%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC109+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 : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 20:49:42 EDT 2023 % Result : Theorem 54.54s 7.89s % Output : Proof 108.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC109+1 : TPTP v8.1.2. Released v2.4.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n018.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 15:49:17 EDT 2023 % 0.12/0.34 % 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 5.98/1.51 Prover 1: Preprocessing ... % 5.98/1.52 Prover 4: Preprocessing ... % 5.98/1.55 Prover 6: Preprocessing ... % 5.98/1.55 Prover 0: Preprocessing ... % 5.98/1.55 Prover 2: Preprocessing ... % 5.98/1.55 Prover 3: Preprocessing ... % 5.98/1.55 Prover 5: Preprocessing ... % 15.64/2.83 Prover 2: Proving ... % 15.64/2.89 Prover 1: Constructing countermodel ... % 15.64/2.89 Prover 5: Constructing countermodel ... % 16.26/2.91 Prover 3: Constructing countermodel ... % 16.26/2.94 Prover 6: Proving ... % 22.36/3.78 Prover 4: Constructing countermodel ... % 23.94/3.98 Prover 0: Proving ... % 54.54/7.89 Prover 3: proved (7274ms) % 54.54/7.89 % 54.54/7.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 54.54/7.89 % 54.54/7.89 Prover 2: stopped % 54.54/7.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 54.54/7.89 Prover 0: stopped % 54.54/7.89 Prover 5: stopped % 54.54/7.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 54.54/7.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 54.54/7.90 Prover 6: stopped % 54.54/7.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 54.54/7.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 55.23/8.07 Prover 8: Preprocessing ... % 56.02/8.09 Prover 11: Preprocessing ... % 56.21/8.11 Prover 10: Preprocessing ... % 56.21/8.16 Prover 7: Preprocessing ... % 56.21/8.16 Prover 13: Preprocessing ... % 58.55/8.41 Prover 10: Constructing countermodel ... % 58.55/8.42 Prover 7: Constructing countermodel ... % 59.50/8.57 Prover 13: Constructing countermodel ... % 59.50/8.59 Prover 8: Warning: ignoring some quantifiers % 59.50/8.60 Prover 8: Constructing countermodel ... % 65.69/9.36 Prover 11: Constructing countermodel ... % 88.31/12.40 Prover 13: stopped % 88.31/12.40 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 89.75/12.48 Prover 16: Preprocessing ... % 90.30/12.60 Prover 16: Constructing countermodel ... % 107.86/14.84 Prover 1: Found proof (size 353) % 107.86/14.84 Prover 1: proved (14227ms) % 107.86/14.84 Prover 7: stopped % 107.86/14.84 Prover 8: stopped % 107.86/14.84 Prover 10: stopped % 107.86/14.84 Prover 16: stopped % 107.86/14.84 Prover 4: stopped % 107.86/14.84 Prover 11: stopped % 107.86/14.84 % 107.86/14.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 107.86/14.84 % 107.86/14.86 % SZS output start Proof for theBenchmark % 107.86/14.86 Assumptions after simplification: % 107.86/14.86 --------------------------------- % 107.86/14.86 % 107.86/14.86 (ax13) % 107.86/14.90 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 107.86/14.90 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 107.86/14.90 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 107.86/14.90 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 107.86/14.90 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 107.86/14.90 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 107.86/14.90 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 107.86/14.90 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 107.86/14.90 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 107.86/14.90 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 107.86/14.90 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 107.86/14.90 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 107.86/14.90 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 107.86/14.90 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 107.86/14.90 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 107.86/14.90 % 107.86/14.90 (ax15) % 107.86/14.90 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 107.86/14.90 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 107.86/14.90 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 107.86/14.90 % 107.86/14.90 (ax17) % 107.86/14.90 ssList(nil) = 0 & $i(nil) % 107.86/14.90 % 107.86/14.90 (ax18) % 107.86/14.90 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1, % 107.86/14.90 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) = % 107.86/14.90 v2))) % 107.86/14.90 % 107.86/14.90 (ax2) % 107.86/14.90 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 107.86/14.90 ssItem(v1) = 0 & $i(v1))) % 107.86/14.90 % 107.86/14.90 (ax20) % 107.86/14.90 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 107.86/14.90 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 107.86/14.90 ssItem(v2) = 0 & $i(v2)))) % 107.86/14.90 % 107.86/14.90 (ax23) % 107.86/14.91 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 107.86/14.91 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 107.86/14.91 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 107.86/14.91 % 107.86/14.91 (ax25) % 107.86/14.91 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 107.86/14.91 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 107.86/14.91 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 107.86/14.91 % 107.86/14.91 (ax26) % 107.86/14.91 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 107.86/14.91 ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 107.86/14.91 (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 107.86/14.91 % 107.86/14.91 (ax58) % 107.86/14.91 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ % 107.86/14.91 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 % 107.86/14.91 = nil) & ( ~ (v0 = nil) | v1 = 0))) % 107.86/14.91 % 107.86/14.91 (ax59) % 107.86/14.91 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 107.86/14.91 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 107.86/14.91 (v2 = 0) | v3 = 0))) % 107.86/14.91 % 107.86/14.91 (ax61) % 107.86/14.91 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 107.86/14.91 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 107.86/14.91 (v2 = 0) | v3 = 0))) % 107.86/14.91 % 107.86/14.91 (ax63) % 107.86/14.91 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 107.86/14.91 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 107.86/14.91 (v2 = 0) | v3 = 0))) % 107.86/14.91 % 107.86/14.91 (ax65) % 107.86/14.91 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 107.86/14.91 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 107.86/14.91 (v2 = 0) | v3 = 0))) % 107.86/14.91 % 107.86/14.91 (ax68) % 107.86/14.91 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 107.86/14.91 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 107.86/14.91 ~ (v2 = 0) | v3 = 0))) % 107.86/14.91 % 107.86/14.91 (ax7) % 107.86/14.92 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 107.86/14.92 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 107.86/14.92 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] : % 107.86/14.92 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] : % 107.86/14.92 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3: % 107.86/14.92 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5: % 107.86/14.92 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~ % 107.86/14.92 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & % 107.86/14.92 ssList(v5) = v6))))))) % 107.86/14.92 % 107.86/14.92 (ax71) % 107.86/14.92 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 107.86/14.92 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 107.86/14.92 ~ (v2 = 0) | v3 = 0))) % 107.86/14.92 % 107.86/14.92 (ax72) % 107.86/14.92 duplicatefreeP(nil) = 0 & $i(nil) % 107.86/14.92 % 107.86/14.92 (ax73) % 107.86/14.92 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 107.86/14.92 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 107.86/14.92 (v2 = 0) | v3 = 0))) % 107.86/14.92 % 107.86/14.92 (ax82) % 107.86/14.92 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 107.86/14.92 ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 107.86/14.92 ssList(v1) = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ (app(v2, v3) = v4) | % 107.86/14.92 ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : (ssList(v3) = v5 & % 107.86/14.92 app(v1, v3) = v6 & app(v0, v6) = v7 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | % 107.86/14.92 v7 = v4))))) % 107.86/14.92 % 107.86/14.92 (co1) % 107.86/14.92 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 107.86/14.92 $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (segmentP(v2, v0) = v4 % 107.86/14.92 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ( ? [v5: $i] : ? [v6: $i] % 107.86/14.92 : (cons(v5, nil) = v6 & ssItem(v5) = 0 & $i(v6) & $i(v5) & ? [v7: $i] : % 107.86/14.92 ? [v8: $i] : (ssList(v7) = 0 & app(v7, v0) = v8 & $i(v8) & $i(v7) & % 107.86/14.92 ? [v9: $i] : (v6 = v0 & ssList(v9) = 0 & app(v8, v9) = v2 & $i(v9) & % 107.86/14.92 ! [v10: $i] : ( ~ (memberP(v9, v10) = 0) | ~ $i(v10) | ? [v11: % 107.86/14.92 any] : ? [v12: any] : (lt(v10, v5) = v12 & ssItem(v10) = v11 % 107.86/14.92 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v10: $i] : ( ~ % 107.86/14.92 (memberP(v7, v10) = 0) | ~ $i(v10) | ? [v11: any] : ? [v12: % 107.86/14.92 any] : (lt(v5, v10) = v12 & ssItem(v10) = v11 & ( ~ (v12 = 0) % 107.86/14.92 | ~ (v11 = 0))))))) | (v2 = nil & v0 = nil)) & ((v3 = 0 & ( % 107.86/14.92 ~ (v4 = 0) | ~ (v1 = 0))) | (v2 = nil & ~ (v0 = nil))))) % 107.86/14.92 % 107.86/14.93 (function-axioms) % 107.86/14.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 107.86/14.95 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 107.86/14.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 107.86/14.95 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 107.86/14.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 107.86/14.95 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 107.86/14.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 107.86/14.95 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 107.86/14.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 107.86/14.95 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 107.86/14.95 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 107.86/14.95 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 107.86/14.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 107.86/14.95 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 107.86/14.95 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 107.86/14.95 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 107.86/14.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 107.86/14.95 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 107.86/14.95 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 107.86/14.95 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 107.86/14.95 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 107.86/14.95 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 107.86/14.95 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 107.86/14.95 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 107.86/14.95 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 107.86/14.95 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 107.86/14.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 107.86/14.95 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 107.86/14.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 107.86/14.95 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 107.86/14.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 107.86/14.95 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 107.86/14.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 107.86/14.95 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 107.86/14.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 107.86/14.95 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 107.86/14.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 107.86/14.95 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 107.86/14.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 107.86/14.95 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 107.86/14.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 107.86/14.95 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 107.86/14.95 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 107.86/14.95 % 107.86/14.95 Further assumptions not needed in the proof: % 107.86/14.95 -------------------------------------------- % 107.86/14.95 ax1, ax10, ax11, ax12, ax14, ax16, ax19, ax21, ax22, ax24, ax27, ax28, ax29, % 107.86/14.95 ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, % 107.86/14.95 ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, % 107.86/14.95 ax53, ax54, ax55, ax56, ax57, ax6, ax60, ax62, ax64, ax66, ax67, ax69, ax70, % 107.86/14.95 ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax83, ax84, ax85, ax86, % 107.86/14.95 ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 107.86/14.95 % 107.86/14.95 Those formulas are unsatisfiable: % 107.86/14.95 --------------------------------- % 107.86/14.95 % 107.86/14.95 Begin of proof % 107.86/14.95 | % 107.86/14.95 | ALPHA: (ax17) implies: % 107.86/14.95 | (1) ssList(nil) = 0 % 107.86/14.95 | % 107.86/14.95 | ALPHA: (ax20) implies: % 107.86/14.95 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 107.86/14.95 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 107.86/14.95 | ssItem(v2) = 0 & $i(v2)))) % 107.86/14.95 | % 107.86/14.95 | ALPHA: (ax58) implies: % 107.86/14.95 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ $i(v0) | % 107.86/14.95 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 = % 107.86/14.95 | nil) & ( ~ (v0 = nil) | v1 = 0))) % 107.86/14.95 | % 107.86/14.95 | ALPHA: (ax59) implies: % 107.86/14.95 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.95 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 107.86/14.95 | ~ (v2 = 0) | v3 = 0))) % 107.86/14.95 | % 107.86/14.95 | ALPHA: (ax61) implies: % 107.86/14.96 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.96 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 107.86/14.96 | ( ~ (v2 = 0) | v3 = 0))) % 107.86/14.96 | % 107.86/14.96 | ALPHA: (ax63) implies: % 107.86/14.96 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.96 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 107.86/14.96 | ( ~ (v2 = 0) | v3 = 0))) % 107.86/14.96 | % 107.86/14.96 | ALPHA: (ax65) implies: % 107.86/14.96 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.96 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 107.86/14.96 | & ( ~ (v2 = 0) | v3 = 0))) % 107.86/14.96 | % 107.86/14.96 | ALPHA: (ax68) implies: % 107.86/14.96 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.96 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 107.86/14.96 | & ( ~ (v2 = 0) | v3 = 0))) % 107.86/14.96 | % 107.86/14.96 | ALPHA: (ax71) implies: % 107.86/14.96 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.96 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 107.86/14.96 | & ( ~ (v2 = 0) | v3 = 0))) % 107.86/14.96 | % 107.86/14.96 | ALPHA: (ax72) implies: % 107.86/14.96 | (10) duplicatefreeP(nil) = 0 % 107.86/14.96 | % 107.86/14.96 | ALPHA: (ax73) implies: % 107.86/14.96 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.96 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 107.86/14.96 | ( ~ (v2 = 0) | v3 = 0))) % 107.86/14.96 | % 107.86/14.96 | ALPHA: (co1) implies: % 107.86/14.96 | (12) $i(nil) % 107.86/14.96 | (13) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 107.86/14.96 | $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (segmentP(v2, % 107.86/14.96 | v0) = v4 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ( ? % 107.86/14.96 | [v5: $i] : ? [v6: $i] : (cons(v5, nil) = v6 & ssItem(v5) = 0 & % 107.86/14.96 | $i(v6) & $i(v5) & ? [v7: $i] : ? [v8: $i] : (ssList(v7) = 0 % 107.86/14.96 | & app(v7, v0) = v8 & $i(v8) & $i(v7) & ? [v9: $i] : (v6 = % 107.86/14.96 | v0 & ssList(v9) = 0 & app(v8, v9) = v2 & $i(v9) & ! [v10: % 107.86/14.96 | $i] : ( ~ (memberP(v9, v10) = 0) | ~ $i(v10) | ? [v11: % 107.86/14.96 | any] : ? [v12: any] : (lt(v10, v5) = v12 & % 107.86/14.96 | ssItem(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & % 107.86/14.96 | ! [v10: $i] : ( ~ (memberP(v7, v10) = 0) | ~ $i(v10) | ? % 107.86/14.96 | [v11: any] : ? [v12: any] : (lt(v5, v10) = v12 & % 107.86/14.96 | ssItem(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))))) % 107.86/14.96 | | (v2 = nil & v0 = nil)) & ((v3 = 0 & ( ~ (v4 = 0) | ~ (v1 = % 107.86/14.96 | 0))) | (v2 = nil & ~ (v0 = nil))))) % 107.86/14.96 | % 107.86/14.96 | ALPHA: (function-axioms) implies: % 107.86/14.97 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 107.86/14.97 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 107.86/14.97 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 107.86/14.97 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 107.86/14.97 | % 107.86/14.97 | DELTA: instantiating (ax2) with fresh symbol all_91_0 gives: % 107.86/14.97 | (16) ssItem(all_91_0) = 0 & $i(all_91_0) & ? [v0: any] : ( ~ (v0 = % 107.86/14.97 | all_91_0) & ssItem(v0) = 0 & $i(v0)) % 107.86/14.97 | % 107.86/14.97 | ALPHA: (16) implies: % 107.86/14.97 | (17) $i(all_91_0) % 107.86/14.97 | (18) ssItem(all_91_0) = 0 % 107.86/14.97 | % 107.86/14.97 | DELTA: instantiating (13) with fresh symbols all_93_0, all_93_1 gives: % 107.86/14.97 | (19) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) & % 107.86/14.97 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (segmentP(v0, all_93_1) = % 107.86/14.97 | v2 & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ( ? [v3: $i] : ? % 107.86/14.97 | [v4: $i] : (cons(v3, nil) = v4 & ssItem(v3) = 0 & $i(v4) & $i(v3) % 107.86/14.97 | & ? [v5: $i] : ? [v6: $i] : (ssList(v5) = 0 & app(v5, % 107.86/14.97 | all_93_1) = v6 & $i(v6) & $i(v5) & ? [v7: $i] : (v4 = % 107.86/14.97 | all_93_1 & ssList(v7) = 0 & app(v6, v7) = v0 & $i(v7) & ! % 107.86/14.97 | [v8: $i] : ( ~ (memberP(v7, v8) = 0) | ~ $i(v8) | ? [v9: % 107.86/14.97 | any] : ? [v10: any] : (lt(v8, v3) = v10 & ssItem(v8) = % 107.86/14.97 | v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v8: $i] : ( ~ % 107.86/14.97 | (memberP(v5, v8) = 0) | ~ $i(v8) | ? [v9: any] : ? % 107.86/14.97 | [v10: any] : (lt(v3, v8) = v10 & ssItem(v8) = v9 & ( ~ % 107.86/14.97 | (v10 = 0) | ~ (v9 = 0))))))) | (v0 = nil & all_93_1 = % 107.86/14.97 | nil)) & ((v1 = 0 & ( ~ (v2 = 0) | ~ (all_93_0 = 0))) | (v0 = % 107.86/14.97 | nil & ~ (all_93_1 = nil)))) % 107.86/14.97 | % 107.86/14.97 | ALPHA: (19) implies: % 107.86/14.97 | (20) $i(all_93_1) % 107.86/14.97 | (21) neq(all_93_1, nil) = all_93_0 % 107.86/14.97 | (22) ssList(all_93_1) = 0 % 107.86/14.98 | (23) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (segmentP(v0, all_93_1) = % 107.86/14.98 | v2 & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ( ? [v3: $i] : ? % 107.86/14.98 | [v4: $i] : (cons(v3, nil) = v4 & ssItem(v3) = 0 & $i(v4) & $i(v3) % 107.86/14.98 | & ? [v5: $i] : ? [v6: $i] : (ssList(v5) = 0 & app(v5, % 107.86/14.98 | all_93_1) = v6 & $i(v6) & $i(v5) & ? [v7: $i] : (v4 = % 107.86/14.98 | all_93_1 & ssList(v7) = 0 & app(v6, v7) = v0 & $i(v7) & ! % 107.86/14.98 | [v8: $i] : ( ~ (memberP(v7, v8) = 0) | ~ $i(v8) | ? [v9: % 107.86/14.98 | any] : ? [v10: any] : (lt(v8, v3) = v10 & ssItem(v8) = % 107.86/14.98 | v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v8: $i] : ( ~ % 107.86/14.98 | (memberP(v5, v8) = 0) | ~ $i(v8) | ? [v9: any] : ? % 107.86/14.98 | [v10: any] : (lt(v3, v8) = v10 & ssItem(v8) = v9 & ( ~ % 107.86/14.98 | (v10 = 0) | ~ (v9 = 0))))))) | (v0 = nil & all_93_1 = % 107.86/14.98 | nil)) & ((v1 = 0 & ( ~ (v2 = 0) | ~ (all_93_0 = 0))) | (v0 = % 107.86/14.98 | nil & ~ (all_93_1 = nil)))) % 107.86/14.98 | % 107.86/14.98 | DELTA: instantiating (23) with fresh symbols all_97_0, all_97_1, all_97_2 % 107.86/14.98 | gives: % 107.86/14.98 | (24) segmentP(all_97_2, all_93_1) = all_97_0 & ssList(all_97_2) = 0 & % 107.86/14.98 | neq(all_97_2, nil) = all_97_1 & $i(all_97_2) & ( ? [v0: $i] : ? [v1: % 107.86/14.98 | $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & $i(v1) & $i(v0) & ? % 107.86/14.98 | [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, all_93_1) = v3 % 107.86/14.98 | & $i(v3) & $i(v2) & ? [v4: $i] : (v1 = all_93_1 & ssList(v4) = % 107.86/14.98 | 0 & app(v3, v4) = all_97_2 & $i(v4) & ! [v5: $i] : ( ~ % 107.86/14.98 | (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: % 107.86/14.98 | any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | % 107.86/14.98 | ~ (v6 = 0)))) & ! [v5: $i] : ( ~ (memberP(v2, v5) = 0) % 107.86/14.98 | | ~ $i(v5) | ? [v6: any] : ? [v7: any] : (lt(v0, v5) = v7 % 107.86/14.98 | & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))))) | % 107.86/14.98 | (all_97_2 = nil & all_93_1 = nil)) & ((all_97_1 = 0 & ( ~ (all_97_0 % 107.86/14.98 | = 0) | ~ (all_93_0 = 0))) | (all_97_2 = nil & ~ (all_93_1 = % 107.86/14.98 | nil))) % 107.86/14.98 | % 107.86/14.98 | ALPHA: (24) implies: % 107.86/14.98 | (25) $i(all_97_2) % 107.86/14.98 | (26) neq(all_97_2, nil) = all_97_1 % 107.86/14.98 | (27) ssList(all_97_2) = 0 % 107.86/14.98 | (28) segmentP(all_97_2, all_93_1) = all_97_0 % 107.86/14.98 | (29) (all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = % 107.86/14.98 | nil & ~ (all_93_1 = nil)) % 107.86/14.98 | (30) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & % 107.86/14.98 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & % 107.86/14.98 | app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (v1 = % 107.86/14.98 | all_93_1 & ssList(v4) = 0 & app(v3, v4) = all_97_2 & $i(v4) & ! % 107.86/14.98 | [v5: $i] : ( ~ (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6: any] % 107.86/14.98 | : ? [v7: any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 & ( ~ (v7 % 107.86/14.98 | = 0) | ~ (v6 = 0)))) & ! [v5: $i] : ( ~ (memberP(v2, % 107.86/14.98 | v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] : % 107.86/14.98 | (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 107.86/14.98 | 0))))))) | (all_97_2 = nil & all_93_1 = nil) % 107.86/14.98 | % 107.86/14.99 | GROUND_INST: instantiating (ax7) with nil, simplifying with (1), (12) gives: % 107.86/14.99 | (31) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ $i(v0) % 107.86/14.99 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 107.86/14.99 | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0) = v3 & % 107.86/14.99 | $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 & app(v3, v4) % 107.86/14.99 | = nil & $i(v4)))) & (v1 = 0 | ! [v2: $i] : ! [v3: $i] : ( % 107.86/14.99 | ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) % 107.86/14.99 | & ssList(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, v4) = nil) | % 107.86/14.99 | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v4) = % 107.86/14.99 | v5)))))) % 107.86/14.99 | % 107.86/14.99 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (12) gives: % 107.86/14.99 | (32) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.99 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 107.86/14.99 | ( ~ (v2 = 0) | v3 = nil))) % 107.86/14.99 | % 107.86/14.99 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (12) gives: % 107.86/14.99 | (33) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 107.86/14.99 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 107.86/14.99 | ( ~ (v2 = 0) | v3 = v0))) % 107.86/14.99 | % 107.86/14.99 | GROUND_INST: instantiating (ax18) with nil, simplifying with (1), (12) gives: % 107.86/14.99 | (34) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : ( % 107.86/14.99 | ~ (v1 = 0) & ssItem(v0) = v1)) % 107.86/14.99 | % 107.86/14.99 | GROUND_INST: instantiating (2) with all_93_1, simplifying with (20), (22) % 107.86/14.99 | gives: % 107.86/14.99 | (35) all_93_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 107.86/14.99 | : (cons(v1, v0) = all_93_1 & ssItem(v1) = 0 & $i(v1))) % 107.86/14.99 | % 107.86/14.99 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (20), (22) % 107.86/14.99 | gives: % 107.86/14.99 | (36) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0) % 107.86/14.99 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 107.86/14.99 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1))) % 107.86/14.99 | % 107.86/14.99 | GROUND_INST: instantiating (ax7) with all_97_2, simplifying with (25), (27) % 107.86/14.99 | gives: % 108.53/14.99 | (37) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_97_2, v0) = v1) | ~ % 108.53/14.99 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 108.53/14.99 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0) % 108.53/14.99 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 & % 108.53/14.99 | app(v3, v4) = all_97_2 & $i(v4)))) & (v1 = 0 | ! [v2: $i] : % 108.53/14.99 | ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: int] % 108.53/14.99 | : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, % 108.53/14.99 | v4) = all_97_2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = % 108.53/14.99 | 0) & ssList(v4) = v5)))))) % 108.53/14.99 | % 108.53/14.99 | GROUND_INST: instantiating (ax15) with all_97_2, simplifying with (25), (27) % 108.53/14.99 | gives: % 108.53/15.00 | (38) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_2, v0) = v1) | ~ $i(v0) % 108.53/15.00 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 108.53/15.00 | ~ (v0 = all_97_2)) & (v1 = 0 | v0 = all_97_2))) % 108.53/15.00 | % 108.53/15.00 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (10), (12) % 108.53/15.00 | gives: % 108.53/15.00 | (39) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 108.53/15.00 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 108.53/15.00 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 108.53/15.00 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 108.53/15.00 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 108.53/15.00 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 108.53/15.00 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 108.53/15.00 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 108.53/15.00 | v8)))))) % 108.53/15.00 | % 108.53/15.00 | GROUND_INST: instantiating (38) with nil, all_97_1, simplifying with (12), % 108.53/15.00 | (26) gives: % 108.53/15.00 | (40) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_1 = 0) % 108.53/15.00 | | ~ (all_97_2 = nil)) & (all_97_1 = 0 | all_97_2 = nil)) % 108.53/15.00 | % 108.53/15.00 | GROUND_INST: instantiating (37) with all_93_1, all_97_0, simplifying with % 108.53/15.00 | (20), (28) gives: % 108.53/15.00 | (41) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0 % 108.53/15.00 | = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, % 108.53/15.00 | all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = % 108.53/15.00 | 0 & app(v1, v2) = all_97_2 & $i(v2)))) & (all_97_0 = 0 | ! % 108.53/15.00 | [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ $i(v0) % 108.53/15.00 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : % 108.53/15.00 | ( ~ (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ % 108.53/15.00 | (v3 = 0) & ssList(v2) = v3))))) % 108.53/15.00 | % 108.53/15.00 | GROUND_INST: instantiating (36) with nil, all_93_0, simplifying with (12), % 108.53/15.00 | (21) gives: % 108.53/15.00 | (42) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0) % 108.53/15.00 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil)) % 108.53/15.00 | % 108.53/15.00 | BETA: splitting (39) gives: % 108.53/15.00 | % 108.53/15.00 | Case 1: % 108.53/15.00 | | % 108.53/15.00 | | (43) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 108.53/15.00 | | % 108.53/15.00 | | DELTA: instantiating (43) with fresh symbol all_324_0 gives: % 108.53/15.00 | | (44) ~ (all_324_0 = 0) & ssList(nil) = all_324_0 % 108.53/15.00 | | % 108.53/15.00 | | REF_CLOSE: (1), (15), (44) are inconsistent by sub-proof #2. % 108.53/15.00 | | % 108.53/15.00 | Case 2: % 108.53/15.00 | | % 108.53/15.00 | | (45) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 108.53/15.00 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 108.53/15.00 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 108.53/15.00 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 108.53/15.00 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 108.53/15.00 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 108.53/15.00 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 108.53/15.00 | | 0) & ssList(v6) = v8)))))) % 108.53/15.00 | | % 108.53/15.00 | | BETA: splitting (29) gives: % 108.53/15.00 | | % 108.53/15.00 | | Case 1: % 108.53/15.00 | | | % 108.53/15.00 | | | (46) all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0)) % 108.53/15.00 | | | % 108.53/15.00 | | | ALPHA: (46) implies: % 108.53/15.00 | | | (47) all_97_1 = 0 % 108.53/15.01 | | | (48) ~ (all_97_0 = 0) | ~ (all_93_0 = 0) % 108.53/15.01 | | | % 108.53/15.01 | | | BETA: splitting (40) gives: % 108.53/15.01 | | | % 108.53/15.01 | | | Case 1: % 108.53/15.01 | | | | % 108.53/15.01 | | | | (49) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 108.53/15.01 | | | | % 108.53/15.01 | | | | DELTA: instantiating (49) with fresh symbol all_324_0 gives: % 108.53/15.01 | | | | (50) ~ (all_324_0 = 0) & ssList(nil) = all_324_0 % 108.53/15.01 | | | | % 108.53/15.01 | | | | REF_CLOSE: (1), (15), (50) are inconsistent by sub-proof #2. % 108.53/15.01 | | | | % 108.53/15.01 | | | Case 2: % 108.53/15.01 | | | | % 108.53/15.01 | | | | (51) ( ~ (all_97_1 = 0) | ~ (all_97_2 = nil)) & (all_97_1 = 0 | % 108.53/15.01 | | | | all_97_2 = nil) % 108.53/15.01 | | | | % 108.53/15.01 | | | | ALPHA: (51) implies: % 108.53/15.01 | | | | (52) ~ (all_97_1 = 0) | ~ (all_97_2 = nil) % 108.53/15.01 | | | | % 108.53/15.01 | | | | BETA: splitting (52) gives: % 108.53/15.01 | | | | % 108.53/15.01 | | | | Case 1: % 108.53/15.01 | | | | | % 108.53/15.01 | | | | | (53) ~ (all_97_2 = nil) % 108.53/15.01 | | | | | % 108.53/15.01 | | | | | BETA: splitting (30) gives: % 108.53/15.01 | | | | | % 108.53/15.01 | | | | | Case 1: % 108.53/15.01 | | | | | | % 108.53/15.01 | | | | | | (54) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) % 108.53/15.01 | | | | | | = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : % 108.53/15.01 | | | | | | (ssList(v2) = 0 & app(v2, all_93_1) = v3 & $i(v3) & $i(v2) % 108.53/15.01 | | | | | | & ? [v4: $i] : (v1 = all_93_1 & ssList(v4) = 0 & % 108.53/15.01 | | | | | | app(v3, v4) = all_97_2 & $i(v4) & ! [v5: $i] : ( ~ % 108.53/15.01 | | | | | | (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6: any] : % 108.53/15.01 | | | | | | ? [v7: any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 & ( % 108.53/15.01 | | | | | | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v5: $i] : ( ~ % 108.53/15.01 | | | | | | (memberP(v2, v5) = 0) | ~ $i(v5) | ? [v6: any] : % 108.53/15.01 | | | | | | ? [v7: any] : (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( % 108.53/15.01 | | | | | | ~ (v7 = 0) | ~ (v6 = 0))))))) % 108.53/15.01 | | | | | | % 108.53/15.01 | | | | | | DELTA: instantiating (54) with fresh symbols all_315_0, all_315_1 % 108.53/15.01 | | | | | | gives: % 108.53/15.01 | | | | | | (55) cons(all_315_1, nil) = all_315_0 & ssItem(all_315_1) = 0 & % 108.53/15.01 | | | | | | $i(all_315_0) & $i(all_315_1) & ? [v0: $i] : ? [v1: $i] : % 108.53/15.01 | | | | | | (ssList(v0) = 0 & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & % 108.53/15.01 | | | | | | ? [v2: $i] : (all_315_0 = all_93_1 & ssList(v2) = 0 & % 108.53/15.01 | | | | | | app(v1, v2) = all_97_2 & $i(v2) & ! [v3: $i] : ( ~ % 108.53/15.01 | | | | | | (memberP(v2, v3) = 0) | ~ $i(v3) | ? [v4: any] : ? % 108.53/15.01 | | | | | | [v5: any] : (lt(v3, all_315_1) = v5 & ssItem(v3) = v4 % 108.53/15.01 | | | | | | & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v3: $i] : ( ~ % 108.53/15.01 | | | | | | (memberP(v0, v3) = 0) | ~ $i(v3) | ? [v4: any] : ? % 108.53/15.01 | | | | | | [v5: any] : (lt(all_315_1, v3) = v5 & ssItem(v3) = v4 % 108.53/15.01 | | | | | | & ( ~ (v5 = 0) | ~ (v4 = 0)))))) % 108.53/15.01 | | | | | | % 108.53/15.01 | | | | | | ALPHA: (55) implies: % 108.53/15.01 | | | | | | (56) $i(all_315_1) % 108.53/15.01 | | | | | | (57) ssItem(all_315_1) = 0 % 108.53/15.01 | | | | | | (58) cons(all_315_1, nil) = all_315_0 % 108.53/15.01 | | | | | | (59) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, % 108.53/15.01 | | | | | | all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : % 108.53/15.01 | | | | | | (all_315_0 = all_93_1 & ssList(v2) = 0 & app(v1, v2) = % 108.53/15.01 | | | | | | all_97_2 & $i(v2) & ! [v3: $i] : ( ~ (memberP(v2, v3) = % 108.53/15.01 | | | | | | 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : % 108.53/15.01 | | | | | | (lt(v3, all_315_1) = v5 & ssItem(v3) = v4 & ( ~ (v5 = % 108.53/15.01 | | | | | | 0) | ~ (v4 = 0)))) & ! [v3: $i] : ( ~ % 108.53/15.01 | | | | | | (memberP(v0, v3) = 0) | ~ $i(v3) | ? [v4: any] : ? % 108.53/15.01 | | | | | | [v5: any] : (lt(all_315_1, v3) = v5 & ssItem(v3) = v4 % 108.53/15.01 | | | | | | & ( ~ (v5 = 0) | ~ (v4 = 0)))))) % 108.53/15.01 | | | | | | % 108.53/15.01 | | | | | | DELTA: instantiating (59) with fresh symbols all_317_0, all_317_1 % 108.53/15.01 | | | | | | gives: % 108.53/15.01 | | | | | | (60) ssList(all_317_1) = 0 & app(all_317_1, all_93_1) = all_317_0 % 108.53/15.01 | | | | | | & $i(all_317_0) & $i(all_317_1) & ? [v0: $i] : (all_315_0 = % 108.53/15.01 | | | | | | all_93_1 & ssList(v0) = 0 & app(all_317_0, v0) = all_97_2 % 108.53/15.01 | | | | | | & $i(v0) & ! [v1: $i] : ( ~ (memberP(v0, v1) = 0) | ~ % 108.53/15.01 | | | | | | $i(v1) | ? [v2: any] : ? [v3: any] : (lt(v1, % 108.53/15.01 | | | | | | all_315_1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | % 108.53/15.01 | | | | | | ~ (v2 = 0)))) & ! [v1: $i] : ( ~ % 108.53/15.01 | | | | | | (memberP(all_317_1, v1) = 0) | ~ $i(v1) | ? [v2: any] % 108.53/15.01 | | | | | | : ? [v3: any] : (lt(all_315_1, v1) = v3 & ssItem(v1) = % 108.53/15.01 | | | | | | v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 108.53/15.01 | | | | | | % 108.53/15.01 | | | | | | ALPHA: (60) implies: % 108.53/15.01 | | | | | | (61) $i(all_317_1) % 108.53/15.01 | | | | | | (62) app(all_317_1, all_93_1) = all_317_0 % 108.53/15.01 | | | | | | (63) ssList(all_317_1) = 0 % 108.53/15.02 | | | | | | (64) ? [v0: $i] : (all_315_0 = all_93_1 & ssList(v0) = 0 & % 108.53/15.02 | | | | | | app(all_317_0, v0) = all_97_2 & $i(v0) & ! [v1: $i] : ( ~ % 108.53/15.02 | | | | | | (memberP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? % 108.53/15.02 | | | | | | [v3: any] : (lt(v1, all_315_1) = v3 & ssItem(v1) = v2 & % 108.53/15.02 | | | | | | ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~ % 108.53/15.02 | | | | | | (memberP(all_317_1, v1) = 0) | ~ $i(v1) | ? [v2: any] % 108.53/15.02 | | | | | | : ? [v3: any] : (lt(all_315_1, v1) = v3 & ssItem(v1) = % 108.53/15.02 | | | | | | v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 108.53/15.02 | | | | | | % 108.53/15.02 | | | | | | DELTA: instantiating (64) with fresh symbol all_319_0 gives: % 108.53/15.02 | | | | | | (65) all_315_0 = all_93_1 & ssList(all_319_0) = 0 & % 108.53/15.02 | | | | | | app(all_317_0, all_319_0) = all_97_2 & $i(all_319_0) & ! % 108.53/15.02 | | | | | | [v0: $i] : ( ~ (memberP(all_319_0, v0) = 0) | ~ $i(v0) | ? % 108.53/15.02 | | | | | | [v1: any] : ? [v2: any] : (lt(v0, all_315_1) = v2 & % 108.53/15.02 | | | | | | ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) & ! % 108.53/15.02 | | | | | | [v0: $i] : ( ~ (memberP(all_317_1, v0) = 0) | ~ $i(v0) | ? % 108.53/15.02 | | | | | | [v1: any] : ? [v2: any] : (lt(all_315_1, v0) = v2 & % 108.53/15.02 | | | | | | ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 108.53/15.02 | | | | | | % 108.53/15.02 | | | | | | ALPHA: (65) implies: % 108.53/15.02 | | | | | | (66) all_315_0 = all_93_1 % 108.53/15.02 | | | | | | (67) $i(all_319_0) % 108.53/15.02 | | | | | | (68) app(all_317_0, all_319_0) = all_97_2 % 108.53/15.02 | | | | | | (69) ssList(all_319_0) = 0 % 108.53/15.02 | | | | | | % 108.53/15.02 | | | | | | REDUCE: (58), (66) imply: % 108.53/15.02 | | | | | | (70) cons(all_315_1, nil) = all_93_1 % 108.53/15.02 | | | | | | % 108.53/15.02 | | | | | | BETA: splitting (35) gives: % 108.53/15.02 | | | | | | % 108.53/15.02 | | | | | | Case 1: % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | (71) all_93_1 = nil % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | REDUCE: (70), (71) imply: % 108.53/15.02 | | | | | | | (72) cons(all_315_1, nil) = nil % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | GROUND_INST: instantiating (34) with all_315_1, simplifying with % 108.53/15.02 | | | | | | | (56), (72) gives: % 108.53/15.02 | | | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_315_1) = v0) % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | GROUND_INST: instantiating (32) with all_315_1, nil, simplifying % 108.53/15.02 | | | | | | | with (56), (72) gives: % 108.53/15.02 | | | | | | | (74) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 & % 108.53/15.02 | | | | | | | ssItem(all_315_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 108.53/15.02 | | | | | | | nil)) % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | GROUND_INST: instantiating (33) with all_315_1, nil, simplifying % 108.53/15.02 | | | | | | | with (56), (72) gives: % 108.53/15.02 | | | | | | | (75) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 & % 108.53/15.02 | | | | | | | ssItem(all_315_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 108.53/15.02 | | | | | | | all_315_1)) % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | DELTA: instantiating (73) with fresh symbol all_664_0 gives: % 108.53/15.02 | | | | | | | (76) ~ (all_664_0 = 0) & ssItem(all_315_1) = all_664_0 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | ALPHA: (76) implies: % 108.53/15.02 | | | | | | | (77) ~ (all_664_0 = 0) % 108.53/15.02 | | | | | | | (78) ssItem(all_315_1) = all_664_0 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | DELTA: instantiating (74) with fresh symbols all_666_0, all_666_1 % 108.53/15.02 | | | | | | | gives: % 108.53/15.02 | | | | | | | (79) tl(nil) = all_666_0 & ssItem(all_315_1) = all_666_1 & % 108.53/15.02 | | | | | | | $i(all_666_0) & ( ~ (all_666_1 = 0) | all_666_0 = nil) % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | ALPHA: (79) implies: % 108.53/15.02 | | | | | | | (80) ssItem(all_315_1) = all_666_1 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | DELTA: instantiating (75) with fresh symbols all_668_0, all_668_1 % 108.53/15.02 | | | | | | | gives: % 108.53/15.02 | | | | | | | (81) hd(nil) = all_668_0 & ssItem(all_315_1) = all_668_1 & % 108.53/15.02 | | | | | | | $i(all_668_0) & ( ~ (all_668_1 = 0) | all_668_0 = % 108.53/15.02 | | | | | | | all_315_1) % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | ALPHA: (81) implies: % 108.53/15.02 | | | | | | | (82) ssItem(all_315_1) = all_668_1 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | GROUND_INST: instantiating (14) with 0, all_666_1, all_315_1, % 108.53/15.02 | | | | | | | simplifying with (57), (80) gives: % 108.53/15.02 | | | | | | | (83) all_666_1 = 0 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | GROUND_INST: instantiating (14) with all_666_1, all_668_1, % 108.53/15.02 | | | | | | | all_315_1, simplifying with (80), (82) gives: % 108.53/15.02 | | | | | | | (84) all_668_1 = all_666_1 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | GROUND_INST: instantiating (14) with all_664_0, all_668_1, % 108.53/15.02 | | | | | | | all_315_1, simplifying with (78), (82) gives: % 108.53/15.02 | | | | | | | (85) all_668_1 = all_664_0 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | COMBINE_EQS: (84), (85) imply: % 108.53/15.02 | | | | | | | (86) all_666_1 = all_664_0 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | SIMP: (86) implies: % 108.53/15.02 | | | | | | | (87) all_666_1 = all_664_0 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | COMBINE_EQS: (83), (87) imply: % 108.53/15.02 | | | | | | | (88) all_664_0 = 0 % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | REDUCE: (77), (88) imply: % 108.53/15.02 | | | | | | | (89) $false % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | CLOSE: (89) is inconsistent. % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | Case 2: % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | (90) ~ (all_93_1 = nil) % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | BETA: splitting (42) gives: % 108.53/15.02 | | | | | | | % 108.53/15.02 | | | | | | | Case 1: % 108.53/15.02 | | | | | | | | % 108.53/15.02 | | | | | | | | (91) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 108.53/15.02 | | | | | | | | % 108.53/15.02 | | | | | | | | DELTA: instantiating (91) with fresh symbol all_324_0 gives: % 108.53/15.02 | | | | | | | | (92) ~ (all_324_0 = 0) & ssList(nil) = all_324_0 % 108.53/15.02 | | | | | | | | % 108.53/15.02 | | | | | | | | REF_CLOSE: (1), (15), (92) are inconsistent by sub-proof #2. % 108.53/15.02 | | | | | | | | % 108.53/15.02 | | | | | | | Case 2: % 108.53/15.02 | | | | | | | | % 108.53/15.02 | | | | | | | | (93) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = % 108.53/15.02 | | | | | | | | 0 | all_93_1 = nil) % 108.53/15.02 | | | | | | | | % 108.53/15.02 | | | | | | | | ALPHA: (93) implies: % 108.53/15.02 | | | | | | | | (94) all_93_0 = 0 | all_93_1 = nil % 108.53/15.02 | | | | | | | | % 108.53/15.02 | | | | | | | | BETA: splitting (94) gives: % 108.53/15.02 | | | | | | | | % 108.53/15.02 | | | | | | | | Case 1: % 108.53/15.02 | | | | | | | | | % 108.53/15.02 | | | | | | | | | (95) all_93_1 = nil % 108.53/15.02 | | | | | | | | | % 108.53/15.02 | | | | | | | | | REDUCE: (90), (95) imply: % 108.53/15.02 | | | | | | | | | (96) $false % 108.53/15.02 | | | | | | | | | % 108.53/15.02 | | | | | | | | | CLOSE: (96) is inconsistent. % 108.53/15.02 | | | | | | | | | % 108.53/15.02 | | | | | | | | Case 2: % 108.53/15.02 | | | | | | | | | % 108.53/15.02 | | | | | | | | | (97) all_93_0 = 0 % 108.53/15.02 | | | | | | | | | % 108.53/15.02 | | | | | | | | | BETA: splitting (48) gives: % 108.53/15.02 | | | | | | | | | % 108.53/15.02 | | | | | | | | | Case 1: % 108.53/15.02 | | | | | | | | | | % 108.53/15.02 | | | | | | | | | | (98) ~ (all_97_0 = 0) % 108.53/15.02 | | | | | | | | | | % 108.53/15.02 | | | | | | | | | | BETA: splitting (41) gives: % 108.53/15.02 | | | | | | | | | | % 108.53/15.02 | | | | | | | | | | Case 1: % 108.53/15.02 | | | | | | | | | | | % 108.53/15.02 | | | | | | | | | | | (99) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = % 108.53/15.02 | | | | | | | | | | | v0) % 108.53/15.02 | | | | | | | | | | | % 108.53/15.02 | | | | | | | | | | | DELTA: instantiating (99) with fresh symbol all_345_0 % 108.53/15.02 | | | | | | | | | | | gives: % 108.53/15.02 | | | | | | | | | | | (100) ~ (all_345_0 = 0) & ssList(all_93_1) = all_345_0 % 108.53/15.02 | | | | | | | | | | | % 108.53/15.02 | | | | | | | | | | | ALPHA: (100) implies: % 108.53/15.03 | | | | | | | | | | | (101) ~ (all_345_0 = 0) % 108.53/15.03 | | | | | | | | | | | (102) ssList(all_93_1) = all_345_0 % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_345_0, all_93_1, % 108.53/15.03 | | | | | | | | | | | simplifying with (22), (102) gives: % 108.53/15.03 | | | | | | | | | | | (103) all_345_0 = 0 % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | REDUCE: (101), (103) imply: % 108.53/15.03 | | | | | | | | | | | (104) $false % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | CLOSE: (104) is inconsistent. % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | Case 2: % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | (105) ( ~ (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : % 108.53/15.03 | | | | | | | | | | | (ssList(v0) = 0 & app(v0, all_93_1) = v1 & % 108.53/15.03 | | | | | | | | | | | $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = % 108.53/15.03 | | | | | | | | | | | 0 & app(v1, v2) = all_97_2 & $i(v2)))) & % 108.53/15.03 | | | | | | | | | | | (all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 108.53/15.03 | | | | | | | | | | | (app(v0, all_93_1) = v1) | ~ $i(v0) | ? [v2: % 108.53/15.03 | | | | | | | | | | | int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! % 108.53/15.03 | | | | | | | | | | | [v2: $i] : ( ~ (app(v1, v2) = all_97_2) | ~ % 108.53/15.03 | | | | | | | | | | | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 108.53/15.03 | | | | | | | | | | | ssList(v2) = v3)))) % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | ALPHA: (105) implies: % 108.53/15.03 | | | | | | | | | | | (106) all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 108.53/15.03 | | | | | | | | | | | (app(v0, all_93_1) = v1) | ~ $i(v0) | ? [v2: % 108.53/15.03 | | | | | | | | | | | int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! % 108.53/15.03 | | | | | | | | | | | [v2: $i] : ( ~ (app(v1, v2) = all_97_2) | ~ % 108.53/15.03 | | | | | | | | | | | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 108.53/15.03 | | | | | | | | | | | ssList(v2) = v3))) % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | BETA: splitting (106) gives: % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | Case 1: % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | (107) all_97_0 = 0 % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | REDUCE: (98), (107) imply: % 108.53/15.03 | | | | | | | | | | | | (108) $false % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | CLOSE: (108) is inconsistent. % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | Case 2: % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | (109) ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) % 108.53/15.03 | | | | | | | | | | | | = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 108.53/15.03 | | | | | | | | | | | | 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ % 108.53/15.03 | | | | | | | | | | | | (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: % 108.53/15.03 | | | | | | | | | | | | int] : ( ~ (v3 = 0) & ssList(v2) = v3))) % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | GROUND_INST: instantiating (109) with all_317_1, all_317_0, % 108.53/15.03 | | | | | | | | | | | | simplifying with (61), (62) gives: % 108.53/15.03 | | | | | | | | | | | | (110) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_317_1) = % 108.53/15.03 | | | | | | | | | | | | v0) | ! [v0: $i] : ( ~ (app(all_317_0, v0) = % 108.53/15.03 | | | | | | | | | | | | all_97_2) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 108.53/15.03 | | | | | | | | | | | | = 0) & ssList(v0) = v1)) % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | BETA: splitting (110) gives: % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | Case 1: % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | (111) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_317_1) = % 108.53/15.03 | | | | | | | | | | | | | v0) % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | DELTA: instantiating (111) with fresh symbol all_1028_0 % 108.53/15.03 | | | | | | | | | | | | | gives: % 108.53/15.03 | | | | | | | | | | | | | (112) ~ (all_1028_0 = 0) & ssList(all_317_1) = % 108.53/15.03 | | | | | | | | | | | | | all_1028_0 % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | ALPHA: (112) implies: % 108.53/15.03 | | | | | | | | | | | | | (113) ~ (all_1028_0 = 0) % 108.53/15.03 | | | | | | | | | | | | | (114) ssList(all_317_1) = all_1028_0 % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_1028_0, all_317_1, % 108.53/15.03 | | | | | | | | | | | | | simplifying with (63), (114) gives: % 108.53/15.03 | | | | | | | | | | | | | (115) all_1028_0 = 0 % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | REDUCE: (113), (115) imply: % 108.53/15.03 | | | | | | | | | | | | | (116) $false % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | CLOSE: (116) is inconsistent. % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | Case 2: % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | (117) ! [v0: $i] : ( ~ (app(all_317_0, v0) = all_97_2) % 108.53/15.03 | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 108.53/15.03 | | | | | | | | | | | | | ssList(v0) = v1)) % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | GROUND_INST: instantiating (117) with all_319_0, simplifying % 108.53/15.03 | | | | | | | | | | | | | with (67), (68) gives: % 108.53/15.03 | | | | | | | | | | | | | (118) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_319_0) = % 108.53/15.03 | | | | | | | | | | | | | v0) % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | DELTA: instantiating (118) with fresh symbol all_1029_0 % 108.53/15.03 | | | | | | | | | | | | | gives: % 108.53/15.03 | | | | | | | | | | | | | (119) ~ (all_1029_0 = 0) & ssList(all_319_0) = % 108.53/15.03 | | | | | | | | | | | | | all_1029_0 % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | ALPHA: (119) implies: % 108.53/15.03 | | | | | | | | | | | | | (120) ~ (all_1029_0 = 0) % 108.53/15.03 | | | | | | | | | | | | | (121) ssList(all_319_0) = all_1029_0 % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_1029_0, all_319_0, % 108.53/15.03 | | | | | | | | | | | | | simplifying with (69), (121) gives: % 108.53/15.03 | | | | | | | | | | | | | (122) all_1029_0 = 0 % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | REDUCE: (120), (122) imply: % 108.53/15.03 | | | | | | | | | | | | | (123) $false % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 108.53/15.03 | | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | | End of split % 108.53/15.03 | | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | | End of split % 108.53/15.03 | | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | End of split % 108.53/15.03 | | | | | | | | | | % 108.53/15.03 | | | | | | | | | Case 2: % 108.53/15.03 | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | (124) ~ (all_93_0 = 0) % 108.53/15.03 | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | REDUCE: (97), (124) imply: % 108.53/15.03 | | | | | | | | | | (125) $false % 108.53/15.03 | | | | | | | | | | % 108.53/15.03 | | | | | | | | | | CLOSE: (125) is inconsistent. % 108.53/15.03 | | | | | | | | | | % 108.53/15.03 | | | | | | | | | End of split % 108.53/15.03 | | | | | | | | | % 108.53/15.03 | | | | | | | | End of split % 108.53/15.03 | | | | | | | | % 108.53/15.03 | | | | | | | End of split % 108.53/15.03 | | | | | | | % 108.53/15.03 | | | | | | End of split % 108.53/15.03 | | | | | | % 108.53/15.03 | | | | | Case 2: % 108.53/15.03 | | | | | | % 108.53/15.03 | | | | | | (126) all_97_2 = nil & all_93_1 = nil % 108.53/15.03 | | | | | | % 108.53/15.03 | | | | | | ALPHA: (126) implies: % 108.53/15.03 | | | | | | (127) all_97_2 = nil % 108.53/15.03 | | | | | | % 108.53/15.03 | | | | | | REDUCE: (53), (127) imply: % 108.53/15.03 | | | | | | (128) $false % 108.53/15.03 | | | | | | % 108.53/15.03 | | | | | | CLOSE: (128) is inconsistent. % 108.53/15.03 | | | | | | % 108.53/15.03 | | | | | End of split % 108.53/15.03 | | | | | % 108.53/15.03 | | | | Case 2: % 108.53/15.03 | | | | | % 108.53/15.03 | | | | | (129) ~ (all_97_1 = 0) % 108.53/15.03 | | | | | % 108.53/15.03 | | | | | REDUCE: (47), (129) imply: % 108.53/15.03 | | | | | (130) $false % 108.53/15.03 | | | | | % 108.53/15.03 | | | | | CLOSE: (130) is inconsistent. % 108.53/15.03 | | | | | % 108.53/15.03 | | | | End of split % 108.53/15.03 | | | | % 108.53/15.03 | | | End of split % 108.53/15.03 | | | % 108.53/15.03 | | Case 2: % 108.53/15.03 | | | % 108.53/15.03 | | | (131) all_97_2 = nil & ~ (all_93_1 = nil) % 108.53/15.03 | | | % 108.53/15.03 | | | ALPHA: (131) implies: % 108.53/15.03 | | | (132) all_97_2 = nil % 108.53/15.03 | | | (133) ~ (all_93_1 = nil) % 108.53/15.03 | | | % 108.53/15.03 | | | REDUCE: (28), (132) imply: % 108.53/15.04 | | | (134) segmentP(nil, all_93_1) = all_97_0 % 108.53/15.04 | | | % 108.53/15.04 | | | BETA: splitting (30) gives: % 108.53/15.04 | | | % 108.53/15.04 | | | Case 1: % 108.53/15.04 | | | | % 108.53/15.04 | | | | (135) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = % 108.53/15.04 | | | | 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) % 108.53/15.04 | | | | = 0 & app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? [v4: % 108.53/15.04 | | | | $i] : (v1 = all_93_1 & ssList(v4) = 0 & app(v3, v4) = % 108.53/15.04 | | | | all_97_2 & $i(v4) & ! [v5: $i] : ( ~ (memberP(v4, v5) = % 108.53/15.04 | | | | 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] : % 108.53/15.04 | | | | (lt(v5, v0) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ % 108.53/15.04 | | | | (v6 = 0)))) & ! [v5: $i] : ( ~ (memberP(v2, v5) = % 108.53/15.04 | | | | 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] : % 108.53/15.04 | | | | (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ % 108.53/15.04 | | | | (v6 = 0))))))) % 108.53/15.04 | | | | % 108.53/15.04 | | | | DELTA: instantiating (135) with fresh symbols all_310_0, all_310_1 % 108.53/15.04 | | | | gives: % 108.53/15.04 | | | | (136) cons(all_310_1, nil) = all_310_0 & ssItem(all_310_1) = 0 & % 108.53/15.04 | | | | $i(all_310_0) & $i(all_310_1) & ? [v0: $i] : ? [v1: $i] : % 108.53/15.04 | | | | (ssList(v0) = 0 & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? % 108.53/15.04 | | | | [v2: $i] : (all_310_0 = all_93_1 & ssList(v2) = 0 & app(v1, % 108.53/15.04 | | | | v2) = all_97_2 & $i(v2) & ! [v3: $i] : ( ~ (memberP(v2, % 108.53/15.04 | | | | v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : % 108.53/15.04 | | | | (lt(v3, all_310_1) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) % 108.53/15.04 | | | | | ~ (v4 = 0)))) & ! [v3: $i] : ( ~ (memberP(v0, v3) % 108.53/15.04 | | | | = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : % 108.53/15.04 | | | | (lt(all_310_1, v3) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) % 108.53/15.04 | | | | | ~ (v4 = 0)))))) % 108.53/15.04 | | | | % 108.53/15.04 | | | | ALPHA: (136) implies: % 108.53/15.04 | | | | (137) $i(all_310_1) % 108.53/15.04 | | | | (138) $i(all_310_0) % 108.53/15.04 | | | | (139) ssItem(all_310_1) = 0 % 108.53/15.04 | | | | (140) cons(all_310_1, nil) = all_310_0 % 108.53/15.04 | | | | (141) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_93_1) % 108.53/15.04 | | | | = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (all_310_0 = all_93_1 % 108.53/15.04 | | | | & ssList(v2) = 0 & app(v1, v2) = all_97_2 & $i(v2) & ! % 108.53/15.04 | | | | [v3: $i] : ( ~ (memberP(v2, v3) = 0) | ~ $i(v3) | ? [v4: % 108.53/15.04 | | | | any] : ? [v5: any] : (lt(v3, all_310_1) = v5 & % 108.53/15.04 | | | | ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! % 108.53/15.04 | | | | [v3: $i] : ( ~ (memberP(v0, v3) = 0) | ~ $i(v3) | ? [v4: % 108.53/15.04 | | | | any] : ? [v5: any] : (lt(all_310_1, v3) = v5 & % 108.53/15.04 | | | | ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))) % 108.53/15.04 | | | | % 108.53/15.04 | | | | DELTA: instantiating (141) with fresh symbols all_312_0, all_312_1 % 108.53/15.04 | | | | gives: % 108.53/15.04 | | | | (142) ssList(all_312_1) = 0 & app(all_312_1, all_93_1) = all_312_0 & % 108.53/15.04 | | | | $i(all_312_0) & $i(all_312_1) & ? [v0: $i] : (all_310_0 = % 108.53/15.04 | | | | all_93_1 & ssList(v0) = 0 & app(all_312_0, v0) = all_97_2 & % 108.53/15.04 | | | | $i(v0) & ! [v1: $i] : ( ~ (memberP(v0, v1) = 0) | ~ $i(v1) % 108.53/15.04 | | | | | ? [v2: any] : ? [v3: any] : (lt(v1, all_310_1) = v3 & % 108.53/15.04 | | | | ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v1: % 108.53/15.04 | | | | $i] : ( ~ (memberP(all_312_1, v1) = 0) | ~ $i(v1) | ? % 108.53/15.04 | | | | [v2: any] : ? [v3: any] : (lt(all_310_1, v1) = v3 & % 108.53/15.04 | | | | ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 108.53/15.04 | | | | % 108.53/15.04 | | | | ALPHA: (142) implies: % 108.53/15.04 | | | | (143) $i(all_312_1) % 108.53/15.04 | | | | (144) app(all_312_1, all_93_1) = all_312_0 % 108.53/15.04 | | | | (145) ssList(all_312_1) = 0 % 108.53/15.04 | | | | (146) ? [v0: $i] : (all_310_0 = all_93_1 & ssList(v0) = 0 & % 108.53/15.04 | | | | app(all_312_0, v0) = all_97_2 & $i(v0) & ! [v1: $i] : ( ~ % 108.53/15.04 | | | | (memberP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: % 108.53/15.04 | | | | any] : (lt(v1, all_310_1) = v3 & ssItem(v1) = v2 & ( ~ % 108.53/15.04 | | | | (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~ % 108.53/15.04 | | | | (memberP(all_312_1, v1) = 0) | ~ $i(v1) | ? [v2: any] : % 108.53/15.04 | | | | ? [v3: any] : (lt(all_310_1, v1) = v3 & ssItem(v1) = v2 & ( % 108.53/15.04 | | | | ~ (v3 = 0) | ~ (v2 = 0))))) % 108.53/15.04 | | | | % 108.53/15.04 | | | | DELTA: instantiating (146) with fresh symbol all_314_0 gives: % 108.53/15.04 | | | | (147) all_310_0 = all_93_1 & ssList(all_314_0) = 0 & app(all_312_0, % 108.53/15.04 | | | | all_314_0) = all_97_2 & $i(all_314_0) & ! [v0: $i] : ( ~ % 108.53/15.04 | | | | (memberP(all_314_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 108.53/15.04 | | | | [v2: any] : (lt(v0, all_310_1) = v2 & ssItem(v0) = v1 & ( ~ % 108.53/15.04 | | | | (v2 = 0) | ~ (v1 = 0)))) & ! [v0: $i] : ( ~ % 108.53/15.04 | | | | (memberP(all_312_1, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 108.53/15.04 | | | | [v2: any] : (lt(all_310_1, v0) = v2 & ssItem(v0) = v1 & ( ~ % 108.53/15.04 | | | | (v2 = 0) | ~ (v1 = 0)))) % 108.53/15.04 | | | | % 108.53/15.04 | | | | ALPHA: (147) implies: % 108.53/15.04 | | | | (148) all_310_0 = all_93_1 % 108.53/15.04 | | | | (149) $i(all_314_0) % 108.53/15.04 | | | | (150) app(all_312_0, all_314_0) = all_97_2 % 108.53/15.05 | | | | (151) ssList(all_314_0) = 0 % 108.53/15.05 | | | | % 108.53/15.05 | | | | REDUCE: (140), (148) imply: % 108.53/15.05 | | | | (152) cons(all_310_1, nil) = all_93_1 % 108.53/15.05 | | | | % 108.53/15.05 | | | | REDUCE: (132), (150) imply: % 108.53/15.05 | | | | (153) app(all_312_0, all_314_0) = nil % 108.53/15.05 | | | | % 108.53/15.05 | | | | BETA: splitting (42) gives: % 108.53/15.05 | | | | % 108.53/15.05 | | | | Case 1: % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | (154) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | DELTA: instantiating (154) with fresh symbol all_324_0 gives: % 108.53/15.05 | | | | | (155) ~ (all_324_0 = 0) & ssList(nil) = all_324_0 % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | REF_CLOSE: (1), (15), (155) are inconsistent by sub-proof #2. % 108.53/15.05 | | | | | % 108.53/15.05 | | | | Case 2: % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (45) with all_310_1, simplifying with % 108.53/15.05 | | | | | (137), (139) gives: % 108.53/15.05 | | | | | (156) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] % 108.53/15.05 | | | | | : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: % 108.53/15.05 | | | | | $i] : ! [v4: $i] : ( ~ (cons(all_310_1, v2) = v3) | ~ % 108.53/15.05 | | | | | (app(v1, v3) = v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 % 108.53/15.05 | | | | | = 0) & ssList(v2) = v5) | ! [v5: $i] : ! [v6: $i] % 108.53/15.05 | | | | | : ( ~ (v0 = all_310_1) | ~ (cons(all_310_1, v5) = v6) % 108.53/15.05 | | | | | | ~ (app(v4, v6) = nil) | ~ $i(v5) | ? [v7: int] : % 108.53/15.05 | | | | | ( ~ (v7 = 0) & ssList(v5) = v7))))) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (32) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (157) ? [v0: any] : ? [v1: $i] : (tl(all_93_1) = v1 & % 108.53/15.05 | | | | | ssItem(all_310_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (33) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (158) ? [v0: any] : ? [v1: $i] : (hd(all_93_1) = v1 & % 108.53/15.05 | | | | | ssItem(all_310_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 108.53/15.05 | | | | | all_310_1)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (11) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (159) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_1) = v1 & % 108.53/15.05 | | | | | ssItem(all_310_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (9) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (160) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_1) = v1 % 108.53/15.05 | | | | | & ssItem(all_310_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (8) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (161) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_1) = v1 % 108.53/15.05 | | | | | & ssItem(all_310_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (7) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (162) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_1) = v1 & % 108.53/15.05 | | | | | ssItem(all_310_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (6) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (163) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_1) = v1 & % 108.53/15.05 | | | | | ssItem(all_310_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (5) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (164) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_1) = v1 & % 108.53/15.05 | | | | | ssItem(all_310_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (4) with all_310_1, all_93_1, simplifying % 108.53/15.05 | | | | | with (137), (152) gives: % 108.53/15.05 | | | | | (165) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_1) = v1 & % 108.53/15.05 | | | | | ssItem(all_310_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (ax26) with all_312_1, simplifying with % 108.53/15.05 | | | | | (143), (145) gives: % 108.53/15.05 | | | | | (166) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_312_1, v0) = v1) | % 108.53/15.05 | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (ssList(v1) = v3 & % 108.53/15.05 | | | | | ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (ax82) with all_312_1, simplifying with % 108.53/15.05 | | | | | (143), (145) gives: % 108.53/15.05 | | | | | (167) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_312_1, v0) = v1) | % 108.53/15.05 | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | % 108.53/15.05 | | | | | ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1, v2) = v3) | ~ % 108.53/15.05 | | | | | $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 108.53/15.05 | | | | | (ssList(v2) = v4 & app(v0, v2) = v5 & app(all_312_1, v5) % 108.53/15.05 | | | | | = v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = v3)))) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (3) with all_93_1, all_97_0, simplifying % 108.53/15.05 | | | | | with (20), (134) gives: % 108.53/15.05 | | | | | (168) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ % 108.53/15.05 | | | | | (all_97_0 = 0) | all_93_1 = nil) & ( ~ (all_93_1 = nil) | % 108.53/15.05 | | | | | all_97_0 = 0)) % 108.53/15.05 | | | | | % 108.53/15.05 | | | | | GROUND_INST: instantiating (31) with all_93_1, all_97_0, simplifying % 108.53/15.05 | | | | | with (20), (134) gives: % 108.53/15.06 | | | | | (169) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ % 108.53/15.06 | | | | | (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) % 108.53/15.06 | | | | | = 0 & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? % 108.53/15.06 | | | | | [v2: $i] : (ssList(v2) = 0 & app(v1, v2) = nil & % 108.53/15.06 | | | | | $i(v2)))) & (all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] % 108.53/15.06 | | | | | : ( ~ (app(v0, all_93_1) = v1) | ~ $i(v0) | ? [v2: int] % 108.53/15.06 | | | | | : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ % 108.53/15.06 | | | | | (app(v1, v2) = nil) | ~ $i(v2) | ? [v3: int] : ( ~ % 108.53/15.06 | | | | | (v3 = 0) & ssList(v2) = v3))))) % 108.53/15.06 | | | | | % 108.53/15.06 | | | | | GROUND_INST: instantiating (167) with all_93_1, all_312_0, simplifying % 108.53/15.06 | | | | | with (20), (144) gives: % 108.53/15.06 | | | | | (170) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | ! % 108.53/15.06 | | | | | [v0: $i] : ! [v1: $i] : ( ~ (app(all_312_0, v0) = v1) | ~ % 108.53/15.06 | | | | | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 108.53/15.06 | | | | | (ssList(v0) = v2 & app(all_312_1, v3) = v4 & app(all_93_1, % 108.53/15.06 | | | | | v0) = v3 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = v1))) % 108.53/15.06 | | | | | % 108.53/15.06 | | | | | GROUND_INST: instantiating (166) with all_93_1, all_312_0, simplifying % 108.53/15.06 | | | | | with (20), (144) gives: % 108.53/15.06 | | | | | (171) ? [v0: any] : ? [v1: any] : (ssList(all_312_0) = v1 & % 108.53/15.06 | | | | | ssList(all_93_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 108.53/15.06 | | | | | % 108.53/15.06 | | | | | GROUND_INST: instantiating (156) with all_91_0, simplifying with (17), % 108.53/15.06 | | | | | (18) gives: % 108.94/15.06 | | | | | (172) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] % 108.94/15.06 | | | | | : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(all_310_1, v1) = % 108.94/15.06 | | | | | v2) | ~ (app(v0, v2) = v3) | ~ $i(v1) | ? [v4: int] % 108.94/15.06 | | | | | : ( ~ (v4 = 0) & ssList(v1) = v4) | ! [v4: $i] : ! [v5: % 108.94/15.06 | | | | | $i] : ( ~ (all_310_1 = all_91_0) | ~ (cons(all_91_0, % 108.94/15.06 | | | | | v4) = v5) | ~ (app(v3, v5) = nil) | ~ $i(v4) | ? % 108.94/15.06 | | | | | [v6: int] : ( ~ (v6 = 0) & ssList(v4) = v6)))) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | GROUND_INST: instantiating (172) with all_312_1, simplifying with % 108.94/15.06 | | | | | (143), (145) gives: % 108.94/15.06 | | | | | (173) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 108.94/15.06 | | | | | (cons(all_310_1, v0) = v1) | ~ (app(all_312_1, v1) = v2) | % 108.94/15.06 | | | | | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v0) = v3) % 108.94/15.06 | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (all_310_1 = all_91_0) | % 108.94/15.06 | | | | | ~ (cons(all_91_0, v3) = v4) | ~ (app(v2, v4) = nil) | ~ % 108.94/15.06 | | | | | $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v3) = v5))) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | GROUND_INST: instantiating (173) with nil, all_93_1, all_312_0, % 108.94/15.06 | | | | | simplifying with (12), (144), (152) gives: % 108.94/15.06 | | | | | (174) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] % 108.94/15.06 | | | | | : ! [v1: $i] : ( ~ (all_310_1 = all_91_0) | ~ % 108.94/15.06 | | | | | (cons(all_91_0, v0) = v1) | ~ (app(all_312_0, v1) = nil) | % 108.94/15.06 | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (165) with fresh symbols all_657_0, all_657_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (175) cyclefreeP(all_93_1) = all_657_0 & ssItem(all_310_1) = % 108.94/15.06 | | | | | all_657_1 & ( ~ (all_657_1 = 0) | all_657_0 = 0) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (175) implies: % 108.94/15.06 | | | | | (176) ssItem(all_310_1) = all_657_1 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (163) with fresh symbols all_659_0, all_659_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (177) strictorderP(all_93_1) = all_659_0 & ssItem(all_310_1) = % 108.94/15.06 | | | | | all_659_1 & ( ~ (all_659_1 = 0) | all_659_0 = 0) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (177) implies: % 108.94/15.06 | | | | | (178) ssItem(all_310_1) = all_659_1 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (162) with fresh symbols all_661_0, all_661_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (179) totalorderedP(all_93_1) = all_661_0 & ssItem(all_310_1) = % 108.94/15.06 | | | | | all_661_1 & ( ~ (all_661_1 = 0) | all_661_0 = 0) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (179) implies: % 108.94/15.06 | | | | | (180) ssItem(all_310_1) = all_661_1 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (164) with fresh symbols all_663_0, all_663_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (181) totalorderP(all_93_1) = all_663_0 & ssItem(all_310_1) = % 108.94/15.06 | | | | | all_663_1 & ( ~ (all_663_1 = 0) | all_663_0 = 0) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (181) implies: % 108.94/15.06 | | | | | (182) ssItem(all_310_1) = all_663_1 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (161) with fresh symbols all_665_0, all_665_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (183) strictorderedP(all_93_1) = all_665_0 & ssItem(all_310_1) = % 108.94/15.06 | | | | | all_665_1 & ( ~ (all_665_1 = 0) | all_665_0 = 0) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (183) implies: % 108.94/15.06 | | | | | (184) ssItem(all_310_1) = all_665_1 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (160) with fresh symbols all_667_0, all_667_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (185) duplicatefreeP(all_93_1) = all_667_0 & ssItem(all_310_1) = % 108.94/15.06 | | | | | all_667_1 & ( ~ (all_667_1 = 0) | all_667_0 = 0) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (185) implies: % 108.94/15.06 | | | | | (186) ssItem(all_310_1) = all_667_1 % 108.94/15.06 | | | | | (187) ~ (all_667_1 = 0) | all_667_0 = 0 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (159) with fresh symbols all_669_0, all_669_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (188) equalelemsP(all_93_1) = all_669_0 & ssItem(all_310_1) = % 108.94/15.06 | | | | | all_669_1 & ( ~ (all_669_1 = 0) | all_669_0 = 0) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (188) implies: % 108.94/15.06 | | | | | (189) ssItem(all_310_1) = all_669_1 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (158) with fresh symbols all_671_0, all_671_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (190) hd(all_93_1) = all_671_0 & ssItem(all_310_1) = all_671_1 & % 108.94/15.06 | | | | | $i(all_671_0) & ( ~ (all_671_1 = 0) | all_671_0 = all_310_1) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (190) implies: % 108.94/15.06 | | | | | (191) ssItem(all_310_1) = all_671_1 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (157) with fresh symbols all_673_0, all_673_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (192) tl(all_93_1) = all_673_0 & ssItem(all_310_1) = all_673_1 & % 108.94/15.06 | | | | | $i(all_673_0) & ( ~ (all_673_1 = 0) | all_673_0 = nil) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (192) implies: % 108.94/15.06 | | | | | (193) ssItem(all_310_1) = all_673_1 % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | DELTA: instantiating (171) with fresh symbols all_675_0, all_675_1 % 108.94/15.06 | | | | | gives: % 108.94/15.06 | | | | | (194) ssList(all_312_0) = all_675_0 & ssList(all_93_1) = all_675_1 % 108.94/15.06 | | | | | & ( ~ (all_675_1 = 0) | all_675_0 = 0) % 108.94/15.06 | | | | | % 108.94/15.06 | | | | | ALPHA: (194) implies: % 108.94/15.07 | | | | | (195) ssList(all_93_1) = all_675_1 % 108.94/15.07 | | | | | % 108.94/15.07 | | | | | BETA: splitting (174) gives: % 108.94/15.07 | | | | | % 108.94/15.07 | | | | | Case 1: % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | (196) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | DELTA: instantiating (196) with fresh symbol all_324_0 gives: % 108.94/15.07 | | | | | | (197) ~ (all_324_0 = 0) & ssList(nil) = all_324_0 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | REF_CLOSE: (1), (15), (197) are inconsistent by sub-proof #2. % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | Case 2: % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with 0, all_663_1, all_310_1, % 108.94/15.07 | | | | | | simplifying with (139), (182) gives: % 108.94/15.07 | | | | | | (198) all_663_1 = 0 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with all_659_1, all_663_1, % 108.94/15.07 | | | | | | all_310_1, simplifying with (178), (182) gives: % 108.94/15.07 | | | | | | (199) all_663_1 = all_659_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with all_663_1, all_669_1, % 108.94/15.07 | | | | | | all_310_1, simplifying with (182), (189) gives: % 108.94/15.07 | | | | | | (200) all_669_1 = all_663_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with all_661_1, all_669_1, % 108.94/15.07 | | | | | | all_310_1, simplifying with (180), (189) gives: % 108.94/15.07 | | | | | | (201) all_669_1 = all_661_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with all_669_1, all_671_1, % 108.94/15.07 | | | | | | all_310_1, simplifying with (189), (191) gives: % 108.94/15.07 | | | | | | (202) all_671_1 = all_669_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with all_665_1, all_671_1, % 108.94/15.07 | | | | | | all_310_1, simplifying with (184), (191) gives: % 108.94/15.07 | | | | | | (203) all_671_1 = all_665_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with all_657_1, all_671_1, % 108.94/15.07 | | | | | | all_310_1, simplifying with (176), (191) gives: % 108.94/15.07 | | | | | | (204) all_671_1 = all_657_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with all_671_1, all_673_1, % 108.94/15.07 | | | | | | all_310_1, simplifying with (191), (193) gives: % 108.94/15.07 | | | | | | (205) all_673_1 = all_671_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (14) with all_667_1, all_673_1, % 108.94/15.07 | | | | | | all_310_1, simplifying with (186), (193) gives: % 108.94/15.07 | | | | | | (206) all_673_1 = all_667_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | GROUND_INST: instantiating (15) with 0, all_675_1, all_93_1, % 108.94/15.07 | | | | | | simplifying with (22), (195) gives: % 108.94/15.07 | | | | | | (207) all_675_1 = 0 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (205), (206) imply: % 108.94/15.07 | | | | | | (208) all_671_1 = all_667_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | SIMP: (208) implies: % 108.94/15.07 | | | | | | (209) all_671_1 = all_667_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (202), (209) imply: % 108.94/15.07 | | | | | | (210) all_669_1 = all_667_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | SIMP: (210) implies: % 108.94/15.07 | | | | | | (211) all_669_1 = all_667_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (203), (209) imply: % 108.94/15.07 | | | | | | (212) all_667_1 = all_665_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (204), (209) imply: % 108.94/15.07 | | | | | | (213) all_667_1 = all_657_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (200), (201) imply: % 108.94/15.07 | | | | | | (214) all_663_1 = all_661_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | SIMP: (214) implies: % 108.94/15.07 | | | | | | (215) all_663_1 = all_661_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (201), (211) imply: % 108.94/15.07 | | | | | | (216) all_667_1 = all_661_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | SIMP: (216) implies: % 108.94/15.07 | | | | | | (217) all_667_1 = all_661_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (212), (213) imply: % 108.94/15.07 | | | | | | (218) all_665_1 = all_657_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (212), (217) imply: % 108.94/15.07 | | | | | | (219) all_665_1 = all_661_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (218), (219) imply: % 108.94/15.07 | | | | | | (220) all_661_1 = all_657_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | SIMP: (220) implies: % 108.94/15.07 | | | | | | (221) all_661_1 = all_657_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (199), (215) imply: % 108.94/15.07 | | | | | | (222) all_661_1 = all_659_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | SIMP: (222) implies: % 108.94/15.07 | | | | | | (223) all_661_1 = all_659_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (198), (199) imply: % 108.94/15.07 | | | | | | (224) all_659_1 = 0 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (221), (223) imply: % 108.94/15.07 | | | | | | (225) all_659_1 = all_657_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | SIMP: (225) implies: % 108.94/15.07 | | | | | | (226) all_659_1 = all_657_1 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (224), (226) imply: % 108.94/15.07 | | | | | | (227) all_657_1 = 0 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (218), (227) imply: % 108.94/15.07 | | | | | | (228) all_665_1 = 0 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | COMBINE_EQS: (212), (228) imply: % 108.94/15.07 | | | | | | (229) all_667_1 = 0 % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | BETA: splitting (168) gives: % 108.94/15.07 | | | | | | % 108.94/15.07 | | | | | | Case 1: % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | (230) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | DELTA: instantiating (230) with fresh symbol all_734_0 gives: % 108.94/15.07 | | | | | | | (231) ~ (all_734_0 = 0) & ssList(all_93_1) = all_734_0 % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | ALPHA: (231) implies: % 108.94/15.07 | | | | | | | (232) ~ (all_734_0 = 0) % 108.94/15.07 | | | | | | | (233) ssList(all_93_1) = all_734_0 % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | GROUND_INST: instantiating (15) with 0, all_734_0, all_93_1, % 108.94/15.07 | | | | | | | simplifying with (22), (233) gives: % 108.94/15.07 | | | | | | | (234) all_734_0 = 0 % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | REDUCE: (232), (234) imply: % 108.94/15.07 | | | | | | | (235) $false % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | CLOSE: (235) is inconsistent. % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | Case 2: % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | (236) ( ~ (all_97_0 = 0) | all_93_1 = nil) & ( ~ (all_93_1 = % 108.94/15.07 | | | | | | | nil) | all_97_0 = 0) % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | ALPHA: (236) implies: % 108.94/15.07 | | | | | | | (237) ~ (all_97_0 = 0) | all_93_1 = nil % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | BETA: splitting (170) gives: % 108.94/15.07 | | | | | | | % 108.94/15.07 | | | | | | | Case 1: % 108.94/15.07 | | | | | | | | % 108.94/15.07 | | | | | | | | (238) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 108.94/15.07 | | | | | | | | % 108.94/15.07 | | | | | | | | REF_CLOSE: (15), (22), (41), (133), (187), (229), (237), (238) % 108.94/15.07 | | | | | | | | are inconsistent by sub-proof #1. % 108.94/15.07 | | | | | | | | % 108.94/15.07 | | | | | | | Case 2: % 108.94/15.07 | | | | | | | | % 108.94/15.07 | | | | | | | | (239) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_312_0, v0) = % 108.94/15.07 | | | | | | | | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? % 108.94/15.07 | | | | | | | | [v4: $i] : (ssList(v0) = v2 & app(all_312_1, v3) = v4 % 108.94/15.07 | | | | | | | | & app(all_93_1, v0) = v3 & $i(v4) & $i(v3) & ( ~ % 108.94/15.07 | | | | | | | | (v2 = 0) | v4 = v1))) % 108.94/15.07 | | | | | | | | % 108.94/15.07 | | | | | | | | GROUND_INST: instantiating (239) with all_314_0, nil, % 108.94/15.07 | | | | | | | | simplifying with (149), (153) gives: % 108.94/15.07 | | | | | | | | (240) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 108.94/15.07 | | | | | | | | (ssList(all_314_0) = v0 & app(all_312_1, v1) = v2 & % 108.94/15.07 | | | | | | | | app(all_93_1, all_314_0) = v1 & $i(v2) & $i(v1) & ( ~ % 108.94/15.07 | | | | | | | | (v0 = 0) | v2 = nil)) % 108.94/15.07 | | | | | | | | % 108.94/15.07 | | | | | | | | DELTA: instantiating (240) with fresh symbols all_755_0, % 108.94/15.07 | | | | | | | | all_755_1, all_755_2 gives: % 108.94/15.08 | | | | | | | | (241) ssList(all_314_0) = all_755_2 & app(all_312_1, % 108.94/15.08 | | | | | | | | all_755_1) = all_755_0 & app(all_93_1, all_314_0) = % 108.94/15.08 | | | | | | | | all_755_1 & $i(all_755_0) & $i(all_755_1) & ( ~ % 108.94/15.08 | | | | | | | | (all_755_2 = 0) | all_755_0 = nil) % 108.94/15.08 | | | | | | | | % 108.94/15.08 | | | | | | | | ALPHA: (241) implies: % 108.94/15.08 | | | | | | | | (242) ssList(all_314_0) = all_755_2 % 108.94/15.08 | | | | | | | | % 108.94/15.08 | | | | | | | | BETA: splitting (237) gives: % 108.94/15.08 | | | | | | | | % 108.94/15.08 | | | | | | | | Case 1: % 108.94/15.08 | | | | | | | | | % 108.94/15.08 | | | | | | | | | (243) ~ (all_97_0 = 0) % 108.94/15.08 | | | | | | | | | % 108.94/15.08 | | | | | | | | | BETA: splitting (169) gives: % 108.94/15.08 | | | | | | | | | % 108.94/15.08 | | | | | | | | | Case 1: % 108.94/15.08 | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | (244) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = % 108.94/15.08 | | | | | | | | | | v0) % 108.94/15.08 | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | REF_CLOSE: (15), (22), (41), (133), (187), (229), (237), % 108.94/15.08 | | | | | | | | | | (244) are inconsistent by sub-proof #1. % 108.94/15.08 | | | | | | | | | | % 108.94/15.08 | | | | | | | | | Case 2: % 108.94/15.08 | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | (245) ( ~ (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : % 108.94/15.08 | | | | | | | | | | (ssList(v0) = 0 & app(v0, all_93_1) = v1 & $i(v1) % 108.94/15.08 | | | | | | | | | | & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & % 108.94/15.08 | | | | | | | | | | app(v1, v2) = nil & $i(v2)))) & (all_97_0 = 0 % 108.94/15.08 | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, % 108.94/15.08 | | | | | | | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] % 108.94/15.08 | | | | | | | | | | : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] % 108.94/15.08 | | | | | | | | | | : ( ~ (app(v1, v2) = nil) | ~ $i(v2) | ? [v3: % 108.94/15.08 | | | | | | | | | | int] : ( ~ (v3 = 0) & ssList(v2) = v3)))) % 108.94/15.08 | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | ALPHA: (245) implies: % 108.94/15.08 | | | | | | | | | | (246) all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 108.94/15.08 | | | | | | | | | | (app(v0, all_93_1) = v1) | ~ $i(v0) | ? [v2: % 108.94/15.08 | | | | | | | | | | int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! % 108.94/15.08 | | | | | | | | | | [v2: $i] : ( ~ (app(v1, v2) = nil) | ~ $i(v2) | % 108.94/15.08 | | | | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3))) % 108.94/15.08 | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | BETA: splitting (246) gives: % 108.94/15.08 | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | Case 1: % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | (247) all_97_0 = 0 % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | REDUCE: (243), (247) imply: % 108.94/15.08 | | | | | | | | | | | (248) $false % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | CLOSE: (248) is inconsistent. % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | Case 2: % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | (249) ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) % 108.94/15.08 | | | | | | | | | | | = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 108.94/15.08 | | | | | | | | | | | 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ % 108.94/15.08 | | | | | | | | | | | (app(v1, v2) = nil) | ~ $i(v2) | ? [v3: int] % 108.94/15.08 | | | | | | | | | | | : ( ~ (v3 = 0) & ssList(v2) = v3))) % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | GROUND_INST: instantiating (249) with all_312_1, all_312_0, % 108.94/15.08 | | | | | | | | | | | simplifying with (143), (144) gives: % 108.94/15.08 | | | | | | | | | | | (250) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_312_1) = % 108.94/15.08 | | | | | | | | | | | v0) | ! [v0: $i] : ( ~ (app(all_312_0, v0) = % 108.94/15.08 | | | | | | | | | | | nil) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 108.94/15.08 | | | | | | | | | | | & ssList(v0) = v1)) % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | BETA: splitting (250) gives: % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | Case 1: % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | (251) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_312_1) = % 108.94/15.08 | | | | | | | | | | | | v0) % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | DELTA: instantiating (251) with fresh symbol all_836_0 % 108.94/15.08 | | | | | | | | | | | | gives: % 108.94/15.08 | | | | | | | | | | | | (252) ~ (all_836_0 = 0) & ssList(all_312_1) = all_836_0 % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | ALPHA: (252) implies: % 108.94/15.08 | | | | | | | | | | | | (253) ~ (all_836_0 = 0) % 108.94/15.08 | | | | | | | | | | | | (254) ssList(all_312_1) = all_836_0 % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_836_0, all_312_1, % 108.94/15.08 | | | | | | | | | | | | simplifying with (145), (254) gives: % 108.94/15.08 | | | | | | | | | | | | (255) all_836_0 = 0 % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | REDUCE: (253), (255) imply: % 108.94/15.08 | | | | | | | | | | | | (256) $false % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | CLOSE: (256) is inconsistent. % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | Case 2: % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | (257) ! [v0: $i] : ( ~ (app(all_312_0, v0) = nil) | ~ % 108.94/15.08 | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 108.94/15.08 | | | | | | | | | | | | ssList(v0) = v1)) % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | GROUND_INST: instantiating (257) with all_314_0, simplifying % 108.94/15.08 | | | | | | | | | | | | with (149), (153) gives: % 108.94/15.08 | | | | | | | | | | | | (258) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_314_0) = % 108.94/15.08 | | | | | | | | | | | | v0) % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | DELTA: instantiating (258) with fresh symbol all_837_0 % 108.94/15.08 | | | | | | | | | | | | gives: % 108.94/15.08 | | | | | | | | | | | | (259) ~ (all_837_0 = 0) & ssList(all_314_0) = all_837_0 % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | ALPHA: (259) implies: % 108.94/15.08 | | | | | | | | | | | | (260) ~ (all_837_0 = 0) % 108.94/15.08 | | | | | | | | | | | | (261) ssList(all_314_0) = all_837_0 % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_837_0, all_314_0, % 108.94/15.08 | | | | | | | | | | | | simplifying with (151), (261) gives: % 108.94/15.08 | | | | | | | | | | | | (262) all_837_0 = 0 % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_755_2, all_837_0, % 108.94/15.08 | | | | | | | | | | | | all_314_0, simplifying with (242), (261) gives: % 108.94/15.08 | | | | | | | | | | | | (263) all_837_0 = all_755_2 % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | COMBINE_EQS: (262), (263) imply: % 108.94/15.08 | | | | | | | | | | | | (264) all_755_2 = 0 % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | REDUCE: (260), (262) imply: % 108.94/15.08 | | | | | | | | | | | | (265) $false % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | | CLOSE: (265) is inconsistent. % 108.94/15.08 | | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | | End of split % 108.94/15.08 | | | | | | | | | | | % 108.94/15.08 | | | | | | | | | | End of split % 108.94/15.08 | | | | | | | | | | % 108.94/15.08 | | | | | | | | | End of split % 108.94/15.08 | | | | | | | | | % 108.94/15.08 | | | | | | | | Case 2: % 108.94/15.08 | | | | | | | | | % 108.94/15.08 | | | | | | | | | (266) all_93_1 = nil % 108.94/15.08 | | | | | | | | | % 108.94/15.08 | | | | | | | | | REDUCE: (133), (266) imply: % 108.94/15.08 | | | | | | | | | (267) $false % 108.94/15.08 | | | | | | | | | % 108.94/15.08 | | | | | | | | | CLOSE: (267) is inconsistent. % 108.94/15.08 | | | | | | | | | % 108.94/15.08 | | | | | | | | End of split % 108.94/15.08 | | | | | | | | % 108.94/15.08 | | | | | | | End of split % 108.94/15.08 | | | | | | | % 108.94/15.08 | | | | | | End of split % 108.94/15.08 | | | | | | % 108.94/15.08 | | | | | End of split % 108.94/15.08 | | | | | % 108.94/15.08 | | | | End of split % 108.94/15.08 | | | | % 108.94/15.08 | | | Case 2: % 108.94/15.08 | | | | % 108.94/15.08 | | | | (268) all_97_2 = nil & all_93_1 = nil % 108.94/15.08 | | | | % 108.94/15.08 | | | | ALPHA: (268) implies: % 108.94/15.08 | | | | (269) all_93_1 = nil % 108.94/15.08 | | | | % 108.94/15.08 | | | | REDUCE: (133), (269) imply: % 108.94/15.08 | | | | (270) $false % 108.94/15.08 | | | | % 108.94/15.08 | | | | CLOSE: (270) is inconsistent. % 108.94/15.08 | | | | % 108.94/15.08 | | | End of split % 108.94/15.08 | | | % 108.94/15.08 | | End of split % 108.94/15.08 | | % 108.94/15.08 | End of split % 108.94/15.08 | % 108.94/15.08 End of proof % 108.94/15.08 % 108.94/15.08 Sub-proof #1 shows that the following formulas are inconsistent: % 108.94/15.08 ---------------------------------------------------------------- % 108.94/15.09 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 108.94/15.09 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 108.94/15.09 (2) ~ (all_667_1 = 0) | all_667_0 = 0 % 108.94/15.09 (3) ~ (all_97_0 = 0) | all_93_1 = nil % 108.94/15.09 (4) ssList(all_93_1) = 0 % 108.94/15.09 (5) ~ (all_93_1 = nil) % 108.94/15.09 (6) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0 = % 108.94/15.09 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, % 108.94/15.09 all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 % 108.94/15.09 & app(v1, v2) = all_97_2 & $i(v2)))) & (all_97_0 = 0 | ! [v0: % 108.94/15.09 $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ $i(v0) | ? % 108.94/15.09 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ % 108.94/15.09 (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 108.94/15.09 0) & ssList(v2) = v3))))) % 108.94/15.09 (7) all_667_1 = 0 % 108.94/15.09 (8) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) % 108.94/15.09 % 108.94/15.09 Begin of proof % 108.94/15.09 | % 108.94/15.09 | DELTA: instantiating (8) with fresh symbol all_734_0 gives: % 108.94/15.09 | (9) ~ (all_734_0 = 0) & ssList(all_93_1) = all_734_0 % 108.94/15.09 | % 108.94/15.09 | ALPHA: (9) implies: % 108.94/15.09 | (10) ~ (all_734_0 = 0) % 108.94/15.09 | (11) ssList(all_93_1) = all_734_0 % 108.94/15.09 | % 108.94/15.09 | BETA: splitting (2) gives: % 108.94/15.09 | % 108.94/15.09 | Case 1: % 108.94/15.09 | | % 108.94/15.09 | | (12) ~ (all_667_1 = 0) % 108.94/15.09 | | % 108.94/15.09 | | REDUCE: (7), (12) imply: % 108.94/15.09 | | (13) $false % 108.94/15.09 | | % 108.94/15.09 | | CLOSE: (13) is inconsistent. % 108.94/15.09 | | % 108.94/15.09 | Case 2: % 108.94/15.09 | | % 108.94/15.09 | | % 108.94/15.09 | | DELTA: instantiating (8) with fresh symbol all_758_0 gives: % 108.94/15.09 | | (14) ~ (all_758_0 = 0) & ssList(all_93_1) = all_758_0 % 108.94/15.09 | | % 108.94/15.09 | | ALPHA: (14) implies: % 108.94/15.09 | | (15) ssList(all_93_1) = all_758_0 % 108.94/15.09 | | % 108.94/15.09 | | BETA: splitting (3) gives: % 108.94/15.09 | | % 108.94/15.09 | | Case 1: % 108.94/15.09 | | | % 108.94/15.09 | | | (16) ~ (all_97_0 = 0) % 108.94/15.09 | | | % 108.94/15.09 | | | BETA: splitting (6) gives: % 108.94/15.09 | | | % 108.94/15.09 | | | Case 1: % 108.94/15.09 | | | | % 108.94/15.09 | | | | % 108.94/15.09 | | | | DELTA: instantiating (8) with fresh symbol all_804_0 gives: % 108.94/15.09 | | | | (17) ~ (all_804_0 = 0) & ssList(all_93_1) = all_804_0 % 108.94/15.09 | | | | % 108.94/15.09 | | | | ALPHA: (17) implies: % 108.94/15.09 | | | | (18) ssList(all_93_1) = all_804_0 % 108.94/15.09 | | | | % 108.94/15.09 | | | | GROUND_INST: instantiating (1) with 0, all_804_0, all_93_1, simplifying % 108.94/15.09 | | | | with (4), (18) gives: % 108.94/15.09 | | | | (19) all_804_0 = 0 % 108.94/15.09 | | | | % 108.94/15.09 | | | | GROUND_INST: instantiating (1) with all_758_0, all_804_0, all_93_1, % 108.94/15.09 | | | | simplifying with (15), (18) gives: % 108.94/15.09 | | | | (20) all_804_0 = all_758_0 % 108.94/15.09 | | | | % 108.94/15.09 | | | | GROUND_INST: instantiating (1) with all_734_0, all_804_0, all_93_1, % 108.94/15.09 | | | | simplifying with (11), (18) gives: % 108.94/15.09 | | | | (21) all_804_0 = all_734_0 % 108.94/15.09 | | | | % 108.94/15.09 | | | | COMBINE_EQS: (20), (21) imply: % 108.94/15.09 | | | | (22) all_758_0 = all_734_0 % 108.94/15.09 | | | | % 108.94/15.09 | | | | COMBINE_EQS: (19), (20) imply: % 108.94/15.09 | | | | (23) all_758_0 = 0 % 108.94/15.09 | | | | % 108.94/15.09 | | | | COMBINE_EQS: (22), (23) imply: % 108.94/15.09 | | | | (24) all_734_0 = 0 % 108.94/15.09 | | | | % 108.94/15.09 | | | | REDUCE: (10), (24) imply: % 108.94/15.09 | | | | (25) $false % 108.94/15.09 | | | | % 108.94/15.09 | | | | CLOSE: (25) is inconsistent. % 108.94/15.09 | | | | % 108.94/15.09 | | | Case 2: % 108.94/15.09 | | | | % 108.94/15.09 | | | | (26) ( ~ (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 % 108.94/15.09 | | | | & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : % 108.94/15.09 | | | | (ssList(v2) = 0 & app(v1, v2) = all_97_2 & $i(v2)))) & % 108.94/15.09 | | | | (all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, % 108.94/15.09 | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 108.94/15.09 | | | | 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = % 108.94/15.09 | | | | all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 108.94/15.09 | | | | ssList(v2) = v3)))) % 108.94/15.09 | | | | % 108.94/15.09 | | | | ALPHA: (26) implies: % 108.94/15.09 | | | | (27) all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, % 108.94/15.09 | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) % 108.94/15.09 | | | | & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = % 108.94/15.09 | | | | all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 108.94/15.09 | | | | ssList(v2) = v3))) % 108.94/15.09 | | | | % 108.94/15.09 | | | | BETA: splitting (27) gives: % 108.94/15.09 | | | | % 108.94/15.09 | | | | Case 1: % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | (28) all_97_0 = 0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | REDUCE: (16), (28) imply: % 108.94/15.09 | | | | | (29) $false % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | CLOSE: (29) is inconsistent. % 108.94/15.09 | | | | | % 108.94/15.09 | | | | Case 2: % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | DELTA: instantiating (8) with fresh symbol all_812_0 gives: % 108.94/15.09 | | | | | (30) ~ (all_812_0 = 0) & ssList(all_93_1) = all_812_0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | ALPHA: (30) implies: % 108.94/15.09 | | | | | (31) ssList(all_93_1) = all_812_0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | GROUND_INST: instantiating (1) with all_734_0, all_758_0, all_93_1, % 108.94/15.09 | | | | | simplifying with (11), (15) gives: % 108.94/15.09 | | | | | (32) all_758_0 = all_734_0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | GROUND_INST: instantiating (1) with 0, all_812_0, all_93_1, % 108.94/15.09 | | | | | simplifying with (4), (31) gives: % 108.94/15.09 | | | | | (33) all_812_0 = 0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | GROUND_INST: instantiating (1) with all_758_0, all_812_0, all_93_1, % 108.94/15.09 | | | | | simplifying with (15), (31) gives: % 108.94/15.09 | | | | | (34) all_812_0 = all_758_0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | COMBINE_EQS: (33), (34) imply: % 108.94/15.09 | | | | | (35) all_758_0 = 0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | SIMP: (35) implies: % 108.94/15.09 | | | | | (36) all_758_0 = 0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | COMBINE_EQS: (32), (36) imply: % 108.94/15.09 | | | | | (37) all_734_0 = 0 % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | REDUCE: (10), (37) imply: % 108.94/15.09 | | | | | (38) $false % 108.94/15.09 | | | | | % 108.94/15.09 | | | | | CLOSE: (38) is inconsistent. % 108.94/15.09 | | | | | % 108.94/15.09 | | | | End of split % 108.94/15.09 | | | | % 108.94/15.09 | | | End of split % 108.94/15.09 | | | % 108.94/15.09 | | Case 2: % 108.94/15.09 | | | % 108.94/15.09 | | | (39) all_93_1 = nil % 108.94/15.09 | | | % 108.94/15.09 | | | REDUCE: (5), (39) imply: % 108.94/15.09 | | | (40) $false % 108.94/15.09 | | | % 108.94/15.09 | | | CLOSE: (40) is inconsistent. % 108.94/15.09 | | | % 108.94/15.09 | | End of split % 108.94/15.09 | | % 108.94/15.09 | End of split % 108.94/15.09 | % 108.94/15.09 End of proof % 108.94/15.09 % 108.94/15.09 Sub-proof #2 shows that the following formulas are inconsistent: % 108.94/15.09 ---------------------------------------------------------------- % 108.94/15.09 (1) ~ (all_324_0 = 0) & ssList(nil) = all_324_0 % 108.94/15.09 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 108.94/15.09 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 108.94/15.09 (3) ssList(nil) = 0 % 108.94/15.09 % 108.94/15.09 Begin of proof % 108.94/15.09 | % 108.94/15.09 | ALPHA: (1) implies: % 108.94/15.09 | (4) ~ (all_324_0 = 0) % 108.94/15.09 | (5) ssList(nil) = all_324_0 % 108.94/15.09 | % 108.94/15.09 | GROUND_INST: instantiating (2) with 0, all_324_0, nil, simplifying with (3), % 108.94/15.09 | (5) gives: % 108.94/15.10 | (6) all_324_0 = 0 % 108.94/15.10 | % 108.94/15.10 | REDUCE: (4), (6) imply: % 108.94/15.10 | (7) $false % 108.94/15.10 | % 108.94/15.10 | CLOSE: (7) is inconsistent. % 108.94/15.10 | % 108.94/15.10 End of proof % 108.94/15.10 % SZS output end Proof for theBenchmark % 108.94/15.10 % 108.94/15.10 14499ms %------------------------------------------------------------------------------