all_139_1) = all_336_0 % 157.16/21.95 | | | % 157.16/21.95 | | | ALPHA: (58) implies: % 157.16/21.95 | | | (59) ~ (all_336_0 = 0) % 157.16/21.95 | | | (60) ssList(all_139_1) = all_336_0 % 157.16/21.95 | | | % 157.16/21.95 | | | GROUND_INST: instantiating (14) with 0, all_336_0, all_139_1, simplifying % 157.16/21.95 | | | with (38), (60) gives: % 157.16/21.95 | | | (61) all_336_0 = 0 % 157.16/21.95 | | | % 157.16/21.95 | | | REDUCE: (59), (61) imply: % 157.16/21.95 | | | (62) $false % 157.16/21.95 | | | % 157.16/21.95 | | | CLOSE: (62) is inconsistent. % 157.16/21.95 | | | % 157.16/21.95 | | Case 2: % 157.16/21.95 | | | % 157.16/21.96 | | | (63) ( ~ (all_139_0 = 0) | ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ % 157.16/21.96 | | | $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ (leq(v0, v1) = v2) | % 157.16/21.96 | | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | % 157.16/21.96 | | | ! [v3: $i] : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] % 157.16/21.96 | | | : ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v0, v4) = v5) | ~ % 157.16/21.96 | | | (app(v3, v5) = v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 % 157.16/21.96 | | | = 0) & ssList(v4) = v7) | ! [v7: $i] : ! [v8: $i] % 157.16/21.96 | | | : (v2 = 0 | ~ (cons(v1, v7) = v8) | ~ (app(v6, v8) = % 157.16/21.96 | | | all_139_1) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) % 157.16/21.96 | | | & ssList(v7) = v9))))))) & (all_139_0 = 0 | ? [v0: % 157.16/21.96 | | | $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 157.16/21.96 | | | (leq(v0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ? [v3: $i] : % 157.16/21.96 | | | (ssList(v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: $i] : ? % 157.16/21.96 | | | [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) = v5 & app(v3, % 157.38/21.96 | | | v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? [v7: $i] : ? % 157.38/21.96 | | | [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & cons(v1, v7) % 157.38/21.96 | | | = v8 & app(v6, v8) = all_139_1 & $i(v8) & $i(v7))))))) % 157.38/21.96 | | | % 157.38/21.96 | | | ALPHA: (63) implies: % 157.38/21.96 | | | (64) all_139_0 = 0 | ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: % 157.38/21.96 | | | $i] : ? [v2: any] : (leq(v0, v1) = v2 & ssItem(v1) = 0 & % 157.38/21.96 | | | $i(v1) & ? [v3: $i] : (ssList(v3) = 0 & $i(v3) & ? [v4: $i] % 157.38/21.96 | | | : ? [v5: $i] : ? [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) % 157.38/21.96 | | | = v5 & app(v3, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? % 157.38/21.96 | | | [v7: $i] : ? [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & % 157.38/21.96 | | | cons(v1, v7) = v8 & app(v6, v8) = all_139_1 & $i(v8) & % 157.38/21.96 | | | $i(v7)))))) % 157.38/21.96 | | | % 157.38/21.96 | | | BETA: splitting (64) gives: % 157.38/21.96 | | | % 157.38/21.96 | | | Case 1: % 157.38/21.96 | | | | % 157.38/21.96 | | | | (65) all_139_0 = 0 % 157.38/21.96 | | | | % 157.38/21.96 | | | | REDUCE: (34), (65) imply: % 157.38/21.96 | | | | (66) $false % 157.38/21.96 | | | | % 157.38/21.96 | | | | CLOSE: (66) is inconsistent. % 157.38/21.96 | | | | % 157.38/21.96 | | | Case 2: % 157.38/21.96 | | | | % 157.38/21.96 | | | | (67) ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 157.38/21.96 | | | | any] : (leq(v0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ? [v3: % 157.38/21.96 | | | | $i] : (ssList(v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: $i] % 157.38/21.96 | | | | : ? [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) = v5 & % 157.38/21.96 | | | | app(v3, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? [v7: % 157.38/21.96 | | | | $i] : ? [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & % 157.38/21.96 | | | | cons(v1, v7) = v8 & app(v6, v8) = all_139_1 & $i(v8) & % 157.38/21.96 | | | | $i(v7)))))) % 157.38/21.96 | | | | % 157.38/21.96 | | | | DELTA: instantiating (67) with fresh symbol all_343_0 gives: % 157.38/21.97 | | | | (68) ssItem(all_343_0) = 0 & $i(all_343_0) & ? [v0: $i] : ? [v1: % 157.38/21.97 | | | | any] : (leq(all_343_0, v0) = v1 & ssItem(v0) = 0 & $i(v0) & ? % 157.38/21.97 | | | | [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: % 157.38/21.97 | | | | $i] : ? [v5: $i] : (ssList(v3) = 0 & cons(all_343_0, v3) % 157.38/21.97 | | | | = v4 & app(v2, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & ? % 157.38/21.97 | | | | [v6: $i] : ? [v7: $i] : ( ~ (v1 = 0) & ssList(v6) = 0 & % 157.38/21.97 | | | | cons(v0, v6) = v7 & app(v5, v7) = all_139_1 & $i(v7) & % 157.38/21.97 | | | | $i(v6))))) % 157.38/21.97 | | | | % 157.38/21.97 | | | | ALPHA: (68) implies: % 157.38/21.97 | | | | (69) $i(all_343_0) % 157.38/21.97 | | | | (70) ssItem(all_343_0) = 0 % 157.38/21.97 | | | | (71) ? [v0: $i] : ? [v1: any] : (leq(all_343_0, v0) = v1 & % 157.38/21.97 | | | | ssItem(v0) = 0 & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & % 157.38/21.97 | | | | $i(v2) & ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 157.38/21.97 | | | | (ssList(v3) = 0 & cons(all_343_0, v3) = v4 & app(v2, v4) = % 157.38/21.97 | | | | v5 & $i(v5) & $i(v4) & $i(v3) & ? [v6: $i] : ? [v7: $i] % 157.38/21.97 | | | | : ( ~ (v1 = 0) & ssList(v6) = 0 & cons(v0, v6) = v7 & % 157.38/21.97 | | | | app(v5, v7) = all_139_1 & $i(v7) & $i(v6))))) % 157.38/21.97 | | | | % 157.38/21.97 | | | | DELTA: instantiating (71) with fresh symbols all_345_0, all_345_1 gives: % 157.38/21.97 | | | | (72) leq(all_343_0, all_345_1) = all_345_0 & ssItem(all_345_1) = 0 & % 157.38/21.97 | | | | $i(all_345_1) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 157.38/21.97 | | | | $i] : ? [v2: $i] : ? [v3: $i] : (ssList(v1) = 0 & % 157.38/21.97 | | | | cons(all_343_0, v1) = v2 & app(v0, v2) = v3 & $i(v3) & % 157.38/21.97 | | | | $i(v2) & $i(v1) & ? [v4: $i] : ? [v5: $i] : ( ~ (all_345_0 % 157.38/21.97 | | | | = 0) & ssList(v4) = 0 & cons(all_345_1, v4) = v5 & % 157.38/21.97 | | | | app(v3, v5) = all_139_1 & $i(v5) & $i(v4)))) % 157.38/21.97 | | | | % 157.38/21.97 | | | | ALPHA: (72) implies: % 157.38/21.97 | | | | (73) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 157.38/21.97 | | | | $i] : ? [v3: $i] : (ssList(v1) = 0 & cons(all_343_0, v1) = % 157.38/21.97 | | | | v2 & app(v0, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & ? [v4: % 157.38/21.97 | | | | $i] : ? [v5: $i] : ( ~ (all_345_0 = 0) & ssList(v4) = 0 & % 157.38/21.97 | | | | cons(all_345_1, v4) = v5 & app(v3, v5) = all_139_1 & % 157.38/21.97 | | | | $i(v5) & $i(v4)))) % 157.38/21.97 | | | | % 157.38/21.97 | | | | DELTA: instantiating (73) with fresh symbol all_347_0 gives: % 157.38/21.97 | | | | (74) ssList(all_347_0) = 0 & $i(all_347_0) & ? [v0: $i] : ? [v1: % 157.38/21.97 | | | | $i] : ? [v2: $i] : (ssList(v0) = 0 & cons(all_343_0, v0) = v1 % 157.38/21.97 | | | | & app(all_347_0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ? [v3: % 157.38/21.97 | | | | $i] : ? [v4: $i] : ( ~ (all_345_0 = 0) & ssList(v3) = 0 & % 157.38/21.97 | | | | cons(all_345_1, v3) = v4 & app(v2, v4) = all_139_1 & $i(v4) % 157.38/21.97 | | | | & $i(v3))) % 157.38/21.97 | | | | % 157.38/21.97 | | | | ALPHA: (74) implies: % 157.38/21.97 | | | | (75) $i(all_347_0) % 157.38/21.97 | | | | (76) ssList(all_347_0) = 0 % 157.38/21.98 | | | | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ssList(v0) = 0 & % 157.38/21.98 | | | | cons(all_343_0, v0) = v1 & app(all_347_0, v1) = v2 & $i(v2) & % 157.38/21.98 | | | | $i(v1) & $i(v0) & ? [v3: $i] : ? [v4: $i] : ( ~ (all_345_0 = % 157.38/21.98 | | | | 0) & ssList(v3) = 0 & cons(all_345_1, v3) = v4 & app(v2, % 157.38/21.98 | | | | v4) = all_139_1 & $i(v4) & $i(v3))) % 157.38/21.98 | | | | % 157.38/21.98 | | | | DELTA: instantiating (77) with fresh symbols all_349_0, all_349_1, % 157.38/21.98 | | | | all_349_2 gives: % 157.38/21.98 | | | | (78) ssList(all_349_2) = 0 & cons(all_343_0, all_349_2) = all_349_1 & % 157.38/21.98 | | | | app(all_347_0, all_349_1) = all_349_0 & $i(all_349_0) & % 157.38/21.98 | | | | $i(all_349_1) & $i(all_349_2) & ? [v0: $i] : ? [v1: $i] : ( ~ % 157.38/21.98 | | | | (all_345_0 = 0) & ssList(v0) = 0 & cons(all_345_1, v0) = v1 & % 157.38/21.98 | | | | app(all_349_0, v1) = all_139_1 & $i(v1) & $i(v0)) % 157.38/21.98 | | | | % 157.38/21.98 | | | | ALPHA: (78) implies: % 157.38/21.98 | | | | (79) $i(all_349_2) % 157.38/21.98 | | | | (80) app(all_347_0, all_349_1) = all_349_0 % 157.38/21.98 | | | | (81) cons(all_343_0, all_349_2) = all_349_1 % 157.38/21.98 | | | | (82) ssList(all_349_2) = 0 % 157.38/21.98 | | | | % 157.38/21.98 | | | | BETA: splitting (37) gives: % 157.38/21.98 | | | | % 157.38/21.98 | | | | Case 1: % 157.38/21.98 | | | | | % 157.38/21.98 | | | | | (83) ~ (all_147_0 = 0) % 157.38/21.98 | | | | | % 157.38/21.98 | | | | | BETA: splitting (45) gives: % 157.38/21.98 | | | | | % 157.38/21.98 | | | | | Case 1: % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | DELTA: instantiating (84) with fresh symbol all_364_0 gives: % 157.38/21.98 | | | | | | (85) ~ (all_364_0 = 0) & ssList(nil) = all_364_0 % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | REF_CLOSE: (1), (14), (85) are inconsistent by sub-proof #1. % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | Case 2: % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | (86) ( ~ (all_147_0 = 0) | ~ (all_143_0 = nil)) & (all_147_0 = 0 % 157.38/21.98 | | | | | | | all_143_0 = nil) % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | ALPHA: (86) implies: % 157.38/21.98 | | | | | | (87) all_147_0 = 0 | all_143_0 = nil % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | BETA: splitting (87) gives: % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | Case 1: % 157.38/21.98 | | | | | | | % 157.38/21.98 | | | | | | | (88) all_143_0 = nil % 157.38/21.98 | | | | | | | % 157.38/21.98 | | | | | | | BETA: splitting (36) gives: % 157.38/21.98 | | | | | | | % 157.38/21.98 | | | | | | | Case 1: % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | | (89) ~ (all_143_0 = nil) % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | | REDUCE: (88), (89) imply: % 157.38/21.98 | | | | | | | | (90) $false % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | | CLOSE: (90) is inconsistent. % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | Case 2: % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | | (91) all_139_1 = nil % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | | REDUCE: (19), (91) imply: % 157.38/21.98 | | | | | | | | (92) totalorderedP(nil) = all_139_0 % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | | GROUND_INST: instantiating (15) with 0, all_139_0, nil, % 157.38/21.98 | | | | | | | | simplifying with (6), (92) gives: % 157.38/21.98 | | | | | | | | (93) all_139_0 = 0 % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | | REDUCE: (34), (93) imply: % 157.38/21.98 | | | | | | | | (94) $false % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | | CLOSE: (94) is inconsistent. % 157.38/21.98 | | | | | | | | % 157.38/21.98 | | | | | | | End of split % 157.38/21.98 | | | | | | | % 157.38/21.98 | | | | | | Case 2: % 157.38/21.98 | | | | | | | % 157.38/21.98 | | | | | | | (95) all_147_0 = 0 % 157.38/21.98 | | | | | | | % 157.38/21.98 | | | | | | | REDUCE: (83), (95) imply: % 157.38/21.98 | | | | | | | (96) $false % 157.38/21.98 | | | | | | | % 157.38/21.98 | | | | | | | CLOSE: (96) is inconsistent. % 157.38/21.98 | | | | | | | % 157.38/21.98 | | | | | | End of split % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | End of split % 157.38/21.98 | | | | | % 157.38/21.98 | | | | Case 2: % 157.38/21.98 | | | | | % 157.38/21.98 | | | | | (97) ? [v0: $i] : (memberP(all_143_0, v0) = 0 & cons(v0, nil) = % 157.38/21.98 | | | | | all_139_1 & ssItem(v0) = 0 & $i(v0)) % 157.38/21.98 | | | | | % 157.38/21.98 | | | | | DELTA: instantiating (97) with fresh symbol all_359_0 gives: % 157.38/21.98 | | | | | (98) memberP(all_143_0, all_359_0) = 0 & cons(all_359_0, nil) = % 157.38/21.98 | | | | | all_139_1 & ssItem(all_359_0) = 0 & $i(all_359_0) % 157.38/21.98 | | | | | % 157.38/21.98 | | | | | ALPHA: (98) implies: % 157.38/21.98 | | | | | (99) $i(all_359_0) % 157.38/21.98 | | | | | (100) ssItem(all_359_0) = 0 % 157.38/21.98 | | | | | (101) cons(all_359_0, nil) = all_139_1 % 157.38/21.98 | | | | | % 157.38/21.98 | | | | | BETA: splitting (45) gives: % 157.38/21.98 | | | | | % 157.38/21.98 | | | | | Case 1: % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | (102) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | DELTA: instantiating (102) with fresh symbol all_364_0 gives: % 157.38/21.98 | | | | | | (103) ~ (all_364_0 = 0) & ssList(nil) = all_364_0 % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | REF_CLOSE: (1), (14), (103) are inconsistent by sub-proof #1. % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | Case 2: % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | % 157.38/21.98 | | | | | | GROUND_INST: instantiating (56) with all_343_0, simplifying with % 157.38/21.98 | | | | | | (69), (70) gives: % 157.38/21.99 | | | | | | (104) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: % 157.38/21.99 | | | | | | $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ! [v2: $i] : % 157.38/21.99 | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (cons(all_343_0, v2) = % 157.38/21.99 | | | | | | v3) | ~ (app(v1, v3) = v4) | ~ $i(v2) | ? [v5: % 157.38/21.99 | | | | | | int] : ( ~ (v5 = 0) & ssList(v2) = v5) | ! [v5: % 157.38/21.99 | | | | | | $i] : ! [v6: $i] : ( ~ (v0 = all_343_0) | ~ % 157.38/21.99 | | | | | | (cons(all_343_0, v5) = v6) | ~ (app(v4, v6) = nil) % 157.38/21.99 | | | | | | | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & % 157.38/21.99 | | | | | | ssList(v5) = v7))))) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (40) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (105) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 & % 157.38/21.99 | | | | | | ssItem(all_359_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 157.38/21.99 | | | | | | nil)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (41) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (106) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 & % 157.38/21.99 | | | | | | ssItem(all_359_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 157.38/21.99 | | | | | | all_359_0)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (10) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (107) ? [v0: any] : ? [v1: any] : (equalelemsP(all_139_1) = v1 % 157.38/21.99 | | | | | | & ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (8) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (108) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_139_1) = % 157.38/21.99 | | | | | | v1 & ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (7) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (109) ? [v0: any] : ? [v1: any] : (strictorderedP(all_139_1) = % 157.38/21.99 | | | | | | v1 & ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (5) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (110) ? [v0: any] : ? [v1: any] : (totalorderedP(all_139_1) = % 157.38/21.99 | | | | | | v1 & ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (4) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (111) ? [v0: any] : ? [v1: any] : (strictorderP(all_139_1) = v1 % 157.38/21.99 | | | | | | & ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (3) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (112) ? [v0: any] : ? [v1: any] : (totalorderP(all_139_1) = v1 % 157.38/21.99 | | | | | | & ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (2) with all_359_0, all_139_1, % 157.38/21.99 | | | | | | simplifying with (99), (101) gives: % 157.38/21.99 | | | | | | (113) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_139_1) = v1 & % 157.38/21.99 | | | | | | ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (104) with all_141_0, simplifying with % 157.38/21.99 | | | | | | (22), (23) gives: % 157.38/21.99 | | | | | | (114) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: % 157.38/21.99 | | | | | | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(all_343_0, % 157.38/21.99 | | | | | | v1) = v2) | ~ (app(v0, v2) = v3) | ~ $i(v1) | ? % 157.38/21.99 | | | | | | [v4: int] : ( ~ (v4 = 0) & ssList(v1) = v4) | ! [v4: % 157.38/21.99 | | | | | | $i] : ! [v5: $i] : ( ~ (all_343_0 = all_141_0) | ~ % 157.38/21.99 | | | | | | (cons(all_141_0, v4) = v5) | ~ (app(v3, v5) = nil) | % 157.38/21.99 | | | | | | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v4) % 157.38/21.99 | | | | | | = v6)))) % 157.38/21.99 | | | | | | % 157.38/21.99 | | | | | | GROUND_INST: instantiating (114) with all_347_0, simplifying with % 157.38/21.99 | | | | | | (75), (76) gives: % 157.38/22.00 | | | | | | (115) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 157.38/22.00 | | | | | | (cons(all_343_0, v0) = v1) | ~ (app(all_347_0, v1) = v2) % 157.38/22.00 | | | | | | | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v0) = % 157.38/22.00 | | | | | | v3) | ! [v3: $i] : ! [v4: $i] : ( ~ (all_343_0 = % 157.38/22.00 | | | | | | all_141_0) | ~ (cons(all_141_0, v3) = v4) | ~ % 157.38/22.00 | | | | | | (app(v2, v4) = nil) | ~ $i(v3) | ? [v5: int] : ( ~ % 157.38/22.00 | | | | | | (v5 = 0) & ssList(v3) = v5))) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | GROUND_INST: instantiating (115) with all_349_2, all_349_1, % 157.38/22.00 | | | | | | all_349_0, simplifying with (79), (80), (81) gives: % 157.38/22.00 | | | | | | (116) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_349_2) = v0) | ! % 157.38/22.00 | | | | | | [v0: $i] : ! [v1: $i] : ( ~ (all_343_0 = all_141_0) | ~ % 157.38/22.00 | | | | | | (cons(all_141_0, v0) = v1) | ~ (app(all_349_0, v1) = % 157.38/22.00 | | | | | | nil) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 157.38/22.00 | | | | | | ssList(v0) = v2)) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (113) with fresh symbols all_1597_0, all_1597_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (117) cyclefreeP(all_139_1) = all_1597_0 & ssItem(all_359_0) = % 157.38/22.00 | | | | | | all_1597_1 & ( ~ (all_1597_1 = 0) | all_1597_0 = 0) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (117) implies: % 157.38/22.00 | | | | | | (118) ssItem(all_359_0) = all_1597_1 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (110) with fresh symbols all_1599_0, all_1599_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (119) totalorderedP(all_139_1) = all_1599_0 & ssItem(all_359_0) = % 157.38/22.00 | | | | | | all_1599_1 & ( ~ (all_1599_1 = 0) | all_1599_0 = 0) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (119) implies: % 157.38/22.00 | | | | | | (120) ssItem(all_359_0) = all_1599_1 % 157.38/22.00 | | | | | | (121) totalorderedP(all_139_1) = all_1599_0 % 157.38/22.00 | | | | | | (122) ~ (all_1599_1 = 0) | all_1599_0 = 0 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (109) with fresh symbols all_1601_0, all_1601_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (123) strictorderedP(all_139_1) = all_1601_0 & ssItem(all_359_0) % 157.38/22.00 | | | | | | = all_1601_1 & ( ~ (all_1601_1 = 0) | all_1601_0 = 0) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (123) implies: % 157.38/22.00 | | | | | | (124) ssItem(all_359_0) = all_1601_1 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (112) with fresh symbols all_1603_0, all_1603_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (125) totalorderP(all_139_1) = all_1603_0 & ssItem(all_359_0) = % 157.38/22.00 | | | | | | all_1603_1 & ( ~ (all_1603_1 = 0) | all_1603_0 = 0) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (125) implies: % 157.38/22.00 | | | | | | (126) ssItem(all_359_0) = all_1603_1 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (111) with fresh symbols all_1605_0, all_1605_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (127) strictorderP(all_139_1) = all_1605_0 & ssItem(all_359_0) = % 157.38/22.00 | | | | | | all_1605_1 & ( ~ (all_1605_1 = 0) | all_1605_0 = 0) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (127) implies: % 157.38/22.00 | | | | | | (128) ssItem(all_359_0) = all_1605_1 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (108) with fresh symbols all_1607_0, all_1607_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (129) duplicatefreeP(all_139_1) = all_1607_0 & ssItem(all_359_0) % 157.38/22.00 | | | | | | = all_1607_1 & ( ~ (all_1607_1 = 0) | all_1607_0 = 0) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (129) implies: % 157.38/22.00 | | | | | | (130) ssItem(all_359_0) = all_1607_1 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (107) with fresh symbols all_1609_0, all_1609_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (131) equalelemsP(all_139_1) = all_1609_0 & ssItem(all_359_0) = % 157.38/22.00 | | | | | | all_1609_1 & ( ~ (all_1609_1 = 0) | all_1609_0 = 0) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (131) implies: % 157.38/22.00 | | | | | | (132) ssItem(all_359_0) = all_1609_1 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (106) with fresh symbols all_1611_0, all_1611_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (133) hd(all_139_1) = all_1611_0 & ssItem(all_359_0) = all_1611_1 % 157.38/22.00 | | | | | | & $i(all_1611_0) & ( ~ (all_1611_1 = 0) | all_1611_0 = % 157.38/22.00 | | | | | | all_359_0) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (133) implies: % 157.38/22.00 | | | | | | (134) ssItem(all_359_0) = all_1611_1 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | DELTA: instantiating (105) with fresh symbols all_1613_0, all_1613_1 % 157.38/22.00 | | | | | | gives: % 157.38/22.00 | | | | | | (135) tl(all_139_1) = all_1613_0 & ssItem(all_359_0) = all_1613_1 % 157.38/22.00 | | | | | | & $i(all_1613_0) & ( ~ (all_1613_1 = 0) | all_1613_0 = nil) % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | ALPHA: (135) implies: % 157.38/22.00 | | | | | | (136) ssItem(all_359_0) = all_1613_1 % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | BETA: splitting (116) gives: % 157.38/22.00 | | | | | | % 157.38/22.00 | | | | | | Case 1: % 157.38/22.00 | | | | | | | % 157.38/22.00 | | | | | | | (137) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_349_2) = v0) % 157.38/22.00 | | | | | | | % 157.38/22.00 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1708_0 gives: % 157.38/22.00 | | | | | | | (138) ~ (all_1708_0 = 0) & ssList(all_349_2) = all_1708_0 % 157.38/22.00 | | | | | | | % 157.38/22.00 | | | | | | | ALPHA: (138) implies: % 157.38/22.01 | | | | | | | (139) ~ (all_1708_0 = 0) % 157.38/22.01 | | | | | | | (140) ssList(all_349_2) = all_1708_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1710_0 gives: % 157.38/22.01 | | | | | | | (141) ~ (all_1710_0 = 0) & ssList(all_349_2) = all_1710_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | ALPHA: (141) implies: % 157.38/22.01 | | | | | | | (142) ssList(all_349_2) = all_1710_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1712_0 gives: % 157.38/22.01 | | | | | | | (143) ~ (all_1712_0 = 0) & ssList(all_349_2) = all_1712_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | ALPHA: (143) implies: % 157.38/22.01 | | | | | | | (144) ssList(all_349_2) = all_1712_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1714_0 gives: % 157.38/22.01 | | | | | | | (145) ~ (all_1714_0 = 0) & ssList(all_349_2) = all_1714_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | ALPHA: (145) implies: % 157.38/22.01 | | | | | | | (146) ssList(all_349_2) = all_1714_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1716_0 gives: % 157.38/22.01 | | | | | | | (147) ~ (all_1716_0 = 0) & ssList(all_349_2) = all_1716_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | ALPHA: (147) implies: % 157.38/22.01 | | | | | | | (148) ssList(all_349_2) = all_1716_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1718_0 gives: % 157.38/22.01 | | | | | | | (149) ~ (all_1718_0 = 0) & ssList(all_349_2) = all_1718_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | ALPHA: (149) implies: % 157.38/22.01 | | | | | | | (150) ssList(all_349_2) = all_1718_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1720_0 gives: % 157.38/22.01 | | | | | | | (151) ~ (all_1720_0 = 0) & ssList(all_349_2) = all_1720_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | ALPHA: (151) implies: % 157.38/22.01 | | | | | | | (152) ssList(all_349_2) = all_1720_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1722_0 gives: % 157.38/22.01 | | | | | | | (153) ~ (all_1722_0 = 0) & ssList(all_349_2) = all_1722_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | ALPHA: (153) implies: % 157.38/22.01 | | | | | | | (154) ssList(all_349_2) = all_1722_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | DELTA: instantiating (137) with fresh symbol all_1724_0 gives: % 157.38/22.01 | | | | | | | (155) ~ (all_1724_0 = 0) & ssList(all_349_2) = all_1724_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | ALPHA: (155) implies: % 157.38/22.01 | | | | | | | (156) ssList(all_349_2) = all_1724_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with 0, all_1720_0, all_349_2, % 157.38/22.01 | | | | | | | simplifying with (82), (152) gives: % 157.38/22.01 | | | | | | | (157) all_1720_0 = 0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with all_1718_0, all_1720_0, % 157.38/22.01 | | | | | | | all_349_2, simplifying with (150), (152) gives: % 157.38/22.01 | | | | | | | (158) all_1720_0 = all_1718_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with all_1716_0, all_1720_0, % 157.38/22.01 | | | | | | | all_349_2, simplifying with (148), (152) gives: % 157.38/22.01 | | | | | | | (159) all_1720_0 = all_1716_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with all_1714_0, all_1720_0, % 157.38/22.01 | | | | | | | all_349_2, simplifying with (146), (152) gives: % 157.38/22.01 | | | | | | | (160) all_1720_0 = all_1714_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with all_1712_0, all_1720_0, % 157.38/22.01 | | | | | | | all_349_2, simplifying with (144), (152) gives: % 157.38/22.01 | | | | | | | (161) all_1720_0 = all_1712_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with all_1720_0, all_1722_0, % 157.38/22.01 | | | | | | | all_349_2, simplifying with (152), (154) gives: % 157.38/22.01 | | | | | | | (162) all_1722_0 = all_1720_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with all_1708_0, all_1722_0, % 157.38/22.01 | | | | | | | all_349_2, simplifying with (140), (154) gives: % 157.38/22.01 | | | | | | | (163) all_1722_0 = all_1708_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with all_1718_0, all_1724_0, % 157.38/22.01 | | | | | | | all_349_2, simplifying with (150), (156) gives: % 157.38/22.01 | | | | | | | (164) all_1724_0 = all_1718_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | GROUND_INST: instantiating (14) with all_1710_0, all_1724_0, % 157.38/22.01 | | | | | | | all_349_2, simplifying with (142), (156) gives: % 157.38/22.01 | | | | | | | (165) all_1724_0 = all_1710_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | COMBINE_EQS: (164), (165) imply: % 157.38/22.01 | | | | | | | (166) all_1718_0 = all_1710_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | SIMP: (166) implies: % 157.38/22.01 | | | | | | | (167) all_1718_0 = all_1710_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | COMBINE_EQS: (162), (163) imply: % 157.38/22.01 | | | | | | | (168) all_1720_0 = all_1708_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | SIMP: (168) implies: % 157.38/22.01 | | | | | | | (169) all_1720_0 = all_1708_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | COMBINE_EQS: (158), (159) imply: % 157.38/22.01 | | | | | | | (170) all_1718_0 = all_1716_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | SIMP: (170) implies: % 157.38/22.01 | | | | | | | (171) all_1718_0 = all_1716_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | COMBINE_EQS: (157), (159) imply: % 157.38/22.01 | | | | | | | (172) all_1716_0 = 0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | COMBINE_EQS: (159), (161) imply: % 157.38/22.01 | | | | | | | (173) all_1716_0 = all_1712_0 % 157.38/22.01 | | | | | | | % 157.38/22.01 | | | | | | | COMBINE_EQS: (159), (169) imply: % 157.38/22.01 | | | | | | | (174) all_1716_0 = all_1708_0 % 157.38/22.01 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (159), (160) imply: % 157.38/22.02 | | | | | | | (175) all_1716_0 = all_1714_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (167), (171) imply: % 157.38/22.02 | | | | | | | (176) all_1716_0 = all_1710_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | SIMP: (176) implies: % 157.38/22.02 | | | | | | | (177) all_1716_0 = all_1710_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (172), (175) imply: % 157.38/22.02 | | | | | | | (178) all_1714_0 = 0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (173), (175) imply: % 157.38/22.02 | | | | | | | (179) all_1714_0 = all_1712_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (174), (175) imply: % 157.38/22.02 | | | | | | | (180) all_1714_0 = all_1708_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (175), (177) imply: % 157.38/22.02 | | | | | | | (181) all_1714_0 = all_1710_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (178), (179) imply: % 157.38/22.02 | | | | | | | (182) all_1712_0 = 0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (179), (180) imply: % 157.38/22.02 | | | | | | | (183) all_1712_0 = all_1708_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (179), (181) imply: % 157.38/22.02 | | | | | | | (184) all_1712_0 = all_1710_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (182), (184) imply: % 157.38/22.02 | | | | | | | (185) all_1710_0 = 0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (183), (184) imply: % 157.38/22.02 | | | | | | | (186) all_1710_0 = all_1708_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (185), (186) imply: % 157.38/22.02 | | | | | | | (187) all_1708_0 = 0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | REDUCE: (139), (187) imply: % 157.38/22.02 | | | | | | | (188) $false % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | CLOSE: (188) is inconsistent. % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | Case 2: % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_1601_1, all_1603_1, % 157.38/22.02 | | | | | | | all_359_0, simplifying with (124), (126) gives: % 157.38/22.02 | | | | | | | (189) all_1603_1 = all_1601_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_1599_1, all_1603_1, % 157.38/22.02 | | | | | | | all_359_0, simplifying with (120), (126) gives: % 157.38/22.02 | | | | | | | (190) all_1603_1 = all_1599_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_1597_1, all_1607_1, % 157.38/22.02 | | | | | | | all_359_0, simplifying with (118), (130) gives: % 157.38/22.02 | | | | | | | (191) all_1607_1 = all_1597_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with 0, all_1609_1, all_359_0, % 157.38/22.02 | | | | | | | simplifying with (100), (132) gives: % 157.38/22.02 | | | | | | | (192) all_1609_1 = 0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_1603_1, all_1609_1, % 157.38/22.02 | | | | | | | all_359_0, simplifying with (126), (132) gives: % 157.38/22.02 | | | | | | | (193) all_1609_1 = all_1603_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_1607_1, all_1611_1, % 157.38/22.02 | | | | | | | all_359_0, simplifying with (130), (134) gives: % 157.38/22.02 | | | | | | | (194) all_1611_1 = all_1607_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_1603_1, all_1611_1, % 157.38/22.02 | | | | | | | all_359_0, simplifying with (126), (134) gives: % 157.38/22.02 | | | | | | | (195) all_1611_1 = all_1603_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_1611_1, all_1613_1, % 157.38/22.02 | | | | | | | all_359_0, simplifying with (134), (136) gives: % 157.38/22.02 | | | | | | | (196) all_1613_1 = all_1611_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (13) with all_1605_1, all_1613_1, % 157.38/22.02 | | | | | | | all_359_0, simplifying with (128), (136) gives: % 157.38/22.02 | | | | | | | (197) all_1613_1 = all_1605_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | GROUND_INST: instantiating (15) with all_139_0, all_1599_0, % 157.38/22.02 | | | | | | | all_139_1, simplifying with (19), (121) gives: % 157.38/22.02 | | | | | | | (198) all_1599_0 = all_139_0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (196), (197) imply: % 157.38/22.02 | | | | | | | (199) all_1611_1 = all_1605_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | SIMP: (199) implies: % 157.38/22.02 | | | | | | | (200) all_1611_1 = all_1605_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (194), (200) imply: % 157.38/22.02 | | | | | | | (201) all_1607_1 = all_1605_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | SIMP: (201) implies: % 157.38/22.02 | | | | | | | (202) all_1607_1 = all_1605_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (195), (200) imply: % 157.38/22.02 | | | | | | | (203) all_1605_1 = all_1603_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (192), (193) imply: % 157.38/22.02 | | | | | | | (204) all_1603_1 = 0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | SIMP: (204) implies: % 157.38/22.02 | | | | | | | (205) all_1603_1 = 0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (191), (202) imply: % 157.38/22.02 | | | | | | | (206) all_1605_1 = all_1597_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | SIMP: (206) implies: % 157.38/22.02 | | | | | | | (207) all_1605_1 = all_1597_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (203), (207) imply: % 157.38/22.02 | | | | | | | (208) all_1603_1 = all_1597_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | SIMP: (208) implies: % 157.38/22.02 | | | | | | | (209) all_1603_1 = all_1597_1 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (189), (205) imply: % 157.38/22.02 | | | | | | | (210) all_1601_1 = 0 % 157.38/22.02 | | | | | | | % 157.38/22.02 | | | | | | | COMBINE_EQS: (189), (190) imply: % 157.38/22.03 | | | | | | | (211) all_1601_1 = all_1599_1 % 157.38/22.03 | | | | | | | % 157.38/22.03 | | | | | | | COMBINE_EQS: (189), (209) imply: % 157.38/22.03 | | | | | | | (212) all_1601_1 = all_1597_1 % 157.38/22.03 | | | | | | | % 157.38/22.03 | | | | | | | COMBINE_EQS: (210), (211) imply: % 157.38/22.03 | | | | | | | (213) all_1599_1 = 0 % 157.38/22.03 | | | | | | | % 157.38/22.03 | | | | | | | COMBINE_EQS: (211), (212) imply: % 157.38/22.03 | | | | | | | (214) all_1599_1 = all_1597_1 % 157.38/22.03 | | | | | | | % 157.38/22.03 | | | | | | | COMBINE_EQS: (213), (214) imply: % 157.38/22.03 | | | | | | | (215) all_1597_1 = 0 % 157.38/22.03 | | | | | | | % 157.38/22.03 | | | | | | | BETA: splitting (122) gives: % 157.38/22.03 | | | | | | | % 157.38/22.03 | | | | | | | Case 1: % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | | (216) ~ (all_1599_1 = 0) % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | | REDUCE: (213), (216) imply: % 157.38/22.03 | | | | | | | | (217) $false % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | | CLOSE: (217) is inconsistent. % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | Case 2: % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | | (218) all_1599_0 = 0 % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | | COMBINE_EQS: (198), (218) imply: % 157.38/22.03 | | | | | | | | (219) all_139_0 = 0 % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | | SIMP: (219) implies: % 157.38/22.03 | | | | | | | | (220) all_139_0 = 0 % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | | REDUCE: (34), (220) imply: % 157.38/22.03 | | | | | | | | (221) $false % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | | CLOSE: (221) is inconsistent. % 157.38/22.03 | | | | | | | | % 157.38/22.03 | | | | | | | End of split % 157.38/22.03 | | | | | | | % 157.38/22.03 | | | | | | End of split % 157.38/22.03 | | | | | | % 157.38/22.03 | | | | | End of split % 157.38/22.03 | | | | | % 157.38/22.03 | | | | End of split % 157.38/22.03 | | | | % 157.38/22.03 | | | End of split % 157.38/22.03 | | | % 157.38/22.03 | | End of split % 157.38/22.03 | | % 157.38/22.03 | End of split % 157.38/22.03 | % 157.38/22.03 End of proof % 157.38/22.03 % 157.38/22.03 Sub-proof #1 shows that the following formulas are inconsistent: % 157.38/22.03 ---------------------------------------------------------------- % 157.38/22.03 (1) ~ (all_364_0 = 0) & ssList(nil) = all_364_0 % 157.38/22.03 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 157.38/22.03 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 157.38/22.03 (3) ssList(nil) = 0 % 157.38/22.03 % 157.38/22.03 Begin of proof % 157.38/22.03 | % 157.38/22.03 | ALPHA: (1) implies: % 157.38/22.03 | (4) ~ (all_364_0 = 0) % 157.38/22.03 | (5) ssList(nil) = all_364_0 % 157.38/22.03 | % 157.38/22.03 | GROUND_INST: instantiating (2) with 0, all_364_0, nil, simplifying with (3), % 157.38/22.03 | (5) gives: % 157.38/22.03 | (6) all_364_0 = 0 % 157.38/22.03 | % 157.38/22.03 | REDUCE: (4), (6) imply: % 157.38/22.03 | (7) $false % 157.38/22.03 | % 157.38/22.03 | CLOSE: (7) is inconsistent. % 157.38/22.03 | % 157.38/22.03 End of proof % 157.38/22.03 % SZS output end Proof for theBenchmark % 157.38/22.03 % 157.38/22.03 21421ms %------------------------------------------------------------------------------