%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC322+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 : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 20:50:49 EDT 2023 % Result : Theorem 24.77s 4.25s % Output : Proof 82.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC322+1 : TPTP v8.1.2. Released v2.4.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n015.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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 16:55:55 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.65 ________ _____ % 0.19/0.65 ___ __ \_________(_)________________________________ % 0.19/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.65 % 0.19/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.65 (2023-06-19) % 0.19/0.65 % 0.19/0.65 (c) Philipp Rümmer, 2009-2023 % 0.19/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.65 Amanda Stjerna. % 0.19/0.65 Free software under BSD-3-Clause. % 0.19/0.65 % 0.19/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.65 % 0.19/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.67 Running up to 7 provers in parallel. % 0.19/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 6.20/1.74 Prover 4: Preprocessing ... % 6.20/1.75 Prover 1: Preprocessing ... % 6.88/1.80 Prover 5: Preprocessing ... % 6.88/1.80 Prover 0: Preprocessing ... % 6.88/1.80 Prover 3: Preprocessing ... % 6.88/1.80 Prover 2: Preprocessing ... % 6.88/1.80 Prover 6: Preprocessing ... % 16.27/3.10 Prover 2: Proving ... % 16.68/3.14 Prover 5: Constructing countermodel ... % 16.92/3.15 Prover 6: Proving ... % 16.92/3.16 Prover 1: Constructing countermodel ... % 16.92/3.21 Prover 3: Constructing countermodel ... % 22.72/3.96 Prover 4: Constructing countermodel ... % 23.95/4.21 Prover 0: Proving ... % 24.77/4.25 Prover 3: proved (3559ms) % 24.77/4.25 % 24.77/4.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 24.77/4.25 % 24.77/4.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.77/4.26 Prover 6: stopped % 24.77/4.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.77/4.26 Prover 2: stopped % 24.77/4.26 Prover 5: stopped % 25.28/4.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 25.28/4.30 Prover 0: stopped % 25.28/4.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 25.28/4.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 26.94/4.52 Prover 7: Preprocessing ... % 26.94/4.54 Prover 10: Preprocessing ... % 27.43/4.59 Prover 13: Preprocessing ... % 27.43/4.61 Prover 11: Preprocessing ... % 27.43/4.61 Prover 8: Preprocessing ... % 28.27/4.83 Prover 10: Constructing countermodel ... % 29.59/4.87 Prover 7: Constructing countermodel ... % 30.44/5.03 Prover 13: Constructing countermodel ... % 30.99/5.11 Prover 8: Warning: ignoring some quantifiers % 31.48/5.12 Prover 8: Constructing countermodel ... % 38.77/6.16 Prover 11: Constructing countermodel ... % 66.01/9.67 Prover 13: stopped % 66.01/9.67 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 66.62/9.75 Prover 16: Preprocessing ... % 67.72/9.87 Prover 16: Constructing countermodel ... % 81.18/11.61 Prover 1: Found proof (size 308) % 81.18/11.61 Prover 1: proved (10926ms) % 81.18/11.61 Prover 10: stopped % 81.18/11.61 Prover 7: stopped % 81.18/11.61 Prover 8: stopped % 81.18/11.62 Prover 4: stopped % 81.18/11.62 Prover 11: stopped % 81.18/11.63 Prover 16: stopped % 81.18/11.63 % 81.18/11.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 81.18/11.63 % 81.18/11.65 % SZS output start Proof for theBenchmark % 81.18/11.65 Assumptions after simplification: % 81.18/11.65 --------------------------------- % 81.18/11.65 % 81.18/11.65 (ax13) % 81.56/11.68 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 81.56/11.68 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 81.56/11.68 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 81.56/11.68 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 81.56/11.68 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 81.56/11.68 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 81.56/11.68 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 81.56/11.68 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 81.56/11.69 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 81.56/11.69 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 81.56/11.69 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 81.56/11.69 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 81.56/11.69 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 81.56/11.69 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 81.56/11.69 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 81.56/11.69 % 81.56/11.69 (ax16) % 81.56/11.69 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 81.56/11.69 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 81.56/11.69 (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 81.56/11.69 % 81.56/11.69 (ax17) % 81.56/11.69 ssList(nil) = 0 & $i(nil) % 81.56/11.69 % 81.56/11.69 (ax20) % 81.56/11.69 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 81.56/11.69 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 81.56/11.69 ssItem(v2) = 0 & $i(v2)))) % 81.56/11.69 % 81.56/11.69 (ax23) % 81.56/11.69 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 81.56/11.69 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 81.56/11.69 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 81.56/11.69 % 81.56/11.69 (ax25) % 81.56/11.69 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 81.56/11.69 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 81.56/11.69 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 81.56/11.69 % 81.56/11.69 (ax26) % 81.56/11.69 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 81.56/11.69 ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 81.56/11.69 (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 81.56/11.69 % 81.56/11.69 (ax59) % 81.56/11.69 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 81.56/11.69 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 81.56/11.69 (v2 = 0) | v3 = 0))) % 81.56/11.69 % 81.56/11.69 (ax61) % 81.56/11.70 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 81.56/11.70 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 81.56/11.70 (v2 = 0) | v3 = 0))) % 81.56/11.70 % 81.56/11.70 (ax63) % 81.56/11.70 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 81.56/11.70 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 81.56/11.70 (v2 = 0) | v3 = 0))) % 81.56/11.70 % 81.56/11.70 (ax65) % 81.56/11.70 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 81.56/11.70 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 81.56/11.70 (v2 = 0) | v3 = 0))) % 81.56/11.70 % 81.56/11.70 (ax68) % 81.56/11.70 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 81.56/11.70 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 81.56/11.70 ~ (v2 = 0) | v3 = 0))) % 81.56/11.70 % 81.56/11.70 (ax71) % 81.56/11.70 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 81.56/11.70 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 81.56/11.70 ~ (v2 = 0) | v3 = 0))) % 81.56/11.70 % 81.56/11.70 (ax72) % 81.56/11.70 duplicatefreeP(nil) = 0 & $i(nil) % 81.56/11.70 % 81.56/11.70 (ax73) % 81.56/11.70 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 81.56/11.70 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 81.56/11.70 (v2 = 0) | v3 = 0))) % 81.56/11.70 % 81.56/11.70 (ax81) % 81.56/11.70 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 81.56/11.70 [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | % 81.56/11.70 ~ $i(v1) | ? [v4: any] : ? [v5: $i] : (cons(v1, v0) = v5 & ssItem(v1) = % 81.56/11.70 v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3)))) % 81.56/11.70 % 81.56/11.70 (ax83) % 81.56/11.70 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 81.56/11.70 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 81.56/11.70 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1 % 81.56/11.70 = nil) | ~ (v0 = nil) | v2 = nil)))) % 81.56/11.70 % 81.56/11.70 (co1) % 81.56/11.70 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 81.56/11.70 0 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ % 81.56/11.70 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : % 81.56/11.70 ! [v5: $i] : (v5 = v0 | ~ (app(v3, v4) = v5) | ~ $i(v4) | ? [v6: any] % 81.56/11.70 : ? [v7: $i] : (ssList(v4) = v6 & app(v4, v3) = v7 & $i(v7) & ( ~ (v7 % 81.56/11.70 = v1) | ~ (v6 = 0))))) & ( ~ (v1 = nil) | v0 = nil) & ( ? [v2: % 81.56/11.70 $i] : ? [v3: $i] : (cons(v2, nil) = v3 & ssItem(v2) = 0 & $i(v3) & % 81.56/11.70 $i(v2) & ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v0) & ssList(v4) = 0 & % 81.56/11.70 app(v4, v3) = v1 & app(v3, v4) = v5 & $i(v5) & $i(v4))) | (v1 = nil % 81.56/11.70 & ~ (v0 = nil))))) % 81.56/11.70 % 81.56/11.71 (function-axioms) % 81.56/11.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 81.56/11.71 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 81.56/11.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 81.56/11.71 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 81.56/11.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 81.56/11.71 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 81.56/11.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 81.56/11.71 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 81.56/11.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 81.56/11.71 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 81.56/11.71 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 81.56/11.71 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 81.56/11.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 81.56/11.71 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 81.56/11.71 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 81.56/11.71 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 81.56/11.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 81.56/11.71 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 81.56/11.71 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 81.56/11.71 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 81.56/11.71 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 81.56/11.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 81.56/11.71 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 81.56/11.71 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 81.56/11.71 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 81.56/11.71 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 81.56/11.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 81.56/11.71 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 81.56/11.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 81.56/11.71 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 81.56/11.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 81.56/11.71 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 81.56/11.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 81.56/11.71 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 81.56/11.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 81.56/11.71 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 81.56/11.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 81.56/11.71 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 81.56/11.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 81.56/11.71 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 81.56/11.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 81.56/11.71 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 81.56/11.71 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 81.56/11.71 % 81.56/11.71 Further assumptions not needed in the proof: % 81.56/11.71 -------------------------------------------- % 81.56/11.71 ax1, ax10, ax11, ax12, ax14, ax15, ax18, ax19, ax2, ax21, ax22, ax24, ax27, % 81.56/11.71 ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, % 81.56/11.71 ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, % 81.56/11.71 ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, ax66, % 81.56/11.71 ax67, ax69, ax7, ax70, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax82, % 81.56/11.71 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 81.56/11.71 % 81.56/11.71 Those formulas are unsatisfiable: % 81.56/11.71 --------------------------------- % 81.56/11.71 % 81.56/11.71 Begin of proof % 81.56/11.71 | % 81.56/11.71 | ALPHA: (ax17) implies: % 81.56/11.71 | (1) ssList(nil) = 0 % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax20) implies: % 81.56/11.72 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 81.56/11.72 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 81.56/11.72 | ssItem(v2) = 0 & $i(v2)))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax59) implies: % 81.56/11.72 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.72 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 81.56/11.72 | ~ (v2 = 0) | v3 = 0))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax61) implies: % 81.56/11.72 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.72 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 81.56/11.72 | ( ~ (v2 = 0) | v3 = 0))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax63) implies: % 81.56/11.72 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.72 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 81.56/11.72 | ( ~ (v2 = 0) | v3 = 0))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax65) implies: % 81.56/11.72 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.72 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 81.56/11.72 | & ( ~ (v2 = 0) | v3 = 0))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax68) implies: % 81.56/11.72 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.72 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 81.56/11.72 | & ( ~ (v2 = 0) | v3 = 0))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax71) implies: % 81.56/11.72 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.72 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 81.56/11.72 | & ( ~ (v2 = 0) | v3 = 0))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax72) implies: % 81.56/11.72 | (9) duplicatefreeP(nil) = 0 % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax73) implies: % 81.56/11.72 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.72 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 81.56/11.72 | ( ~ (v2 = 0) | v3 = 0))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax81) implies: % 81.56/11.72 | (11) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 81.56/11.72 | $i] : ! [v3: $i] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = % 81.56/11.72 | v3) | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : (cons(v1, v0) = % 81.56/11.72 | v5 & ssItem(v1) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3)))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (ax83) implies: % 81.56/11.72 | (12) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 81.56/11.72 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 % 81.56/11.72 | = 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = % 81.56/11.72 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil)))) % 81.56/11.72 | % 81.56/11.72 | ALPHA: (co1) implies: % 81.56/11.73 | (13) $i(nil) % 81.56/11.73 | (14) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 81.56/11.73 | & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | % 81.56/11.73 | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! % 81.56/11.73 | [v4: $i] : ! [v5: $i] : (v5 = v0 | ~ (app(v3, v4) = v5) | ~ % 81.56/11.73 | $i(v4) | ? [v6: any] : ? [v7: $i] : (ssList(v4) = v6 & % 81.56/11.73 | app(v4, v3) = v7 & $i(v7) & ( ~ (v7 = v1) | ~ (v6 = 0))))) % 81.56/11.73 | & ( ~ (v1 = nil) | v0 = nil) & ( ? [v2: $i] : ? [v3: $i] : % 81.56/11.73 | (cons(v2, nil) = v3 & ssItem(v2) = 0 & $i(v3) & $i(v2) & ? [v4: % 81.56/11.73 | $i] : ? [v5: $i] : ( ~ (v5 = v0) & ssList(v4) = 0 & app(v4, % 81.56/11.73 | v3) = v1 & app(v3, v4) = v5 & $i(v5) & $i(v4))) | (v1 = % 81.56/11.73 | nil & ~ (v0 = nil))))) % 81.56/11.73 | % 81.56/11.73 | ALPHA: (function-axioms) implies: % 81.56/11.73 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 81.56/11.73 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 81.56/11.73 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 81.56/11.73 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 81.56/11.73 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 81.56/11.73 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 81.56/11.73 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 81.56/11.73 | (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 81.56/11.73 | % 81.56/11.73 | DELTA: instantiating (14) with fresh symbol all_93_0 gives: % 81.56/11.73 | (19) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 81.56/11.73 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~ % 81.56/11.73 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: % 81.56/11.73 | $i] : ! [v4: int] : (v4 = all_93_0 | ~ (app(v2, v3) = v4) | ~ % 81.56/11.73 | $i(v3) | ? [v5: any] : ? [v6: $i] : (ssList(v3) = v5 & app(v3, % 81.56/11.73 | v2) = v6 & $i(v6) & ( ~ (v6 = v0) | ~ (v5 = 0))))) & ( ~ % 81.56/11.73 | (v0 = nil) | all_93_0 = nil) & ( ? [v1: $i] : ? [v2: $i] : % 81.56/11.73 | (cons(v1, nil) = v2 & ssItem(v1) = 0 & $i(v2) & $i(v1) & ? [v3: % 81.56/11.73 | $i] : ? [v4: any] : ( ~ (v4 = all_93_0) & ssList(v3) = 0 & % 81.56/11.73 | app(v3, v2) = v0 & app(v2, v3) = v4 & $i(v4) & $i(v3))) | (v0 % 81.56/11.73 | = nil & ~ (all_93_0 = nil)))) % 81.56/11.73 | % 81.56/11.73 | ALPHA: (19) implies: % 81.56/11.74 | (20) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( % 81.56/11.74 | ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 81.56/11.74 | ssItem(v1) = v3) | ! [v3: $i] : ! [v4: int] : (v4 = all_93_0 | % 81.56/11.74 | ~ (app(v2, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : % 81.56/11.74 | (ssList(v3) = v5 & app(v3, v2) = v6 & $i(v6) & ( ~ (v6 = v0) | % 81.56/11.74 | ~ (v5 = 0))))) & ( ~ (v0 = nil) | all_93_0 = nil) & ( ? [v1: % 81.56/11.74 | $i] : ? [v2: $i] : (cons(v1, nil) = v2 & ssItem(v1) = 0 & % 81.56/11.74 | $i(v2) & $i(v1) & ? [v3: $i] : ? [v4: any] : ( ~ (v4 = % 81.56/11.74 | all_93_0) & ssList(v3) = 0 & app(v3, v2) = v0 & app(v2, v3) % 81.56/11.74 | = v4 & $i(v4) & $i(v3))) | (v0 = nil & ~ (all_93_0 = nil)))) % 81.56/11.74 | % 81.56/11.74 | DELTA: instantiating (20) with fresh symbol all_97_0 gives: % 81.56/11.74 | (21) ssList(all_97_0) = 0 & $i(all_97_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 81.56/11.74 | (cons(v0, nil) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 81.56/11.74 | ssItem(v0) = v2) | ! [v2: $i] : ! [v3: int] : (v3 = all_93_0 | % 81.56/11.74 | ~ (app(v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : % 81.56/11.74 | (ssList(v2) = v4 & app(v2, v1) = v5 & $i(v5) & ( ~ (v5 = all_97_0) % 81.56/11.74 | | ~ (v4 = 0))))) & ( ~ (all_97_0 = nil) | all_93_0 = nil) & ( % 81.56/11.74 | ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & % 81.56/11.74 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: any] : ( ~ (v3 = all_93_0) % 81.56/11.74 | & ssList(v2) = 0 & app(v2, v1) = all_97_0 & app(v1, v2) = v3 & % 81.56/11.74 | $i(v3) & $i(v2))) | (all_97_0 = nil & ~ (all_93_0 = nil))) % 81.56/11.74 | % 81.56/11.74 | ALPHA: (21) implies: % 81.56/11.74 | (22) $i(all_97_0) % 81.56/11.74 | (23) ssList(all_97_0) = 0 % 81.56/11.74 | (24) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 & % 81.56/11.74 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: any] : ( ~ (v3 = all_93_0) & % 81.56/11.74 | ssList(v2) = 0 & app(v2, v1) = all_97_0 & app(v1, v2) = v3 & % 81.56/11.74 | $i(v3) & $i(v2))) | (all_97_0 = nil & ~ (all_93_0 = nil)) % 81.56/11.74 | (25) ~ (all_97_0 = nil) | all_93_0 = nil % 81.56/11.74 | (26) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.74 | [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | ! [v2: $i] : ! [v3: % 81.56/11.74 | int] : (v3 = all_93_0 | ~ (app(v1, v2) = v3) | ~ $i(v2) | ? % 81.56/11.74 | [v4: any] : ? [v5: $i] : (ssList(v2) = v4 & app(v2, v1) = v5 & % 81.56/11.74 | $i(v5) & ( ~ (v5 = all_97_0) | ~ (v4 = 0))))) % 81.56/11.74 | % 81.56/11.74 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (13) gives: % 81.56/11.74 | (27) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.74 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 81.56/11.74 | ( ~ (v2 = 0) | v3 = nil))) % 81.56/11.74 | % 81.56/11.74 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (13) gives: % 81.56/11.74 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.74 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 81.56/11.74 | ( ~ (v2 = 0) | v3 = v0))) % 81.56/11.74 | % 81.56/11.74 | GROUND_INST: instantiating (ax16) with nil, simplifying with (1), (13) gives: % 81.56/11.75 | (29) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 81.56/11.75 | [v2: any] : ? [v3: any] : (ssList(v1) = v3 & ssItem(v0) = v2 & ( ~ % 81.56/11.75 | (v2 = 0) | v3 = 0))) % 81.56/11.75 | % 81.56/11.75 | GROUND_INST: instantiating (2) with all_97_0, simplifying with (22), (23) % 81.56/11.75 | gives: % 81.56/11.75 | (30) all_97_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 81.56/11.75 | : (cons(v1, v0) = all_97_0 & ssItem(v1) = 0 & $i(v1))) % 81.56/11.75 | % 81.56/11.75 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (9), (13) % 81.56/11.75 | gives: % 81.56/11.75 | (31) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 81.56/11.75 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 81.56/11.75 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 81.56/11.75 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 81.56/11.75 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 81.56/11.75 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 81.56/11.75 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 81.56/11.75 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 81.56/11.75 | v8)))))) % 81.56/11.75 | % 81.56/11.75 | BETA: splitting (31) gives: % 81.56/11.75 | % 81.56/11.75 | Case 1: % 81.56/11.75 | | % 81.56/11.75 | | (32) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 81.56/11.75 | | % 81.56/11.75 | | DELTA: instantiating (32) with fresh symbol all_269_0 gives: % 81.56/11.75 | | (33) ~ (all_269_0 = 0) & ssList(nil) = all_269_0 % 81.56/11.75 | | % 81.56/11.75 | | ALPHA: (33) implies: % 81.56/11.75 | | (34) ~ (all_269_0 = 0) % 81.56/11.75 | | (35) ssList(nil) = all_269_0 % 81.56/11.75 | | % 81.56/11.75 | | DELTA: instantiating (32) with fresh symbol all_271_0 gives: % 81.56/11.75 | | (36) ~ (all_271_0 = 0) & ssList(nil) = all_271_0 % 81.56/11.75 | | % 81.56/11.75 | | ALPHA: (36) implies: % 81.56/11.75 | | (37) ssList(nil) = all_271_0 % 81.56/11.75 | | % 81.56/11.75 | | DELTA: instantiating (32) with fresh symbol all_273_0 gives: % 81.56/11.75 | | (38) ~ (all_273_0 = 0) & ssList(nil) = all_273_0 % 81.56/11.75 | | % 81.56/11.75 | | ALPHA: (38) implies: % 81.56/11.75 | | (39) ssList(nil) = all_273_0 % 81.56/11.75 | | % 81.56/11.75 | | GROUND_INST: instantiating (16) with 0, all_271_0, nil, simplifying with % 81.56/11.75 | | (1), (37) gives: % 81.56/11.75 | | (40) all_271_0 = 0 % 81.56/11.75 | | % 81.56/11.75 | | GROUND_INST: instantiating (16) with all_271_0, all_273_0, nil, simplifying % 81.56/11.75 | | with (37), (39) gives: % 81.56/11.75 | | (41) all_273_0 = all_271_0 % 81.56/11.75 | | % 81.56/11.75 | | GROUND_INST: instantiating (16) with all_269_0, all_273_0, nil, simplifying % 81.56/11.75 | | with (35), (39) gives: % 81.56/11.75 | | (42) all_273_0 = all_269_0 % 81.56/11.75 | | % 81.56/11.75 | | COMBINE_EQS: (41), (42) imply: % 81.56/11.75 | | (43) all_271_0 = all_269_0 % 81.56/11.75 | | % 81.56/11.75 | | SIMP: (43) implies: % 81.56/11.75 | | (44) all_271_0 = all_269_0 % 81.56/11.75 | | % 81.56/11.75 | | COMBINE_EQS: (40), (44) imply: % 81.56/11.75 | | (45) all_269_0 = 0 % 81.56/11.75 | | % 81.56/11.75 | | SIMP: (45) implies: % 81.56/11.75 | | (46) all_269_0 = 0 % 81.56/11.75 | | % 81.56/11.75 | | REDUCE: (34), (46) imply: % 81.56/11.75 | | (47) $false % 81.56/11.75 | | % 81.56/11.75 | | CLOSE: (47) is inconsistent. % 81.56/11.75 | | % 81.56/11.75 | Case 2: % 81.56/11.75 | | % 81.56/11.75 | | (48) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 81.56/11.75 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 81.56/11.75 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 81.56/11.75 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 81.56/11.75 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 81.56/11.75 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 81.56/11.75 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 81.56/11.75 | | 0) & ssList(v6) = v8)))))) % 81.56/11.75 | | % 81.56/11.75 | | BETA: splitting (25) gives: % 81.56/11.75 | | % 81.56/11.75 | | Case 1: % 81.56/11.75 | | | % 81.56/11.75 | | | (49) ~ (all_97_0 = nil) % 81.56/11.75 | | | % 81.56/11.75 | | | BETA: splitting (24) gives: % 81.56/11.75 | | | % 81.56/11.75 | | | Case 1: % 81.56/11.75 | | | | % 81.56/11.76 | | | | (50) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 % 81.56/11.76 | | | | & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: any] : ( ~ (v3 = % 81.56/11.76 | | | | all_93_0) & ssList(v2) = 0 & app(v2, v1) = all_97_0 & % 81.56/11.76 | | | | app(v1, v2) = v3 & $i(v3) & $i(v2))) % 81.56/11.76 | | | | % 81.56/11.76 | | | | DELTA: instantiating (50) with fresh symbols all_299_0, all_299_1 gives: % 81.56/11.76 | | | | (51) cons(all_299_1, nil) = all_299_0 & ssItem(all_299_1) = 0 & % 81.56/11.76 | | | | $i(all_299_0) & $i(all_299_1) & ? [v0: $i] : ? [v1: any] : ( ~ % 81.56/11.76 | | | | (v1 = all_93_0) & ssList(v0) = 0 & app(v0, all_299_0) = % 81.56/11.76 | | | | all_97_0 & app(all_299_0, v0) = v1 & $i(v1) & $i(v0)) % 81.56/11.76 | | | | % 81.56/11.76 | | | | ALPHA: (51) implies: % 81.56/11.76 | | | | (52) $i(all_299_1) % 81.56/11.76 | | | | (53) ssItem(all_299_1) = 0 % 81.56/11.76 | | | | (54) cons(all_299_1, nil) = all_299_0 % 81.56/11.76 | | | | (55) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_93_0) & ssList(v0) = % 81.56/11.76 | | | | 0 & app(v0, all_299_0) = all_97_0 & app(all_299_0, v0) = v1 & % 81.56/11.76 | | | | $i(v1) & $i(v0)) % 81.56/11.76 | | | | % 81.56/11.76 | | | | DELTA: instantiating (55) with fresh symbols all_301_0, all_301_1 gives: % 81.56/11.76 | | | | (56) ~ (all_301_0 = all_93_0) & ssList(all_301_1) = 0 & % 81.56/11.76 | | | | app(all_301_1, all_299_0) = all_97_0 & app(all_299_0, all_301_1) % 81.56/11.76 | | | | = all_301_0 & $i(all_301_0) & $i(all_301_1) % 81.56/11.76 | | | | % 81.56/11.76 | | | | ALPHA: (56) implies: % 81.56/11.76 | | | | (57) ~ (all_301_0 = all_93_0) % 81.56/11.76 | | | | (58) $i(all_301_1) % 81.56/11.76 | | | | (59) app(all_299_0, all_301_1) = all_301_0 % 81.56/11.76 | | | | (60) app(all_301_1, all_299_0) = all_97_0 % 81.56/11.76 | | | | (61) ssList(all_301_1) = 0 % 81.56/11.76 | | | | % 81.56/11.76 | | | | BETA: splitting (30) gives: % 81.56/11.76 | | | | % 81.56/11.76 | | | | Case 1: % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | (62) all_97_0 = nil % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | REDUCE: (49), (62) imply: % 81.56/11.76 | | | | | (63) $false % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | CLOSE: (63) is inconsistent. % 81.56/11.76 | | | | | % 81.56/11.76 | | | | Case 2: % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | (64) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 81.56/11.76 | | | | | (cons(v1, v0) = all_97_0 & ssItem(v1) = 0 & $i(v1))) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | DELTA: instantiating (64) with fresh symbol all_306_0 gives: % 81.56/11.76 | | | | | (65) ssList(all_306_0) = 0 & $i(all_306_0) & ? [v0: $i] : % 81.56/11.76 | | | | | (cons(v0, all_306_0) = all_97_0 & ssItem(v0) = 0 & $i(v0)) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | ALPHA: (65) implies: % 81.56/11.76 | | | | | (66) $i(all_306_0) % 81.56/11.76 | | | | | (67) ssList(all_306_0) = 0 % 81.56/11.76 | | | | | (68) ? [v0: $i] : (cons(v0, all_306_0) = all_97_0 & ssItem(v0) = 0 % 81.56/11.76 | | | | | & $i(v0)) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | DELTA: instantiating (68) with fresh symbol all_308_0 gives: % 81.56/11.76 | | | | | (69) cons(all_308_0, all_306_0) = all_97_0 & ssItem(all_308_0) = 0 % 81.56/11.76 | | | | | & $i(all_308_0) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | ALPHA: (69) implies: % 81.56/11.76 | | | | | (70) $i(all_308_0) % 81.56/11.76 | | | | | (71) ssItem(all_308_0) = 0 % 81.56/11.76 | | | | | (72) cons(all_308_0, all_306_0) = all_97_0 % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | GROUND_INST: instantiating (48) with all_299_1, simplifying with (52), % 81.56/11.76 | | | | | (53) gives: % 81.56/11.76 | | | | | (73) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : % 81.56/11.76 | | | | | ( ~ (ssList(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] % 81.56/11.76 | | | | | : ! [v4: $i] : ( ~ (cons(all_299_1, v2) = v3) | ~ % 81.56/11.76 | | | | | (app(v1, v3) = v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 % 81.56/11.76 | | | | | = 0) & ssList(v2) = v5) | ! [v5: $i] : ! [v6: $i] % 81.56/11.76 | | | | | : ( ~ (v0 = all_299_1) | ~ (cons(all_299_1, v5) = v6) | % 81.56/11.76 | | | | | ~ (app(v4, v6) = nil) | ~ $i(v5) | ? [v7: int] : ( % 81.56/11.76 | | | | | ~ (v7 = 0) & ssList(v5) = v7))))) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | GROUND_INST: instantiating (27) with all_299_1, all_299_0, simplifying % 81.56/11.76 | | | | | with (52), (54) gives: % 81.56/11.76 | | | | | (74) ? [v0: any] : ? [v1: $i] : (tl(all_299_0) = v1 & % 81.56/11.76 | | | | | ssItem(all_299_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | GROUND_INST: instantiating (28) with all_299_1, all_299_0, simplifying % 81.56/11.76 | | | | | with (52), (54) gives: % 81.56/11.76 | | | | | (75) ? [v0: any] : ? [v1: $i] : (hd(all_299_0) = v1 & % 81.56/11.76 | | | | | ssItem(all_299_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 81.56/11.76 | | | | | all_299_1)) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | GROUND_INST: instantiating (10) with all_299_1, all_299_0, simplifying % 81.56/11.76 | | | | | with (52), (54) gives: % 81.56/11.76 | | | | | (76) ? [v0: any] : ? [v1: any] : (equalelemsP(all_299_0) = v1 & % 81.56/11.76 | | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | GROUND_INST: instantiating (8) with all_299_1, all_299_0, simplifying % 81.56/11.76 | | | | | with (52), (54) gives: % 81.56/11.76 | | | | | (77) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_299_0) = v1 % 81.56/11.76 | | | | | & ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | GROUND_INST: instantiating (7) with all_299_1, all_299_0, simplifying % 81.56/11.76 | | | | | with (52), (54) gives: % 81.56/11.76 | | | | | (78) ? [v0: any] : ? [v1: any] : (strictorderedP(all_299_0) = v1 % 81.56/11.76 | | | | | & ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 81.56/11.76 | | | | | % 81.56/11.76 | | | | | GROUND_INST: instantiating (6) with all_299_1, all_299_0, simplifying % 81.56/11.76 | | | | | with (52), (54) gives: % 81.56/11.77 | | | | | (79) ? [v0: any] : ? [v1: any] : (totalorderedP(all_299_0) = v1 & % 81.56/11.77 | | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (5) with all_299_1, all_299_0, simplifying % 81.56/11.77 | | | | | with (52), (54) gives: % 81.56/11.77 | | | | | (80) ? [v0: any] : ? [v1: any] : (strictorderP(all_299_0) = v1 & % 81.56/11.77 | | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (4) with all_299_1, all_299_0, simplifying % 81.56/11.77 | | | | | with (52), (54) gives: % 81.56/11.77 | | | | | (81) ? [v0: any] : ? [v1: any] : (totalorderP(all_299_0) = v1 & % 81.56/11.77 | | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (3) with all_299_1, all_299_0, simplifying % 81.56/11.77 | | | | | with (52), (54) gives: % 81.56/11.77 | | | | | (82) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_299_0) = v1 & % 81.56/11.77 | | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (29) with all_299_1, all_299_0, simplifying % 81.56/11.77 | | | | | with (52), (54) gives: % 81.56/11.77 | | | | | (83) ? [v0: any] : ? [v1: any] : (ssList(all_299_0) = v1 & % 81.56/11.77 | | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (26) with all_299_1, all_299_0, simplifying % 81.56/11.77 | | | | | with (52), (54) gives: % 81.56/11.77 | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_299_1) = v0) | ! % 81.56/11.77 | | | | | [v0: $i] : ! [v1: int] : (v1 = all_93_0 | ~ (app(all_299_0, % 81.56/11.77 | | | | | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 81.56/11.77 | | | | | (ssList(v0) = v2 & app(v0, all_299_0) = v3 & $i(v3) & ( ~ % 81.56/11.77 | | | | | (v3 = all_97_0) | ~ (v2 = 0)))) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (11) with all_301_1, simplifying with (58), % 81.56/11.77 | | | | | (61) gives: % 81.56/11.77 | | | | | (85) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, nil) = % 81.56/11.77 | | | | | v1) | ~ (app(v1, all_301_1) = v2) | ~ $i(v0) | ? [v3: % 81.56/11.77 | | | | | any] : ? [v4: $i] : (cons(v0, all_301_1) = v4 & % 81.56/11.77 | | | | | ssItem(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (ax25) with all_306_0, simplifying with % 81.56/11.77 | | | | | (66), (67) gives: % 81.56/11.77 | | | | | (86) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, all_306_0) = v1) | % 81.56/11.77 | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (tl(v1) = v3 & % 81.56/11.77 | | | | | ssItem(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 81.56/11.77 | | | | | all_306_0))) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (85) with all_299_1, all_299_0, all_301_0, % 81.56/11.77 | | | | | simplifying with (52), (54), (59) gives: % 81.56/11.77 | | | | | (87) ? [v0: any] : ? [v1: $i] : (cons(all_299_1, all_301_1) = v1 % 81.56/11.77 | | | | | & ssItem(all_299_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 81.56/11.77 | | | | | all_301_0)) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (86) with all_308_0, all_97_0, simplifying % 81.56/11.77 | | | | | with (70), (72) gives: % 81.56/11.77 | | | | | (88) ? [v0: any] : ? [v1: $i] : (tl(all_97_0) = v1 & % 81.56/11.77 | | | | | ssItem(all_308_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 81.56/11.77 | | | | | all_306_0)) % 81.56/11.77 | | | | | % 81.56/11.77 | | | | | GROUND_INST: instantiating (73) with all_299_1, simplifying with (52), % 81.56/11.77 | | | | | (53) gives: % 82.05/11.77 | | | | | (89) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : % 82.05/11.77 | | | | | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(all_299_1, v1) = v2) | % 82.05/11.77 | | | | | ~ (app(v0, v2) = v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 % 82.05/11.77 | | | | | = 0) & ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : % 82.05/11.77 | | | | | ( ~ (cons(all_299_1, v4) = v5) | ~ (app(v3, v5) = nil) | % 82.05/11.77 | | | | | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v4) = % 82.05/11.77 | | | | | v6)))) % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | GROUND_INST: instantiating (89) with all_301_1, simplifying with (58), % 82.05/11.77 | | | | | (61) gives: % 82.05/11.77 | | | | | (90) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(all_299_1, % 82.05/11.77 | | | | | v0) = v1) | ~ (app(all_301_1, v1) = v2) | ~ $i(v0) | % 82.05/11.77 | | | | | ? [v3: int] : ( ~ (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] % 82.05/11.77 | | | | | : ! [v4: $i] : ( ~ (cons(all_299_1, v3) = v4) | ~ (app(v2, % 82.05/11.77 | | | | | v4) = nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & % 82.05/11.77 | | | | | ssList(v3) = v5))) % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | GROUND_INST: instantiating (90) with nil, all_299_0, all_97_0, % 82.05/11.77 | | | | | simplifying with (13), (54), (60) gives: % 82.05/11.77 | | | | | (91) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] % 82.05/11.77 | | | | | : ! [v1: $i] : ( ~ (cons(all_299_1, v0) = v1) | ~ % 82.05/11.77 | | | | | (app(all_97_0, v1) = nil) | ~ $i(v0) | ? [v2: int] : ( ~ % 82.05/11.77 | | | | | (v2 = 0) & ssList(v0) = v2)) % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | DELTA: instantiating (83) with fresh symbols all_838_0, all_838_1 % 82.05/11.77 | | | | | gives: % 82.05/11.77 | | | | | (92) ssList(all_299_0) = all_838_0 & ssItem(all_299_1) = all_838_1 % 82.05/11.77 | | | | | & ( ~ (all_838_1 = 0) | all_838_0 = 0) % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | ALPHA: (92) implies: % 82.05/11.77 | | | | | (93) ssItem(all_299_1) = all_838_1 % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | DELTA: instantiating (82) with fresh symbols all_840_0, all_840_1 % 82.05/11.77 | | | | | gives: % 82.05/11.77 | | | | | (94) cyclefreeP(all_299_0) = all_840_0 & ssItem(all_299_1) = % 82.05/11.77 | | | | | all_840_1 & ( ~ (all_840_1 = 0) | all_840_0 = 0) % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | ALPHA: (94) implies: % 82.05/11.77 | | | | | (95) ssItem(all_299_1) = all_840_1 % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | DELTA: instantiating (79) with fresh symbols all_842_0, all_842_1 % 82.05/11.77 | | | | | gives: % 82.05/11.77 | | | | | (96) totalorderedP(all_299_0) = all_842_0 & ssItem(all_299_1) = % 82.05/11.77 | | | | | all_842_1 & ( ~ (all_842_1 = 0) | all_842_0 = 0) % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | ALPHA: (96) implies: % 82.05/11.77 | | | | | (97) ssItem(all_299_1) = all_842_1 % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | DELTA: instantiating (78) with fresh symbols all_844_0, all_844_1 % 82.05/11.77 | | | | | gives: % 82.05/11.77 | | | | | (98) strictorderedP(all_299_0) = all_844_0 & ssItem(all_299_1) = % 82.05/11.77 | | | | | all_844_1 & ( ~ (all_844_1 = 0) | all_844_0 = 0) % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | ALPHA: (98) implies: % 82.05/11.77 | | | | | (99) ssItem(all_299_1) = all_844_1 % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | DELTA: instantiating (77) with fresh symbols all_846_0, all_846_1 % 82.05/11.77 | | | | | gives: % 82.05/11.77 | | | | | (100) duplicatefreeP(all_299_0) = all_846_0 & ssItem(all_299_1) = % 82.05/11.77 | | | | | all_846_1 & ( ~ (all_846_1 = 0) | all_846_0 = 0) % 82.05/11.77 | | | | | % 82.05/11.77 | | | | | ALPHA: (100) implies: % 82.05/11.78 | | | | | (101) ssItem(all_299_1) = all_846_1 % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | DELTA: instantiating (76) with fresh symbols all_848_0, all_848_1 % 82.05/11.78 | | | | | gives: % 82.05/11.78 | | | | | (102) equalelemsP(all_299_0) = all_848_0 & ssItem(all_299_1) = % 82.05/11.78 | | | | | all_848_1 & ( ~ (all_848_1 = 0) | all_848_0 = 0) % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | ALPHA: (102) implies: % 82.05/11.78 | | | | | (103) ssItem(all_299_1) = all_848_1 % 82.05/11.78 | | | | | (104) ~ (all_848_1 = 0) | all_848_0 = 0 % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | DELTA: instantiating (81) with fresh symbols all_850_0, all_850_1 % 82.05/11.78 | | | | | gives: % 82.05/11.78 | | | | | (105) totalorderP(all_299_0) = all_850_0 & ssItem(all_299_1) = % 82.05/11.78 | | | | | all_850_1 & ( ~ (all_850_1 = 0) | all_850_0 = 0) % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | ALPHA: (105) implies: % 82.05/11.78 | | | | | (106) ssItem(all_299_1) = all_850_1 % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | DELTA: instantiating (80) with fresh symbols all_852_0, all_852_1 % 82.05/11.78 | | | | | gives: % 82.05/11.78 | | | | | (107) strictorderP(all_299_0) = all_852_0 & ssItem(all_299_1) = % 82.05/11.78 | | | | | all_852_1 & ( ~ (all_852_1 = 0) | all_852_0 = 0) % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | ALPHA: (107) implies: % 82.05/11.78 | | | | | (108) ssItem(all_299_1) = all_852_1 % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | DELTA: instantiating (75) with fresh symbols all_854_0, all_854_1 % 82.05/11.78 | | | | | gives: % 82.05/11.78 | | | | | (109) hd(all_299_0) = all_854_0 & ssItem(all_299_1) = all_854_1 & % 82.05/11.78 | | | | | $i(all_854_0) & ( ~ (all_854_1 = 0) | all_854_0 = all_299_1) % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | ALPHA: (109) implies: % 82.05/11.78 | | | | | (110) ssItem(all_299_1) = all_854_1 % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | DELTA: instantiating (74) with fresh symbols all_856_0, all_856_1 % 82.05/11.78 | | | | | gives: % 82.05/11.78 | | | | | (111) tl(all_299_0) = all_856_0 & ssItem(all_299_1) = all_856_1 & % 82.05/11.78 | | | | | $i(all_856_0) & ( ~ (all_856_1 = 0) | all_856_0 = nil) % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | ALPHA: (111) implies: % 82.05/11.78 | | | | | (112) ssItem(all_299_1) = all_856_1 % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | DELTA: instantiating (87) with fresh symbols all_858_0, all_858_1 % 82.05/11.78 | | | | | gives: % 82.05/11.78 | | | | | (113) cons(all_299_1, all_301_1) = all_858_0 & ssItem(all_299_1) = % 82.05/11.78 | | | | | all_858_1 & $i(all_858_0) & ( ~ (all_858_1 = 0) | all_858_0 = % 82.05/11.78 | | | | | all_301_0) % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | ALPHA: (113) implies: % 82.05/11.78 | | | | | (114) ssItem(all_299_1) = all_858_1 % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | DELTA: instantiating (88) with fresh symbols all_862_0, all_862_1 % 82.05/11.78 | | | | | gives: % 82.05/11.78 | | | | | (115) tl(all_97_0) = all_862_0 & ssItem(all_308_0) = all_862_1 & % 82.05/11.78 | | | | | $i(all_862_0) & ( ~ (all_862_1 = 0) | all_862_0 = all_306_0) % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | ALPHA: (115) implies: % 82.05/11.78 | | | | | (116) ssItem(all_308_0) = all_862_1 % 82.05/11.78 | | | | | (117) ~ (all_862_1 = 0) | all_862_0 = all_306_0 % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | BETA: splitting (91) gives: % 82.05/11.78 | | | | | % 82.05/11.78 | | | | | Case 1: % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | (118) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | DELTA: instantiating (118) with fresh symbol all_902_0 gives: % 82.05/11.78 | | | | | | (119) ~ (all_902_0 = 0) & ssList(nil) = all_902_0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | ALPHA: (119) implies: % 82.05/11.78 | | | | | | (120) ~ (all_902_0 = 0) % 82.05/11.78 | | | | | | (121) ssList(nil) = all_902_0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | DELTA: instantiating (118) with fresh symbol all_920_0 gives: % 82.05/11.78 | | | | | | (122) ~ (all_920_0 = 0) & ssList(nil) = all_920_0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | ALPHA: (122) implies: % 82.05/11.78 | | | | | | (123) ssList(nil) = all_920_0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (16) with 0, all_920_0, nil, simplifying % 82.05/11.78 | | | | | | with (1), (123) gives: % 82.05/11.78 | | | | | | (124) all_920_0 = 0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (16) with all_902_0, all_920_0, nil, % 82.05/11.78 | | | | | | simplifying with (121), (123) gives: % 82.05/11.78 | | | | | | (125) all_920_0 = all_902_0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (124), (125) imply: % 82.05/11.78 | | | | | | (126) all_902_0 = 0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | REDUCE: (120), (126) imply: % 82.05/11.78 | | | | | | (127) $false % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | CLOSE: (127) is inconsistent. % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | Case 2: % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_842_1, all_844_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (97), (99) gives: % 82.05/11.78 | | | | | | (128) all_844_1 = all_842_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_840_1, all_844_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (95), (99) gives: % 82.05/11.78 | | | | | | (129) all_844_1 = all_840_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_842_1, all_846_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (97), (101) gives: % 82.05/11.78 | | | | | | (130) all_846_1 = all_842_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_850_1, all_854_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (106), (110) gives: % 82.05/11.78 | | | | | | (131) all_854_1 = all_850_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_848_1, all_854_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (103), (110) gives: % 82.05/11.78 | | | | | | (132) all_854_1 = all_848_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_846_1, all_854_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (101), (110) gives: % 82.05/11.78 | | | | | | (133) all_854_1 = all_846_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_850_1, all_856_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (106), (112) gives: % 82.05/11.78 | | | | | | (134) all_856_1 = all_850_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_838_1, all_856_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (93), (112) gives: % 82.05/11.78 | | | | | | (135) all_856_1 = all_838_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with 0, all_858_1, all_299_1, % 82.05/11.78 | | | | | | simplifying with (53), (114) gives: % 82.05/11.78 | | | | | | (136) all_858_1 = 0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_852_1, all_858_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (108), (114) gives: % 82.05/11.78 | | | | | | (137) all_858_1 = all_852_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with all_844_1, all_858_1, % 82.05/11.78 | | | | | | all_299_1, simplifying with (99), (114) gives: % 82.05/11.78 | | | | | | (138) all_858_1 = all_844_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | GROUND_INST: instantiating (15) with 0, all_862_1, all_308_0, % 82.05/11.78 | | | | | | simplifying with (71), (116) gives: % 82.05/11.78 | | | | | | (139) all_862_1 = 0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (137), (138) imply: % 82.05/11.78 | | | | | | (140) all_852_1 = all_844_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (136), (137) imply: % 82.05/11.78 | | | | | | (141) all_852_1 = 0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (134), (135) imply: % 82.05/11.78 | | | | | | (142) all_850_1 = all_838_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | SIMP: (142) implies: % 82.05/11.78 | | | | | | (143) all_850_1 = all_838_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (131), (132) imply: % 82.05/11.78 | | | | | | (144) all_850_1 = all_848_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | SIMP: (144) implies: % 82.05/11.78 | | | | | | (145) all_850_1 = all_848_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (132), (133) imply: % 82.05/11.78 | | | | | | (146) all_848_1 = all_846_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (140), (141) imply: % 82.05/11.78 | | | | | | (147) all_844_1 = 0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | SIMP: (147) implies: % 82.05/11.78 | | | | | | (148) all_844_1 = 0 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (143), (145) imply: % 82.05/11.78 | | | | | | (149) all_848_1 = all_838_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | SIMP: (149) implies: % 82.05/11.78 | | | | | | (150) all_848_1 = all_838_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | COMBINE_EQS: (146), (150) imply: % 82.05/11.78 | | | | | | (151) all_846_1 = all_838_1 % 82.05/11.78 | | | | | | % 82.05/11.78 | | | | | | SIMP: (151) implies: % 82.05/11.78 | | | | | | (152) all_846_1 = all_838_1 % 82.05/11.78 | | | | | | % 82.05/11.79 | | | | | | COMBINE_EQS: (130), (152) imply: % 82.05/11.79 | | | | | | (153) all_842_1 = all_838_1 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | SIMP: (153) implies: % 82.05/11.79 | | | | | | (154) all_842_1 = all_838_1 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | COMBINE_EQS: (128), (129) imply: % 82.05/11.79 | | | | | | (155) all_842_1 = all_840_1 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | SIMP: (155) implies: % 82.05/11.79 | | | | | | (156) all_842_1 = all_840_1 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | COMBINE_EQS: (129), (148) imply: % 82.05/11.79 | | | | | | (157) all_840_1 = 0 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | COMBINE_EQS: (154), (156) imply: % 82.05/11.79 | | | | | | (158) all_840_1 = all_838_1 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | SIMP: (158) implies: % 82.05/11.79 | | | | | | (159) all_840_1 = all_838_1 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | COMBINE_EQS: (157), (159) imply: % 82.05/11.79 | | | | | | (160) all_838_1 = 0 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | COMBINE_EQS: (150), (160) imply: % 82.05/11.79 | | | | | | (161) all_848_1 = 0 % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | BETA: splitting (84) gives: % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | | Case 1: % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | (162) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_299_1) = v0) % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | DELTA: instantiating (162) with fresh symbol all_925_0 gives: % 82.05/11.79 | | | | | | | (163) ~ (all_925_0 = 0) & ssItem(all_299_1) = all_925_0 % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | ALPHA: (163) implies: % 82.05/11.79 | | | | | | | (164) ~ (all_925_0 = 0) % 82.05/11.79 | | | | | | | (165) ssItem(all_299_1) = all_925_0 % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | BETA: splitting (104) gives: % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | Case 1: % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | (166) ~ (all_848_1 = 0) % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | REDUCE: (161), (166) imply: % 82.05/11.79 | | | | | | | | (167) $false % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | CLOSE: (167) is inconsistent. % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | Case 2: % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | DELTA: instantiating (162) with fresh symbol all_935_0 gives: % 82.05/11.79 | | | | | | | | (168) ~ (all_935_0 = 0) & ssItem(all_299_1) = all_935_0 % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | ALPHA: (168) implies: % 82.05/11.79 | | | | | | | | (169) ssItem(all_299_1) = all_935_0 % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | DELTA: instantiating (162) with fresh symbol all_951_0 gives: % 82.05/11.79 | | | | | | | | (170) ~ (all_951_0 = 0) & ssItem(all_299_1) = all_951_0 % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | ALPHA: (170) implies: % 82.05/11.79 | | | | | | | | (171) ssItem(all_299_1) = all_951_0 % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | BETA: splitting (117) gives: % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | Case 1: % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | (172) ~ (all_862_1 = 0) % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | REDUCE: (139), (172) imply: % 82.05/11.79 | | | | | | | | | (173) $false % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | CLOSE: (173) is inconsistent. % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | Case 2: % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | DELTA: instantiating (162) with fresh symbol all_960_0 gives: % 82.05/11.79 | | | | | | | | | (174) ~ (all_960_0 = 0) & ssItem(all_299_1) = all_960_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | ALPHA: (174) implies: % 82.05/11.79 | | | | | | | | | (175) ssItem(all_299_1) = all_960_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_935_0, all_299_1, % 82.05/11.79 | | | | | | | | | simplifying with (53), (169) gives: % 82.05/11.79 | | | | | | | | | (176) all_935_0 = 0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | GROUND_INST: instantiating (15) with all_951_0, all_960_0, % 82.05/11.79 | | | | | | | | | all_299_1, simplifying with (171), (175) gives: % 82.05/11.79 | | | | | | | | | (177) all_960_0 = all_951_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | GROUND_INST: instantiating (15) with all_935_0, all_960_0, % 82.05/11.79 | | | | | | | | | all_299_1, simplifying with (169), (175) gives: % 82.05/11.79 | | | | | | | | | (178) all_960_0 = all_935_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | GROUND_INST: instantiating (15) with all_925_0, all_960_0, % 82.05/11.79 | | | | | | | | | all_299_1, simplifying with (165), (175) gives: % 82.05/11.79 | | | | | | | | | (179) all_960_0 = all_925_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | COMBINE_EQS: (177), (179) imply: % 82.05/11.79 | | | | | | | | | (180) all_951_0 = all_925_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | COMBINE_EQS: (177), (178) imply: % 82.05/11.79 | | | | | | | | | (181) all_951_0 = all_935_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | COMBINE_EQS: (180), (181) imply: % 82.05/11.79 | | | | | | | | | (182) all_935_0 = all_925_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | SIMP: (182) implies: % 82.05/11.79 | | | | | | | | | (183) all_935_0 = all_925_0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | COMBINE_EQS: (176), (183) imply: % 82.05/11.79 | | | | | | | | | (184) all_925_0 = 0 % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | REDUCE: (164), (184) imply: % 82.05/11.79 | | | | | | | | | (185) $false % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | CLOSE: (185) is inconsistent. % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | End of split % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | End of split % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | Case 2: % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | (186) ! [v0: $i] : ! [v1: int] : (v1 = all_93_0 | ~ % 82.05/11.79 | | | | | | | (app(all_299_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 82.05/11.79 | | | | | | | ? [v3: $i] : (ssList(v0) = v2 & app(v0, all_299_0) = v3 % 82.05/11.79 | | | | | | | & $i(v3) & ( ~ (v3 = all_97_0) | ~ (v2 = 0)))) % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | GROUND_INST: instantiating (186) with all_301_1, all_301_0, % 82.05/11.79 | | | | | | | simplifying with (58), (59) gives: % 82.05/11.79 | | | | | | | (187) all_301_0 = all_93_0 | ? [v0: any] : ? [v1: $i] : % 82.05/11.79 | | | | | | | (ssList(all_301_1) = v0 & app(all_301_1, all_299_0) = v1 % 82.05/11.79 | | | | | | | & $i(v1) & ( ~ (v1 = all_97_0) | ~ (v0 = 0))) % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | BETA: splitting (187) gives: % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | | Case 1: % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | (188) all_301_0 = all_93_0 % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | REDUCE: (57), (188) imply: % 82.05/11.79 | | | | | | | | (189) $false % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | CLOSE: (189) is inconsistent. % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | Case 2: % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | (190) ? [v0: any] : ? [v1: $i] : (ssList(all_301_1) = v0 & % 82.05/11.79 | | | | | | | | app(all_301_1, all_299_0) = v1 & $i(v1) & ( ~ (v1 = % 82.05/11.79 | | | | | | | | all_97_0) | ~ (v0 = 0))) % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | DELTA: instantiating (190) with fresh symbols all_1013_0, % 82.05/11.79 | | | | | | | | all_1013_1 gives: % 82.05/11.79 | | | | | | | | (191) ssList(all_301_1) = all_1013_1 & app(all_301_1, % 82.05/11.79 | | | | | | | | all_299_0) = all_1013_0 & $i(all_1013_0) & ( ~ % 82.05/11.79 | | | | | | | | (all_1013_0 = all_97_0) | ~ (all_1013_1 = 0)) % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | ALPHA: (191) implies: % 82.05/11.79 | | | | | | | | (192) app(all_301_1, all_299_0) = all_1013_0 % 82.05/11.79 | | | | | | | | (193) ssList(all_301_1) = all_1013_1 % 82.05/11.79 | | | | | | | | (194) ~ (all_1013_0 = all_97_0) | ~ (all_1013_1 = 0) % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | GROUND_INST: instantiating (17) with all_97_0, all_1013_0, % 82.05/11.79 | | | | | | | | all_299_0, all_301_1, simplifying with (60), (192) % 82.05/11.79 | | | | | | | | gives: % 82.05/11.79 | | | | | | | | (195) all_1013_0 = all_97_0 % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | GROUND_INST: instantiating (16) with 0, all_1013_1, all_301_1, % 82.05/11.79 | | | | | | | | simplifying with (61), (193) gives: % 82.05/11.79 | | | | | | | | (196) all_1013_1 = 0 % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | BETA: splitting (194) gives: % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | | Case 1: % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | (197) ~ (all_1013_1 = 0) % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | REDUCE: (196), (197) imply: % 82.05/11.79 | | | | | | | | | (198) $false % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | CLOSE: (198) is inconsistent. % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | Case 2: % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | (199) ~ (all_1013_0 = all_97_0) % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | REDUCE: (195), (199) imply: % 82.05/11.79 | | | | | | | | | (200) $false % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | | CLOSE: (200) is inconsistent. % 82.05/11.79 | | | | | | | | | % 82.05/11.79 | | | | | | | | End of split % 82.05/11.79 | | | | | | | | % 82.05/11.79 | | | | | | | End of split % 82.05/11.79 | | | | | | | % 82.05/11.79 | | | | | | End of split % 82.05/11.79 | | | | | | % 82.05/11.79 | | | | | End of split % 82.05/11.79 | | | | | % 82.05/11.79 | | | | End of split % 82.05/11.79 | | | | % 82.05/11.79 | | | Case 2: % 82.05/11.79 | | | | % 82.05/11.79 | | | | (201) all_97_0 = nil & ~ (all_93_0 = nil) % 82.05/11.79 | | | | % 82.05/11.79 | | | | ALPHA: (201) implies: % 82.05/11.79 | | | | (202) all_97_0 = nil % 82.05/11.79 | | | | % 82.05/11.79 | | | | REDUCE: (49), (202) imply: % 82.05/11.79 | | | | (203) $false % 82.05/11.79 | | | | % 82.05/11.80 | | | | CLOSE: (203) is inconsistent. % 82.05/11.80 | | | | % 82.05/11.80 | | | End of split % 82.05/11.80 | | | % 82.05/11.80 | | Case 2: % 82.05/11.80 | | | % 82.05/11.80 | | | (204) all_93_0 = nil % 82.05/11.80 | | | (205) all_97_0 = nil % 82.05/11.80 | | | % 82.05/11.80 | | | BETA: splitting (24) gives: % 82.05/11.80 | | | % 82.05/11.80 | | | Case 1: % 82.05/11.80 | | | | % 82.05/11.80 | | | | (206) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = % 82.05/11.80 | | | | 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: any] : ( ~ (v3 = % 82.05/11.80 | | | | all_93_0) & ssList(v2) = 0 & app(v2, v1) = all_97_0 & % 82.05/11.80 | | | | app(v1, v2) = v3 & $i(v3) & $i(v2))) % 82.05/11.80 | | | | % 82.05/11.80 | | | | DELTA: instantiating (206) with fresh symbols all_299_0, all_299_1 % 82.05/11.80 | | | | gives: % 82.17/11.80 | | | | (207) cons(all_299_1, nil) = all_299_0 & ssItem(all_299_1) = 0 & % 82.17/11.80 | | | | $i(all_299_0) & $i(all_299_1) & ? [v0: $i] : ? [v1: any] : ( % 82.17/11.80 | | | | ~ (v1 = all_93_0) & ssList(v0) = 0 & app(v0, all_299_0) = % 82.17/11.80 | | | | all_97_0 & app(all_299_0, v0) = v1 & $i(v1) & $i(v0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | ALPHA: (207) implies: % 82.17/11.80 | | | | (208) $i(all_299_1) % 82.17/11.80 | | | | (209) $i(all_299_0) % 82.17/11.80 | | | | (210) ssItem(all_299_1) = 0 % 82.17/11.80 | | | | (211) cons(all_299_1, nil) = all_299_0 % 82.17/11.80 | | | | (212) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_93_0) & ssList(v0) = % 82.17/11.80 | | | | 0 & app(v0, all_299_0) = all_97_0 & app(all_299_0, v0) = v1 & % 82.17/11.80 | | | | $i(v1) & $i(v0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | DELTA: instantiating (212) with fresh symbols all_301_0, all_301_1 % 82.17/11.80 | | | | gives: % 82.17/11.80 | | | | (213) ~ (all_301_0 = all_93_0) & ssList(all_301_1) = 0 & % 82.17/11.80 | | | | app(all_301_1, all_299_0) = all_97_0 & app(all_299_0, % 82.17/11.80 | | | | all_301_1) = all_301_0 & $i(all_301_0) & $i(all_301_1) % 82.17/11.80 | | | | % 82.17/11.80 | | | | ALPHA: (213) implies: % 82.17/11.80 | | | | (214) ~ (all_301_0 = all_93_0) % 82.17/11.80 | | | | (215) $i(all_301_1) % 82.17/11.80 | | | | (216) app(all_299_0, all_301_1) = all_301_0 % 82.17/11.80 | | | | (217) app(all_301_1, all_299_0) = all_97_0 % 82.17/11.80 | | | | (218) ssList(all_301_1) = 0 % 82.17/11.80 | | | | % 82.17/11.80 | | | | REDUCE: (204), (214) imply: % 82.17/11.80 | | | | (219) ~ (all_301_0 = nil) % 82.17/11.80 | | | | % 82.17/11.80 | | | | REDUCE: (205), (217) imply: % 82.17/11.80 | | | | (220) app(all_301_1, all_299_0) = nil % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (27) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (221) ? [v0: any] : ? [v1: $i] : (tl(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (28) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (222) ? [v0: any] : ? [v1: $i] : (hd(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 82.17/11.80 | | | | all_299_1)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (10) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (223) ? [v0: any] : ? [v1: any] : (equalelemsP(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (8) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (224) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (7) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (225) ? [v0: any] : ? [v1: any] : (strictorderedP(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (6) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (226) ? [v0: any] : ? [v1: any] : (totalorderedP(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (5) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (227) ? [v0: any] : ? [v1: any] : (strictorderP(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (4) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (228) ? [v0: any] : ? [v1: any] : (totalorderP(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (3) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (229) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (29) with all_299_1, all_299_0, simplifying % 82.17/11.80 | | | | with (208), (211) gives: % 82.17/11.80 | | | | (230) ? [v0: any] : ? [v1: any] : (ssList(all_299_0) = v1 & % 82.17/11.80 | | | | ssItem(all_299_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (11) with all_301_1, simplifying with (215), % 82.17/11.80 | | | | (218) gives: % 82.17/11.80 | | | | (231) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, nil) = % 82.17/11.80 | | | | v1) | ~ (app(v1, all_301_1) = v2) | ~ $i(v0) | ? [v3: % 82.17/11.80 | | | | any] : ? [v4: $i] : (cons(v0, all_301_1) = v4 & ssItem(v0) % 82.17/11.80 | | | | = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (ax26) with all_301_1, simplifying with % 82.17/11.80 | | | | (215), (218) gives: % 82.17/11.80 | | | | (232) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_301_1, v0) = v1) | ~ % 82.17/11.80 | | | | $i(v0) | ? [v2: any] : ? [v3: any] : (ssList(v1) = v3 & % 82.17/11.80 | | | | ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 82.17/11.80 | | | | % 82.17/11.80 | | | | GROUND_INST: instantiating (12) with all_301_1, simplifying with (215), % 82.17/11.80 | | | | (218) gives: % 82.17/11.81 | | | | (233) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_301_1, v0) = v1) | ~ % 82.17/11.81 | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( % 82.17/11.81 | | | | ~ (v1 = nil) | (v0 = nil & all_301_1 = nil)) & ( ~ (v0 = % 82.17/11.81 | | | | nil) | ~ (all_301_1 = nil) | v1 = nil))) % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (231) with all_299_1, all_299_0, all_301_0, % 82.17/11.81 | | | | simplifying with (208), (211), (216) gives: % 82.17/11.81 | | | | (234) ? [v0: any] : ? [v1: $i] : (cons(all_299_1, all_301_1) = v1 & % 82.17/11.81 | | | | ssItem(all_299_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 82.17/11.81 | | | | all_301_0)) % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (233) with all_299_0, nil, simplifying with % 82.17/11.81 | | | | (209), (220) gives: % 82.17/11.81 | | | | (235) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_299_0) = v0) | % 82.17/11.81 | | | | (all_301_1 = nil & all_299_0 = nil) % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (232) with all_299_0, nil, simplifying with % 82.17/11.81 | | | | (209), (220) gives: % 82.17/11.81 | | | | (236) ? [v0: any] : ? [v1: any] : (ssList(all_299_0) = v0 & % 82.17/11.81 | | | | ssList(nil) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (226) with fresh symbols all_407_0, all_407_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (237) totalorderedP(all_299_0) = all_407_0 & ssItem(all_299_1) = % 82.17/11.81 | | | | all_407_1 & ( ~ (all_407_1 = 0) | all_407_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (237) implies: % 82.17/11.81 | | | | (238) ssItem(all_299_1) = all_407_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (224) with fresh symbols all_409_0, all_409_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (239) duplicatefreeP(all_299_0) = all_409_0 & ssItem(all_299_1) = % 82.17/11.81 | | | | all_409_1 & ( ~ (all_409_1 = 0) | all_409_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (239) implies: % 82.17/11.81 | | | | (240) ssItem(all_299_1) = all_409_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (223) with fresh symbols all_411_0, all_411_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (241) equalelemsP(all_299_0) = all_411_0 & ssItem(all_299_1) = % 82.17/11.81 | | | | all_411_1 & ( ~ (all_411_1 = 0) | all_411_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (241) implies: % 82.17/11.81 | | | | (242) ssItem(all_299_1) = all_411_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (225) with fresh symbols all_413_0, all_413_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (243) strictorderedP(all_299_0) = all_413_0 & ssItem(all_299_1) = % 82.17/11.81 | | | | all_413_1 & ( ~ (all_413_1 = 0) | all_413_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (243) implies: % 82.17/11.81 | | | | (244) ssItem(all_299_1) = all_413_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (230) with fresh symbols all_415_0, all_415_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (245) ssList(all_299_0) = all_415_0 & ssItem(all_299_1) = all_415_1 & % 82.17/11.81 | | | | ( ~ (all_415_1 = 0) | all_415_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (245) implies: % 82.17/11.81 | | | | (246) ssItem(all_299_1) = all_415_1 % 82.17/11.81 | | | | (247) ssList(all_299_0) = all_415_0 % 82.17/11.81 | | | | (248) ~ (all_415_1 = 0) | all_415_0 = 0 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (229) with fresh symbols all_417_0, all_417_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (249) cyclefreeP(all_299_0) = all_417_0 & ssItem(all_299_1) = % 82.17/11.81 | | | | all_417_1 & ( ~ (all_417_1 = 0) | all_417_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (249) implies: % 82.17/11.81 | | | | (250) ssItem(all_299_1) = all_417_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (228) with fresh symbols all_419_0, all_419_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (251) totalorderP(all_299_0) = all_419_0 & ssItem(all_299_1) = % 82.17/11.81 | | | | all_419_1 & ( ~ (all_419_1 = 0) | all_419_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (251) implies: % 82.17/11.81 | | | | (252) ssItem(all_299_1) = all_419_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (227) with fresh symbols all_421_0, all_421_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (253) strictorderP(all_299_0) = all_421_0 & ssItem(all_299_1) = % 82.17/11.81 | | | | all_421_1 & ( ~ (all_421_1 = 0) | all_421_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (253) implies: % 82.17/11.81 | | | | (254) ssItem(all_299_1) = all_421_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (222) with fresh symbols all_423_0, all_423_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (255) hd(all_299_0) = all_423_0 & ssItem(all_299_1) = all_423_1 & % 82.17/11.81 | | | | $i(all_423_0) & ( ~ (all_423_1 = 0) | all_423_0 = all_299_1) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (255) implies: % 82.17/11.81 | | | | (256) ssItem(all_299_1) = all_423_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (221) with fresh symbols all_425_0, all_425_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (257) tl(all_299_0) = all_425_0 & ssItem(all_299_1) = all_425_1 & % 82.17/11.81 | | | | $i(all_425_0) & ( ~ (all_425_1 = 0) | all_425_0 = nil) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (257) implies: % 82.17/11.81 | | | | (258) ssItem(all_299_1) = all_425_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (234) with fresh symbols all_427_0, all_427_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (259) cons(all_299_1, all_301_1) = all_427_0 & ssItem(all_299_1) = % 82.17/11.81 | | | | all_427_1 & $i(all_427_0) & ( ~ (all_427_1 = 0) | all_427_0 = % 82.17/11.81 | | | | all_301_0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (259) implies: % 82.17/11.81 | | | | (260) ssItem(all_299_1) = all_427_1 % 82.17/11.81 | | | | (261) cons(all_299_1, all_301_1) = all_427_0 % 82.17/11.81 | | | | (262) ~ (all_427_1 = 0) | all_427_0 = all_301_0 % 82.17/11.81 | | | | % 82.17/11.81 | | | | DELTA: instantiating (236) with fresh symbols all_429_0, all_429_1 % 82.17/11.81 | | | | gives: % 82.17/11.81 | | | | (263) ssList(all_299_0) = all_429_1 & ssList(nil) = all_429_0 & ( ~ % 82.17/11.81 | | | | (all_429_1 = 0) | all_429_0 = 0) % 82.17/11.81 | | | | % 82.17/11.81 | | | | ALPHA: (263) implies: % 82.17/11.81 | | | | (264) ssList(all_299_0) = all_429_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with 0, all_417_1, all_299_1, % 82.17/11.81 | | | | simplifying with (210), (250) gives: % 82.17/11.81 | | | | (265) all_417_1 = 0 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_415_1, all_419_1, all_299_1, % 82.17/11.81 | | | | simplifying with (246), (252) gives: % 82.17/11.81 | | | | (266) all_419_1 = all_415_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_409_1, all_419_1, all_299_1, % 82.17/11.81 | | | | simplifying with (240), (252) gives: % 82.17/11.81 | | | | (267) all_419_1 = all_409_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_415_1, all_421_1, all_299_1, % 82.17/11.81 | | | | simplifying with (246), (254) gives: % 82.17/11.81 | | | | (268) all_421_1 = all_415_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_419_1, all_423_1, all_299_1, % 82.17/11.81 | | | | simplifying with (252), (256) gives: % 82.17/11.81 | | | | (269) all_423_1 = all_419_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_411_1, all_423_1, all_299_1, % 82.17/11.81 | | | | simplifying with (242), (256) gives: % 82.17/11.81 | | | | (270) all_423_1 = all_411_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_417_1, all_425_1, all_299_1, % 82.17/11.81 | | | | simplifying with (250), (258) gives: % 82.17/11.81 | | | | (271) all_425_1 = all_417_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_413_1, all_425_1, all_299_1, % 82.17/11.81 | | | | simplifying with (244), (258) gives: % 82.17/11.81 | | | | (272) all_425_1 = all_413_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_409_1, all_425_1, all_299_1, % 82.17/11.81 | | | | simplifying with (240), (258) gives: % 82.17/11.81 | | | | (273) all_425_1 = all_409_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_421_1, all_427_1, all_299_1, % 82.17/11.81 | | | | simplifying with (254), (260) gives: % 82.17/11.81 | | | | (274) all_427_1 = all_421_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (15) with all_407_1, all_427_1, all_299_1, % 82.17/11.81 | | | | simplifying with (238), (260) gives: % 82.17/11.81 | | | | (275) all_427_1 = all_407_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | GROUND_INST: instantiating (16) with all_415_0, all_429_1, all_299_0, % 82.17/11.81 | | | | simplifying with (247), (264) gives: % 82.17/11.81 | | | | (276) all_429_1 = all_415_0 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (274), (275) imply: % 82.17/11.81 | | | | (277) all_421_1 = all_407_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | SIMP: (277) implies: % 82.17/11.81 | | | | (278) all_421_1 = all_407_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (272), (273) imply: % 82.17/11.81 | | | | (279) all_413_1 = all_409_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (271), (272) imply: % 82.17/11.81 | | | | (280) all_417_1 = all_413_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | SIMP: (280) implies: % 82.17/11.81 | | | | (281) all_417_1 = all_413_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (269), (270) imply: % 82.17/11.81 | | | | (282) all_419_1 = all_411_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | SIMP: (282) implies: % 82.17/11.81 | | | | (283) all_419_1 = all_411_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (268), (278) imply: % 82.17/11.81 | | | | (284) all_415_1 = all_407_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | SIMP: (284) implies: % 82.17/11.81 | | | | (285) all_415_1 = all_407_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (267), (283) imply: % 82.17/11.81 | | | | (286) all_411_1 = all_409_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (266), (283) imply: % 82.17/11.81 | | | | (287) all_415_1 = all_411_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | SIMP: (287) implies: % 82.17/11.81 | | | | (288) all_415_1 = all_411_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (265), (281) imply: % 82.17/11.81 | | | | (289) all_413_1 = 0 % 82.17/11.81 | | | | % 82.17/11.81 | | | | SIMP: (289) implies: % 82.17/11.81 | | | | (290) all_413_1 = 0 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (285), (288) imply: % 82.17/11.81 | | | | (291) all_411_1 = all_407_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | SIMP: (291) implies: % 82.17/11.81 | | | | (292) all_411_1 = all_407_1 % 82.17/11.81 | | | | % 82.17/11.81 | | | | COMBINE_EQS: (279), (290) imply: % 82.17/11.81 | | | | (293) all_409_1 = 0 % 82.17/11.82 | | | | % 82.17/11.82 | | | | SIMP: (293) implies: % 82.17/11.82 | | | | (294) all_409_1 = 0 % 82.17/11.82 | | | | % 82.17/11.82 | | | | COMBINE_EQS: (286), (292) imply: % 82.17/11.82 | | | | (295) all_409_1 = all_407_1 % 82.17/11.82 | | | | % 82.17/11.82 | | | | SIMP: (295) implies: % 82.17/11.82 | | | | (296) all_409_1 = all_407_1 % 82.17/11.82 | | | | % 82.17/11.82 | | | | COMBINE_EQS: (294), (296) imply: % 82.17/11.82 | | | | (297) all_407_1 = 0 % 82.17/11.82 | | | | % 82.17/11.82 | | | | SIMP: (297) implies: % 82.17/11.82 | | | | (298) all_407_1 = 0 % 82.17/11.82 | | | | % 82.17/11.82 | | | | COMBINE_EQS: (285), (298) imply: % 82.17/11.82 | | | | (299) all_415_1 = 0 % 82.17/11.82 | | | | % 82.17/11.82 | | | | COMBINE_EQS: (275), (298) imply: % 82.17/11.82 | | | | (300) all_427_1 = 0 % 82.17/11.82 | | | | % 82.17/11.82 | | | | BETA: splitting (248) gives: % 82.17/11.82 | | | | % 82.17/11.82 | | | | Case 1: % 82.17/11.82 | | | | | % 82.17/11.82 | | | | | (301) ~ (all_415_1 = 0) % 82.17/11.82 | | | | | % 82.17/11.82 | | | | | REDUCE: (299), (301) imply: % 82.17/11.82 | | | | | (302) $false % 82.17/11.82 | | | | | % 82.17/11.82 | | | | | CLOSE: (302) is inconsistent. % 82.17/11.82 | | | | | % 82.17/11.82 | | | | Case 2: % 82.17/11.82 | | | | | % 82.17/11.82 | | | | | (303) all_415_0 = 0 % 82.17/11.82 | | | | | % 82.17/11.82 | | | | | REDUCE: (247), (303) imply: % 82.17/11.82 | | | | | (304) ssList(all_299_0) = 0 % 82.17/11.82 | | | | | % 82.17/11.82 | | | | | BETA: splitting (235) gives: % 82.17/11.82 | | | | | % 82.17/11.82 | | | | | Case 1: % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | (305) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_299_0) = v0) % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | DELTA: instantiating (305) with fresh symbol all_475_0 gives: % 82.17/11.82 | | | | | | (306) ~ (all_475_0 = 0) & ssList(all_299_0) = all_475_0 % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | ALPHA: (306) implies: % 82.17/11.82 | | | | | | (307) ~ (all_475_0 = 0) % 82.17/11.82 | | | | | | (308) ssList(all_299_0) = all_475_0 % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | DELTA: instantiating (305) with fresh symbol all_490_0 gives: % 82.17/11.82 | | | | | | (309) ~ (all_490_0 = 0) & ssList(all_299_0) = all_490_0 % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | ALPHA: (309) implies: % 82.17/11.82 | | | | | | (310) ssList(all_299_0) = all_490_0 % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | GROUND_INST: instantiating (16) with all_475_0, all_490_0, % 82.17/11.82 | | | | | | all_299_0, simplifying with (308), (310) gives: % 82.17/11.82 | | | | | | (311) all_490_0 = all_475_0 % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | GROUND_INST: instantiating (16) with 0, all_490_0, all_299_0, % 82.17/11.82 | | | | | | simplifying with (304), (310) gives: % 82.17/11.82 | | | | | | (312) all_490_0 = 0 % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | COMBINE_EQS: (311), (312) imply: % 82.17/11.82 | | | | | | (313) all_475_0 = 0 % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | REDUCE: (307), (313) imply: % 82.17/11.82 | | | | | | (314) $false % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | CLOSE: (314) is inconsistent. % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | Case 2: % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | (315) all_301_1 = nil & all_299_0 = nil % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | ALPHA: (315) implies: % 82.17/11.82 | | | | | | (316) all_299_0 = nil % 82.17/11.82 | | | | | | (317) all_301_1 = nil % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | REDUCE: (261), (317) imply: % 82.17/11.82 | | | | | | (318) cons(all_299_1, nil) = all_427_0 % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | REDUCE: (211), (316) imply: % 82.17/11.82 | | | | | | (319) cons(all_299_1, nil) = nil % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | BETA: splitting (262) gives: % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | | Case 1: % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | | (320) ~ (all_427_1 = 0) % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | | REDUCE: (300), (320) imply: % 82.17/11.82 | | | | | | | (321) $false % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | | CLOSE: (321) is inconsistent. % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | Case 2: % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | | (322) all_427_0 = all_301_0 % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | | REDUCE: (318), (322) imply: % 82.17/11.82 | | | | | | | (323) cons(all_299_1, nil) = all_301_0 % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | | GROUND_INST: instantiating (18) with nil, all_301_0, nil, % 82.17/11.82 | | | | | | | all_299_1, simplifying with (319), (323) gives: % 82.17/11.82 | | | | | | | (324) all_301_0 = nil % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | | REDUCE: (219), (324) imply: % 82.17/11.82 | | | | | | | (325) $false % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | | CLOSE: (325) is inconsistent. % 82.17/11.82 | | | | | | | % 82.17/11.82 | | | | | | End of split % 82.17/11.82 | | | | | | % 82.17/11.82 | | | | | End of split % 82.17/11.82 | | | | | % 82.17/11.82 | | | | End of split % 82.17/11.82 | | | | % 82.17/11.82 | | | Case 2: % 82.17/11.82 | | | | % 82.17/11.82 | | | | (326) all_97_0 = nil & ~ (all_93_0 = nil) % 82.17/11.82 | | | | % 82.17/11.82 | | | | ALPHA: (326) implies: % 82.17/11.82 | | | | (327) ~ (all_93_0 = nil) % 82.17/11.82 | | | | % 82.17/11.82 | | | | REDUCE: (204), (327) imply: % 82.17/11.82 | | | | (328) $false % 82.17/11.82 | | | | % 82.17/11.82 | | | | CLOSE: (328) is inconsistent. % 82.17/11.82 | | | | % 82.17/11.82 | | | End of split % 82.17/11.82 | | | % 82.17/11.82 | | End of split % 82.17/11.82 | | % 82.17/11.82 | End of split % 82.17/11.82 | % 82.17/11.82 End of proof % 82.17/11.82 % SZS output end Proof for theBenchmark % 82.17/11.82 % 82.17/11.82 11168ms %------------------------------------------------------------------------------