%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC292+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 : n006.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 20:50:40 EDT 2023 % Result : Theorem 46.08s 6.75s % Output : Proof 146.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWC292+1 : TPTP v8.1.2. Released v2.4.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 17:26:51 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.49/1.44 Prover 4: Preprocessing ... % 5.69/1.46 Prover 1: Preprocessing ... % 5.69/1.49 Prover 3: Preprocessing ... % 5.69/1.49 Prover 6: Preprocessing ... % 5.69/1.49 Prover 2: Preprocessing ... % 5.69/1.49 Prover 0: Preprocessing ... % 5.69/1.50 Prover 5: Preprocessing ... % 15.17/2.70 Prover 2: Proving ... % 15.39/2.75 Prover 6: Proving ... % 15.39/2.78 Prover 5: Constructing countermodel ... % 15.39/2.80 Prover 1: Constructing countermodel ... % 16.10/2.83 Prover 3: Constructing countermodel ... % 21.16/3.51 Prover 4: Constructing countermodel ... % 21.66/3.58 Prover 0: Proving ... % 46.08/6.75 Prover 3: proved (6115ms) % 46.08/6.75 % 46.08/6.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 46.08/6.75 % 46.08/6.75 Prover 5: stopped % 46.08/6.75 Prover 2: stopped % 46.08/6.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 46.08/6.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 46.08/6.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 46.08/6.76 Prover 6: stopped % 46.08/6.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 46.39/6.78 Prover 0: stopped % 46.39/6.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 47.86/6.97 Prover 8: Preprocessing ... % 48.38/7.03 Prover 7: Preprocessing ... % 48.38/7.03 Prover 11: Preprocessing ... % 48.38/7.06 Prover 10: Preprocessing ... % 48.38/7.10 Prover 13: Preprocessing ... % 48.80/7.21 Prover 10: Constructing countermodel ... % 50.00/7.24 Prover 7: Constructing countermodel ... % 50.26/7.29 Prover 8: Warning: ignoring some quantifiers % 50.26/7.31 Prover 8: Constructing countermodel ... % 50.26/7.33 Prover 13: Constructing countermodel ... % 53.34/7.76 Prover 11: Constructing countermodel ... % 81.79/11.47 Prover 13: stopped % 81.79/11.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 83.17/11.60 Prover 16: Preprocessing ... % 84.31/11.73 Prover 16: Constructing countermodel ... % 116.90/15.98 Prover 1: stopped % 116.90/15.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 117.50/16.09 Prover 19: Preprocessing ... % 120.94/16.53 Prover 19: Warning: ignoring some quantifiers % 120.94/16.58 Prover 19: Constructing countermodel ... % 123.28/16.84 Prover 16: stopped % 142.62/19.57 Prover 19: stopped % 145.87/20.12 Prover 8: Found proof (size 187) % 145.87/20.12 Prover 8: proved (13276ms) % 145.87/20.12 Prover 7: stopped % 145.87/20.12 Prover 11: stopped % 145.87/20.13 Prover 4: stopped % 145.87/20.13 Prover 10: stopped % 145.87/20.13 % 145.87/20.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 145.87/20.13 % 145.87/20.14 % SZS output start Proof for theBenchmark % 145.87/20.15 Assumptions after simplification: % 145.87/20.15 --------------------------------- % 145.87/20.15 % 145.87/20.15 (ax12) % 145.87/20.18 ! [v0: $i] : ! [v1: any] : ( ~ (strictorderedP(v0) = v1) | ~ $i(v0) | ? % 145.87/20.18 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 145.87/20.18 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~ % 145.87/20.18 (lt(v2, v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & % 145.87/20.18 ssItem(v3) = v5) | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5) % 145.87/20.18 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v6) = % 145.87/20.18 v7) | ~ (app(v5, v7) = v8) | ~ $i(v6) | ? [v9: int] : ( ~ % 145.87/20.18 (v9 = 0) & ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : (v4 % 145.87/20.18 = 0 | ~ (cons(v3, v9) = v10) | ~ (app(v8, v10) = v0) | ~ % 145.87/20.18 $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v9) = % 145.87/20.18 v11))))))) & (v1 = 0 | ? [v2: $i] : (ssItem(v2) = 0 & % 145.87/20.18 $i(v2) & ? [v3: $i] : ? [v4: any] : (lt(v2, v3) = v4 & ssItem(v3) = % 145.87/20.18 0 & $i(v3) & ? [v5: $i] : (ssList(v5) = 0 & $i(v5) & ? [v6: $i] : % 145.87/20.18 ? [v7: $i] : ? [v8: $i] : (ssList(v6) = 0 & cons(v2, v6) = v7 & % 145.87/20.18 app(v5, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ? [v9: $i] : ? % 145.87/20.18 [v10: $i] : ( ~ (v4 = 0) & ssList(v9) = 0 & cons(v3, v9) = v10 & % 145.87/20.18 app(v8, v10) = v0 & $i(v10) & $i(v9))))))))) % 145.87/20.18 % 145.87/20.18 (ax13) % 145.87/20.19 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 145.87/20.19 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 145.87/20.19 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 145.87/20.19 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 145.87/20.19 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 145.87/20.19 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 145.87/20.19 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 145.87/20.19 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 145.87/20.19 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 145.87/20.19 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 145.87/20.19 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 145.87/20.19 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 145.87/20.19 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 145.87/20.19 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 145.87/20.19 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 145.87/20.19 % 145.87/20.19 (ax15) % 146.27/20.19 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 146.27/20.19 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 146.27/20.19 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 146.27/20.19 % 146.27/20.19 (ax17) % 146.27/20.19 ssList(nil) = 0 & $i(nil) % 146.27/20.19 % 146.27/20.19 (ax20) % 146.27/20.19 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 146.27/20.19 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 146.27/20.19 ssItem(v2) = 0 & $i(v2)))) % 146.27/20.19 % 146.27/20.19 (ax23) % 146.27/20.19 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 146.27/20.19 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 146.27/20.19 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 146.27/20.19 % 146.27/20.19 (ax63) % 146.27/20.20 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 146.27/20.20 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 146.27/20.20 (v2 = 0) | v3 = 0))) % 146.27/20.20 % 146.27/20.20 (ax68) % 146.27/20.20 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 146.27/20.20 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 146.27/20.20 ~ (v2 = 0) | v3 = 0))) % 146.27/20.20 % 146.27/20.20 (ax69) % 146.27/20.20 strictorderedP(nil) = 0 & $i(nil) % 146.27/20.20 % 146.27/20.20 (ax72) % 146.27/20.20 duplicatefreeP(nil) = 0 & $i(nil) % 146.27/20.20 % 146.27/20.20 (ax73) % 146.27/20.20 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 146.27/20.20 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 146.27/20.20 (v2 = 0) | v3 = 0))) % 146.27/20.20 % 146.27/20.20 (co1) % 146.27/20.20 $i(nil) & ? [v0: $i] : ? [v1: any] : (strictorderedP(v0) = v1 & ssList(v0) = % 146.27/20.20 0 & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : % 146.27/20.20 (ssList(v3) = 0 & $i(v3) & ? [v4: any] : (v3 = v0 & ~ (v1 = 0) & neq(v2, % 146.27/20.20 nil) = v4 & ( ~ (v4 = 0) | ? [v5: $i] : (memberP(v2, v5) = 0 & % 146.27/20.20 cons(v5, nil) = v0 & ssItem(v5) = 0 & $i(v5))) & ( ~ (v2 = nil) | % 146.27/20.20 v0 = nil))))) % 146.27/20.20 % 146.27/20.20 (function-axioms) % 146.27/20.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 146.27/20.21 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 146.27/20.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 146.27/20.21 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 146.27/20.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 146.27/20.21 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 146.27/20.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 146.27/20.21 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 146.27/20.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 146.27/20.21 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 146.27/20.21 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 146.27/20.21 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 146.27/20.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 146.27/20.21 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 146.27/20.21 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 146.27/20.21 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 146.27/20.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 146.27/20.21 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 146.27/20.21 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 146.27/20.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 146.27/20.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 146.27/20.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 146.27/20.21 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 146.27/20.21 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 146.27/20.21 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 146.27/20.21 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 146.27/20.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 146.27/20.21 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 146.27/20.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 146.27/20.21 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 146.27/20.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 146.27/20.21 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 146.27/20.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 146.27/20.21 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 146.27/20.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 146.27/20.21 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 146.27/20.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 146.27/20.21 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 146.27/20.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 146.27/20.21 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 146.27/20.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 146.27/20.21 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 146.27/20.21 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ? % 146.27/20.21 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ? % 146.27/20.21 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ? % 146.27/20.21 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ? % 146.27/20.21 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ? % 146.27/20.21 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2) % 146.27/20.21 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) = % 146.27/20.21 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 146.27/20.21 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 146.27/20.21 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 146.27/20.21 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 146.27/20.21 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 146.27/20.21 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 146.27/20.21 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 146.27/20.21 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 146.27/20.21 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 146.27/20.21 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 146.27/20.21 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 146.27/20.21 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 146.27/20.21 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 146.27/20.21 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0) % 146.27/20.21 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ? % 146.27/20.21 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 146.27/20.21 (hd(v0) = v1 & $i(v1)) % 146.27/20.21 % 146.27/20.21 Further assumptions not needed in the proof: % 146.27/20.21 -------------------------------------------- % 146.27/20.21 ax1, ax10, ax11, ax14, ax16, ax18, ax19, ax2, ax21, ax22, ax24, ax25, ax26, % 146.27/20.21 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, % 146.27/20.21 ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, % 146.27/20.21 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60, ax61, % 146.27/20.21 ax62, ax64, ax65, ax66, ax67, ax7, ax70, ax71, ax74, ax75, ax76, ax77, ax78, % 146.27/20.21 ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, % 146.27/20.21 ax90, ax91, ax92, ax93, ax94, ax95 % 146.27/20.21 % 146.27/20.21 Those formulas are unsatisfiable: % 146.27/20.21 --------------------------------- % 146.27/20.21 % 146.27/20.21 Begin of proof % 146.27/20.22 | % 146.27/20.22 | ALPHA: (ax17) implies: % 146.27/20.22 | (1) ssList(nil) = 0 % 146.27/20.22 | % 146.27/20.22 | ALPHA: (ax20) implies: % 146.27/20.22 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 146.27/20.22 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 146.27/20.22 | ssItem(v2) = 0 & $i(v2)))) % 146.27/20.22 | % 146.27/20.22 | ALPHA: (ax63) implies: % 146.27/20.22 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 146.27/20.22 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 146.27/20.22 | ( ~ (v2 = 0) | v3 = 0))) % 146.27/20.22 | % 146.27/20.22 | ALPHA: (ax68) implies: % 146.27/20.22 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 146.27/20.22 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 146.27/20.22 | & ( ~ (v2 = 0) | v3 = 0))) % 146.27/20.22 | % 146.27/20.22 | ALPHA: (ax69) implies: % 146.27/20.22 | (5) strictorderedP(nil) = 0 % 146.27/20.22 | % 146.27/20.22 | ALPHA: (ax72) implies: % 146.27/20.22 | (6) duplicatefreeP(nil) = 0 % 146.27/20.22 | % 146.27/20.22 | ALPHA: (ax73) implies: % 146.27/20.22 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 146.27/20.22 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 146.27/20.22 | ( ~ (v2 = 0) | v3 = 0))) % 146.27/20.22 | % 146.27/20.22 | ALPHA: (co1) implies: % 146.27/20.22 | (8) $i(nil) % 146.27/20.22 | (9) ? [v0: $i] : ? [v1: any] : (strictorderedP(v0) = v1 & ssList(v0) = 0 % 146.27/20.22 | & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : % 146.27/20.22 | (ssList(v3) = 0 & $i(v3) & ? [v4: any] : (v3 = v0 & ~ (v1 = 0) & % 146.27/20.22 | neq(v2, nil) = v4 & ( ~ (v4 = 0) | ? [v5: $i] : (memberP(v2, % 146.27/20.22 | v5) = 0 & cons(v5, nil) = v0 & ssItem(v5) = 0 & $i(v5))) % 146.27/20.22 | & ( ~ (v2 = nil) | v0 = nil))))) % 146.27/20.22 | % 146.27/20.22 | ALPHA: (function-axioms) implies: % 146.27/20.22 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 146.27/20.22 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 146.27/20.22 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 146.27/20.23 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 146.27/20.23 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 146.27/20.23 | : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = % 146.27/20.23 | v0)) % 146.27/20.23 | % 146.27/20.23 | DELTA: instantiating (9) with fresh symbols all_139_0, all_139_1 gives: % 146.27/20.23 | (13) strictorderedP(all_139_1) = all_139_0 & ssList(all_139_1) = 0 & % 146.27/20.23 | $i(all_139_1) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 146.27/20.23 | (ssList(v1) = 0 & $i(v1) & ? [v2: any] : (v1 = all_139_1 & ~ % 146.27/20.23 | (all_139_0 = 0) & neq(v0, nil) = v2 & ( ~ (v2 = 0) | ? [v3: $i] % 146.27/20.23 | : (memberP(v0, v3) = 0 & cons(v3, nil) = all_139_1 & % 146.27/20.23 | ssItem(v3) = 0 & $i(v3))) & ( ~ (v0 = nil) | all_139_1 = % 146.27/20.23 | nil)))) % 146.27/20.23 | % 146.27/20.23 | ALPHA: (13) implies: % 146.27/20.23 | (14) strictorderedP(all_139_1) = all_139_0 % 146.27/20.23 | (15) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 146.27/20.23 | & $i(v1) & ? [v2: any] : (v1 = all_139_1 & ~ (all_139_0 = 0) & % 146.27/20.23 | neq(v0, nil) = v2 & ( ~ (v2 = 0) | ? [v3: $i] : (memberP(v0, % 146.27/20.23 | v3) = 0 & cons(v3, nil) = all_139_1 & ssItem(v3) = 0 & % 146.27/20.23 | $i(v3))) & ( ~ (v0 = nil) | all_139_1 = nil)))) % 146.27/20.23 | % 146.27/20.23 | DELTA: instantiating (15) with fresh symbol all_143_0 gives: % 146.27/20.23 | (16) ssList(all_143_0) = 0 & $i(all_143_0) & ? [v0: $i] : (ssList(v0) = 0 % 146.27/20.23 | & $i(v0) & ? [v1: any] : (v0 = all_139_1 & ~ (all_139_0 = 0) & % 146.27/20.23 | neq(all_143_0, nil) = v1 & ( ~ (v1 = 0) | ? [v2: $i] : % 146.27/20.23 | (memberP(all_143_0, v2) = 0 & cons(v2, nil) = all_139_1 & % 146.27/20.23 | ssItem(v2) = 0 & $i(v2))) & ( ~ (all_143_0 = nil) | all_139_1 % 146.27/20.23 | = nil))) % 146.27/20.23 | % 146.27/20.23 | ALPHA: (16) implies: % 146.27/20.23 | (17) $i(all_143_0) % 146.27/20.23 | (18) ssList(all_143_0) = 0 % 146.27/20.23 | (19) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: any] : (v0 = % 146.27/20.23 | all_139_1 & ~ (all_139_0 = 0) & neq(all_143_0, nil) = v1 & ( ~ % 146.27/20.23 | (v1 = 0) | ? [v2: $i] : (memberP(all_143_0, v2) = 0 & cons(v2, % 146.27/20.23 | nil) = all_139_1 & ssItem(v2) = 0 & $i(v2))) & ( ~ % 146.27/20.23 | (all_143_0 = nil) | all_139_1 = nil))) % 146.27/20.23 | % 146.27/20.23 | DELTA: instantiating (19) with fresh symbol all_145_0 gives: % 146.27/20.23 | (20) ssList(all_145_0) = 0 & $i(all_145_0) & ? [v0: any] : (all_145_0 = % 146.27/20.23 | all_139_1 & ~ (all_139_0 = 0) & neq(all_143_0, nil) = v0 & ( ~ (v0 % 146.27/20.23 | = 0) | ? [v1: $i] : (memberP(all_143_0, v1) = 0 & cons(v1, nil) % 146.27/20.23 | = all_139_1 & ssItem(v1) = 0 & $i(v1))) & ( ~ (all_143_0 = nil) % 146.27/20.23 | | all_139_1 = nil)) % 146.27/20.23 | % 146.27/20.23 | ALPHA: (20) implies: % 146.27/20.23 | (21) $i(all_145_0) % 146.27/20.24 | (22) ssList(all_145_0) = 0 % 146.27/20.24 | (23) ? [v0: any] : (all_145_0 = all_139_1 & ~ (all_139_0 = 0) & % 146.27/20.24 | neq(all_143_0, nil) = v0 & ( ~ (v0 = 0) | ? [v1: $i] : % 146.27/20.24 | (memberP(all_143_0, v1) = 0 & cons(v1, nil) = all_139_1 & % 146.27/20.24 | ssItem(v1) = 0 & $i(v1))) & ( ~ (all_143_0 = nil) | all_139_1 = % 146.27/20.24 | nil)) % 146.27/20.24 | % 146.27/20.24 | DELTA: instantiating (23) with fresh symbol all_147_0 gives: % 146.27/20.24 | (24) all_145_0 = all_139_1 & ~ (all_139_0 = 0) & neq(all_143_0, nil) = % 146.27/20.24 | all_147_0 & ( ~ (all_147_0 = 0) | ? [v0: $i] : (memberP(all_143_0, % 146.27/20.24 | v0) = 0 & cons(v0, nil) = all_139_1 & ssItem(v0) = 0 & $i(v0))) % 146.27/20.24 | & ( ~ (all_143_0 = nil) | all_139_1 = nil) % 146.27/20.24 | % 146.27/20.24 | ALPHA: (24) implies: % 146.27/20.24 | (25) all_145_0 = all_139_1 % 146.27/20.24 | (26) ~ (all_139_0 = 0) % 146.27/20.24 | (27) neq(all_143_0, nil) = all_147_0 % 146.27/20.24 | (28) ~ (all_143_0 = nil) | all_139_1 = nil % 146.27/20.24 | (29) ~ (all_147_0 = 0) | ? [v0: $i] : (memberP(all_143_0, v0) = 0 & % 146.27/20.24 | cons(v0, nil) = all_139_1 & ssItem(v0) = 0 & $i(v0)) % 146.27/20.24 | % 146.27/20.24 | REDUCE: (22), (25) imply: % 146.27/20.24 | (30) ssList(all_139_1) = 0 % 146.27/20.24 | % 146.27/20.24 | REDUCE: (21), (25) imply: % 146.27/20.24 | (31) $i(all_139_1) % 146.27/20.24 | % 146.27/20.24 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (8) gives: % 146.27/20.24 | (32) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 146.27/20.24 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 146.27/20.24 | ( ~ (v2 = 0) | v3 = v0))) % 146.27/20.24 | % 146.27/20.24 | GROUND_INST: instantiating (2) with all_143_0, simplifying with (17), (18) % 146.27/20.24 | gives: % 146.27/20.24 | (33) all_143_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 146.27/20.24 | : (cons(v1, v0) = all_143_0 & ssItem(v1) = 0 & $i(v1))) % 146.27/20.24 | % 146.27/20.24 | GROUND_INST: instantiating (ax15) with all_143_0, simplifying with (17), (18) % 146.27/20.24 | gives: % 146.27/20.24 | (34) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_143_0, v0) = v1) | ~ $i(v0) % 146.27/20.24 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 146.27/20.24 | ~ (v0 = all_143_0)) & (v1 = 0 | v0 = all_143_0))) % 146.27/20.24 | % 146.27/20.24 | GROUND_INST: instantiating (ax12) with all_139_1, all_139_0, simplifying with % 146.27/20.24 | (14), (31) gives: % 146.27/20.25 | (35) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) | (( ~ % 146.27/20.25 | (all_139_0 = 0) | ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | % 146.27/20.25 | ! [v1: $i] : ! [v2: any] : ( ~ (lt(v0, v1) = v2) | ~ $i(v1) | % 146.27/20.25 | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: $i] : % 146.27/20.25 | ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: $i] : % 146.27/20.25 | ! [v6: $i] : ( ~ (cons(v0, v4) = v5) | ~ (app(v3, v5) = % 146.27/20.25 | v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & % 146.27/20.25 | ssList(v4) = v7) | ! [v7: $i] : ! [v8: $i] : (v2 = 0 | % 146.27/20.25 | ~ (cons(v1, v7) = v8) | ~ (app(v6, v8) = all_139_1) | % 146.27/20.25 | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v7) = % 146.27/20.25 | v9))))))) & (all_139_0 = 0 | ? [v0: $i] : (ssItem(v0) % 146.27/20.25 | = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : (lt(v0, v1) = v2 & % 146.27/20.25 | ssItem(v1) = 0 & $i(v1) & ? [v3: $i] : (ssList(v3) = 0 & % 146.27/20.25 | $i(v3) & ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 146.27/20.25 | (ssList(v4) = 0 & cons(v0, v4) = v5 & app(v3, v5) = v6 & % 146.27/20.25 | $i(v6) & $i(v5) & $i(v4) & ? [v7: $i] : ? [v8: $i] : ( ~ % 146.27/20.25 | (v2 = 0) & ssList(v7) = 0 & cons(v1, v7) = v8 & app(v6, % 146.27/20.25 | v8) = all_139_1 & $i(v8) & $i(v7)))))))) % 146.27/20.25 | % 146.27/20.25 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (6), (8) % 146.27/20.25 | gives: % 146.27/20.25 | (36) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 146.27/20.25 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 146.27/20.25 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 146.27/20.25 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 146.27/20.25 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 146.27/20.25 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 146.27/20.25 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 146.27/20.25 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 146.27/20.25 | v8)))))) % 146.27/20.25 | % 146.27/20.25 | GROUND_INST: instantiating (34) with nil, all_147_0, simplifying with (8), % 146.27/20.25 | (27) gives: % 146.27/20.25 | (37) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_147_0 = 0) % 146.27/20.25 | | ~ (all_143_0 = nil)) & (all_147_0 = 0 | all_143_0 = nil)) % 146.27/20.25 | % 146.27/20.25 | BETA: splitting (36) gives: % 146.27/20.25 | % 146.27/20.25 | Case 1: % 146.27/20.25 | | % 146.27/20.25 | | (38) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 146.27/20.25 | | % 146.27/20.25 | | DELTA: instantiating (38) with fresh symbol all_318_0 gives: % 146.27/20.25 | | (39) ~ (all_318_0 = 0) & ssList(nil) = all_318_0 % 146.27/20.25 | | % 146.27/20.25 | | ALPHA: (39) implies: % 146.27/20.25 | | (40) ~ (all_318_0 = 0) % 146.27/20.25 | | (41) ssList(nil) = all_318_0 % 146.27/20.25 | | % 146.27/20.25 | | DELTA: instantiating (38) with fresh symbol all_320_0 gives: % 146.27/20.25 | | (42) ~ (all_320_0 = 0) & ssList(nil) = all_320_0 % 146.27/20.25 | | % 146.27/20.25 | | ALPHA: (42) implies: % 146.27/20.25 | | (43) ssList(nil) = all_320_0 % 146.27/20.25 | | % 146.27/20.25 | | DELTA: instantiating (38) with fresh symbol all_322_0 gives: % 146.27/20.25 | | (44) ~ (all_322_0 = 0) & ssList(nil) = all_322_0 % 146.27/20.25 | | % 146.27/20.25 | | ALPHA: (44) implies: % 146.27/20.25 | | (45) ssList(nil) = all_322_0 % 146.27/20.25 | | % 146.27/20.25 | | GROUND_INST: instantiating (11) with 0, all_320_0, nil, simplifying with % 146.27/20.25 | | (1), (43) gives: % 146.27/20.25 | | (46) all_320_0 = 0 % 146.27/20.25 | | % 146.27/20.25 | | GROUND_INST: instantiating (11) with all_320_0, all_322_0, nil, simplifying % 146.27/20.25 | | with (43), (45) gives: % 146.27/20.25 | | (47) all_322_0 = all_320_0 % 146.27/20.25 | | % 146.27/20.25 | | GROUND_INST: instantiating (11) with all_318_0, all_322_0, nil, simplifying % 146.27/20.25 | | with (41), (45) gives: % 146.27/20.25 | | (48) all_322_0 = all_318_0 % 146.27/20.25 | | % 146.27/20.26 | | COMBINE_EQS: (47), (48) imply: % 146.27/20.26 | | (49) all_320_0 = all_318_0 % 146.27/20.26 | | % 146.27/20.26 | | SIMP: (49) implies: % 146.27/20.26 | | (50) all_320_0 = all_318_0 % 146.27/20.26 | | % 146.27/20.26 | | COMBINE_EQS: (46), (50) imply: % 146.27/20.26 | | (51) all_318_0 = 0 % 146.27/20.26 | | % 146.27/20.26 | | SIMP: (51) implies: % 146.27/20.26 | | (52) all_318_0 = 0 % 146.27/20.26 | | % 146.27/20.26 | | REDUCE: (40), (52) imply: % 146.27/20.26 | | (53) $false % 146.27/20.26 | | % 146.27/20.26 | | CLOSE: (53) is inconsistent. % 146.27/20.26 | | % 146.27/20.26 | Case 2: % 146.27/20.26 | | % 146.27/20.26 | | (54) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 146.27/20.26 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 146.27/20.26 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 146.27/20.26 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 146.27/20.26 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 146.27/20.26 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 146.27/20.26 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 146.27/20.26 | | 0) & ssList(v6) = v8)))))) % 146.27/20.26 | | % 146.27/20.26 | | BETA: splitting (35) gives: % 146.27/20.26 | | % 146.27/20.26 | | Case 1: % 146.27/20.26 | | | % 146.27/20.26 | | | (55) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 146.27/20.26 | | | % 146.27/20.26 | | | DELTA: instantiating (55) with fresh symbol all_336_0 gives: % 146.27/20.26 | | | (56) ~ (all_336_0 = 0) & ssList(all_139_1) = all_336_0 % 146.27/20.26 | | | % 146.27/20.26 | | | ALPHA: (56) implies: % 146.27/20.26 | | | (57) ~ (all_336_0 = 0) % 146.27/20.26 | | | (58) ssList(all_139_1) = all_336_0 % 146.27/20.26 | | | % 146.27/20.26 | | | GROUND_INST: instantiating (11) with 0, all_336_0, all_139_1, simplifying % 146.27/20.26 | | | with (30), (58) gives: % 146.27/20.26 | | | (59) all_336_0 = 0 % 146.27/20.26 | | | % 146.27/20.26 | | | REDUCE: (57), (59) imply: % 146.27/20.26 | | | (60) $false % 146.27/20.26 | | | % 146.27/20.26 | | | CLOSE: (60) is inconsistent. % 146.27/20.26 | | | % 146.27/20.26 | | Case 2: % 146.27/20.26 | | | % 146.27/20.26 | | | (61) ( ~ (all_139_0 = 0) | ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ % 146.27/20.26 | | | $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ (lt(v0, v1) = v2) | % 146.27/20.26 | | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | % 146.27/20.26 | | | ! [v3: $i] : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] % 146.27/20.26 | | | : ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v0, v4) = v5) | ~ % 146.27/20.26 | | | (app(v3, v5) = v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 % 146.27/20.26 | | | = 0) & ssList(v4) = v7) | ! [v7: $i] : ! [v8: $i] % 146.27/20.26 | | | : (v2 = 0 | ~ (cons(v1, v7) = v8) | ~ (app(v6, v8) = % 146.27/20.27 | | | all_139_1) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) % 146.27/20.27 | | | & ssList(v7) = v9))))))) & (all_139_0 = 0 | ? [v0: % 146.27/20.27 | | | $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 146.27/20.27 | | | (lt(v0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ? [v3: $i] : % 146.27/20.27 | | | (ssList(v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: $i] : ? % 146.27/20.27 | | | [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) = v5 & app(v3, % 146.27/20.27 | | | v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? [v7: $i] : ? % 146.27/20.27 | | | [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & cons(v1, v7) % 146.27/20.27 | | | = v8 & app(v6, v8) = all_139_1 & $i(v8) & $i(v7))))))) % 146.27/20.27 | | | % 146.27/20.27 | | | ALPHA: (61) implies: % 146.27/20.27 | | | (62) all_139_0 = 0 | ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: % 146.27/20.27 | | | $i] : ? [v2: any] : (lt(v0, v1) = v2 & ssItem(v1) = 0 & % 146.27/20.27 | | | $i(v1) & ? [v3: $i] : (ssList(v3) = 0 & $i(v3) & ? [v4: $i] % 146.27/20.27 | | | : ? [v5: $i] : ? [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) % 146.27/20.27 | | | = v5 & app(v3, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? % 146.27/20.27 | | | [v7: $i] : ? [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & % 146.27/20.27 | | | cons(v1, v7) = v8 & app(v6, v8) = all_139_1 & $i(v8) & % 146.27/20.27 | | | $i(v7)))))) % 146.27/20.27 | | | % 146.27/20.27 | | | BETA: splitting (62) gives: % 146.27/20.27 | | | % 146.27/20.27 | | | Case 1: % 146.27/20.27 | | | | % 146.27/20.27 | | | | (63) all_139_0 = 0 % 146.27/20.27 | | | | % 146.27/20.27 | | | | REDUCE: (26), (63) imply: % 146.27/20.27 | | | | (64) $false % 146.27/20.27 | | | | % 146.27/20.27 | | | | CLOSE: (64) is inconsistent. % 146.27/20.27 | | | | % 146.27/20.27 | | | Case 2: % 146.27/20.27 | | | | % 146.27/20.27 | | | | (65) ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 146.27/20.27 | | | | any] : (lt(v0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ? [v3: % 146.27/20.27 | | | | $i] : (ssList(v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: $i] % 146.27/20.27 | | | | : ? [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) = v5 & % 146.27/20.27 | | | | app(v3, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? [v7: % 146.27/20.27 | | | | $i] : ? [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & % 146.27/20.27 | | | | cons(v1, v7) = v8 & app(v6, v8) = all_139_1 & $i(v8) & % 146.27/20.27 | | | | $i(v7)))))) % 146.27/20.27 | | | | % 146.27/20.27 | | | | DELTA: instantiating (65) with fresh symbol all_343_0 gives: % 146.27/20.27 | | | | (66) ssItem(all_343_0) = 0 & $i(all_343_0) & ? [v0: $i] : ? [v1: % 146.27/20.27 | | | | any] : (lt(all_343_0, v0) = v1 & ssItem(v0) = 0 & $i(v0) & ? % 146.27/20.27 | | | | [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: % 146.27/20.27 | | | | $i] : ? [v5: $i] : (ssList(v3) = 0 & cons(all_343_0, v3) % 146.27/20.27 | | | | = v4 & app(v2, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & ? % 146.27/20.28 | | | | [v6: $i] : ? [v7: $i] : ( ~ (v1 = 0) & ssList(v6) = 0 & % 146.27/20.28 | | | | cons(v0, v6) = v7 & app(v5, v7) = all_139_1 & $i(v7) & % 146.27/20.28 | | | | $i(v6))))) % 146.27/20.28 | | | | % 146.27/20.28 | | | | ALPHA: (66) implies: % 146.27/20.28 | | | | (67) $i(all_343_0) % 146.27/20.28 | | | | (68) ssItem(all_343_0) = 0 % 146.69/20.28 | | | | (69) ? [v0: $i] : ? [v1: any] : (lt(all_343_0, v0) = v1 & % 146.69/20.28 | | | | ssItem(v0) = 0 & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & % 146.69/20.28 | | | | $i(v2) & ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 146.69/20.28 | | | | (ssList(v3) = 0 & cons(all_343_0, v3) = v4 & app(v2, v4) = % 146.69/20.28 | | | | v5 & $i(v5) & $i(v4) & $i(v3) & ? [v6: $i] : ? [v7: $i] % 146.69/20.28 | | | | : ( ~ (v1 = 0) & ssList(v6) = 0 & cons(v0, v6) = v7 & % 146.69/20.28 | | | | app(v5, v7) = all_139_1 & $i(v7) & $i(v6))))) % 146.69/20.28 | | | | % 146.69/20.28 | | | | DELTA: instantiating (69) with fresh symbols all_345_0, all_345_1 gives: % 146.69/20.28 | | | | (70) lt(all_343_0, all_345_1) = all_345_0 & ssItem(all_345_1) = 0 & % 146.69/20.28 | | | | $i(all_345_1) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 146.69/20.28 | | | | $i] : ? [v2: $i] : ? [v3: $i] : (ssList(v1) = 0 & % 146.69/20.28 | | | | cons(all_343_0, v1) = v2 & app(v0, v2) = v3 & $i(v3) & % 146.69/20.28 | | | | $i(v2) & $i(v1) & ? [v4: $i] : ? [v5: $i] : ( ~ (all_345_0 % 146.69/20.28 | | | | = 0) & ssList(v4) = 0 & cons(all_345_1, v4) = v5 & % 146.69/20.28 | | | | app(v3, v5) = all_139_1 & $i(v5) & $i(v4)))) % 146.69/20.28 | | | | % 146.69/20.28 | | | | ALPHA: (70) implies: % 146.69/20.28 | | | | (71) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 146.69/20.28 | | | | $i] : ? [v3: $i] : (ssList(v1) = 0 & cons(all_343_0, v1) = % 146.69/20.28 | | | | v2 & app(v0, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & ? [v4: % 146.69/20.28 | | | | $i] : ? [v5: $i] : ( ~ (all_345_0 = 0) & ssList(v4) = 0 & % 146.69/20.28 | | | | cons(all_345_1, v4) = v5 & app(v3, v5) = all_139_1 & % 146.69/20.28 | | | | $i(v5) & $i(v4)))) % 146.69/20.28 | | | | % 146.69/20.28 | | | | DELTA: instantiating (71) with fresh symbol all_347_0 gives: % 146.71/20.28 | | | | (72) ssList(all_347_0) = 0 & $i(all_347_0) & ? [v0: $i] : ? [v1: % 146.71/20.28 | | | | $i] : ? [v2: $i] : (ssList(v0) = 0 & cons(all_343_0, v0) = v1 % 146.71/20.28 | | | | & app(all_347_0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ? [v3: % 146.71/20.28 | | | | $i] : ? [v4: $i] : ( ~ (all_345_0 = 0) & ssList(v3) = 0 & % 146.71/20.28 | | | | cons(all_345_1, v3) = v4 & app(v2, v4) = all_139_1 & $i(v4) % 146.71/20.28 | | | | & $i(v3))) % 146.71/20.28 | | | | % 146.71/20.28 | | | | ALPHA: (72) implies: % 146.71/20.28 | | | | (73) $i(all_347_0) % 146.71/20.28 | | | | (74) ssList(all_347_0) = 0 % 146.71/20.28 | | | | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ssList(v0) = 0 & % 146.71/20.28 | | | | cons(all_343_0, v0) = v1 & app(all_347_0, v1) = v2 & $i(v2) & % 146.71/20.28 | | | | $i(v1) & $i(v0) & ? [v3: $i] : ? [v4: $i] : ( ~ (all_345_0 = % 146.71/20.28 | | | | 0) & ssList(v3) = 0 & cons(all_345_1, v3) = v4 & app(v2, % 146.71/20.28 | | | | v4) = all_139_1 & $i(v4) & $i(v3))) % 146.71/20.28 | | | | % 146.71/20.28 | | | | DELTA: instantiating (75) with fresh symbols all_349_0, all_349_1, % 146.71/20.28 | | | | all_349_2 gives: % 146.71/20.28 | | | | (76) ssList(all_349_2) = 0 & cons(all_343_0, all_349_2) = all_349_1 & % 146.71/20.28 | | | | app(all_347_0, all_349_1) = all_349_0 & $i(all_349_0) & % 146.71/20.28 | | | | $i(all_349_1) & $i(all_349_2) & ? [v0: $i] : ? [v1: $i] : ( ~ % 146.71/20.28 | | | | (all_345_0 = 0) & ssList(v0) = 0 & cons(all_345_1, v0) = v1 & % 146.71/20.28 | | | | app(all_349_0, v1) = all_139_1 & $i(v1) & $i(v0)) % 146.71/20.28 | | | | % 146.71/20.28 | | | | ALPHA: (76) implies: % 146.71/20.28 | | | | (77) $i(all_349_2) % 146.71/20.29 | | | | (78) app(all_347_0, all_349_1) = all_349_0 % 146.71/20.29 | | | | (79) cons(all_343_0, all_349_2) = all_349_1 % 146.71/20.29 | | | | (80) ssList(all_349_2) = 0 % 146.71/20.29 | | | | % 146.71/20.29 | | | | BETA: splitting (29) gives: % 146.71/20.29 | | | | % 146.71/20.29 | | | | Case 1: % 146.71/20.29 | | | | | % 146.71/20.29 | | | | | (81) ~ (all_147_0 = 0) % 146.71/20.29 | | | | | % 146.71/20.29 | | | | | BETA: splitting (37) gives: % 146.71/20.29 | | | | | % 146.71/20.29 | | | | | Case 1: % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | (82) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | DELTA: instantiating (82) with fresh symbol all_364_0 gives: % 146.71/20.29 | | | | | | (83) ~ (all_364_0 = 0) & ssList(nil) = all_364_0 % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | REF_CLOSE: (1), (11), (83) are inconsistent by sub-proof #1. % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | Case 2: % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | (84) ( ~ (all_147_0 = 0) | ~ (all_143_0 = nil)) & (all_147_0 = 0 % 146.71/20.29 | | | | | | | all_143_0 = nil) % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | ALPHA: (84) implies: % 146.71/20.29 | | | | | | (85) all_147_0 = 0 | all_143_0 = nil % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | BETA: splitting (85) gives: % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | Case 1: % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | (86) all_143_0 = nil % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | BETA: splitting (28) gives: % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | Case 1: % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | (87) ~ (all_143_0 = nil) % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | REDUCE: (86), (87) imply: % 146.71/20.29 | | | | | | | | (88) $false % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | CLOSE: (88) is inconsistent. % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | Case 2: % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | (89) all_139_1 = nil % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | REDUCE: (14), (89) imply: % 146.71/20.29 | | | | | | | | (90) strictorderedP(nil) = all_139_0 % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | GROUND_INST: instantiating (12) with 0, all_139_0, nil, % 146.71/20.29 | | | | | | | | simplifying with (5), (90) gives: % 146.71/20.29 | | | | | | | | (91) all_139_0 = 0 % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | REDUCE: (26), (91) imply: % 146.71/20.29 | | | | | | | | (92) $false % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | CLOSE: (92) is inconsistent. % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | End of split % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | Case 2: % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | (93) all_147_0 = 0 % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | REDUCE: (81), (93) imply: % 146.71/20.29 | | | | | | | (94) $false % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | CLOSE: (94) is inconsistent. % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | End of split % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | End of split % 146.71/20.29 | | | | | % 146.71/20.29 | | | | Case 2: % 146.71/20.29 | | | | | % 146.71/20.29 | | | | | (95) all_147_0 = 0 % 146.71/20.29 | | | | | (96) ? [v0: $i] : (memberP(all_143_0, v0) = 0 & cons(v0, nil) = % 146.71/20.29 | | | | | all_139_1 & ssItem(v0) = 0 & $i(v0)) % 146.71/20.29 | | | | | % 146.71/20.29 | | | | | DELTA: instantiating (96) with fresh symbol all_359_0 gives: % 146.71/20.29 | | | | | (97) memberP(all_143_0, all_359_0) = 0 & cons(all_359_0, nil) = % 146.71/20.29 | | | | | all_139_1 & ssItem(all_359_0) = 0 & $i(all_359_0) % 146.71/20.29 | | | | | % 146.71/20.29 | | | | | ALPHA: (97) implies: % 146.71/20.29 | | | | | (98) $i(all_359_0) % 146.71/20.29 | | | | | (99) ssItem(all_359_0) = 0 % 146.71/20.29 | | | | | (100) cons(all_359_0, nil) = all_139_1 % 146.71/20.29 | | | | | % 146.71/20.29 | | | | | BETA: splitting (37) gives: % 146.71/20.29 | | | | | % 146.71/20.29 | | | | | Case 1: % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | (101) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | DELTA: instantiating (101) with fresh symbol all_364_0 gives: % 146.71/20.29 | | | | | | (102) ~ (all_364_0 = 0) & ssList(nil) = all_364_0 % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | REF_CLOSE: (1), (11), (102) are inconsistent by sub-proof #1. % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | Case 2: % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | (103) ( ~ (all_147_0 = 0) | ~ (all_143_0 = nil)) & (all_147_0 = % 146.71/20.29 | | | | | | 0 | all_143_0 = nil) % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | ALPHA: (103) implies: % 146.71/20.29 | | | | | | (104) ~ (all_147_0 = 0) | ~ (all_143_0 = nil) % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | BETA: splitting (104) gives: % 146.71/20.29 | | | | | | % 146.71/20.29 | | | | | | Case 1: % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | (105) ~ (all_143_0 = nil) % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | BETA: splitting (33) gives: % 146.71/20.29 | | | | | | | % 146.71/20.29 | | | | | | | Case 1: % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | (106) all_143_0 = nil % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | REDUCE: (105), (106) imply: % 146.71/20.29 | | | | | | | | (107) $false % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | CLOSE: (107) is inconsistent. % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | Case 2: % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | (108) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 146.71/20.29 | | | | | | | | (cons(v1, v0) = all_143_0 & ssItem(v1) = 0 & $i(v1))) % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | DELTA: instantiating (108) with fresh symbol all_371_0 gives: % 146.71/20.29 | | | | | | | | (109) ssList(all_371_0) = 0 & $i(all_371_0) & ? [v0: $i] : % 146.71/20.29 | | | | | | | | (cons(v0, all_371_0) = all_143_0 & ssItem(v0) = 0 & % 146.71/20.29 | | | | | | | | $i(v0)) % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | ALPHA: (109) implies: % 146.71/20.29 | | | | | | | | (110) ? [v0: $i] : (cons(v0, all_371_0) = all_143_0 & % 146.71/20.29 | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | DELTA: instantiating (110) with fresh symbol all_373_0 gives: % 146.71/20.29 | | | | | | | | (111) cons(all_373_0, all_371_0) = all_143_0 & % 146.71/20.29 | | | | | | | | ssItem(all_373_0) = 0 & $i(all_373_0) % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | ALPHA: (111) implies: % 146.71/20.29 | | | | | | | | (112) $i(all_373_0) % 146.71/20.29 | | | | | | | | (113) ssItem(all_373_0) = 0 % 146.71/20.29 | | | | | | | | % 146.71/20.29 | | | | | | | | GROUND_INST: instantiating (54) with all_343_0, simplifying with % 146.71/20.29 | | | | | | | | (67), (68) gives: % 146.71/20.30 | | | | | | | | (114) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! % 146.71/20.30 | | | | | | | | [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ! [v2: % 146.71/20.30 | | | | | | | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 146.71/20.30 | | | | | | | | (cons(all_343_0, v2) = v3) | ~ (app(v1, v3) = % 146.71/20.30 | | | | | | | | v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & % 146.71/20.30 | | | | | | | | ssList(v2) = v5) | ! [v5: $i] : ! [v6: $i] : % 146.71/20.30 | | | | | | | | ( ~ (v0 = all_343_0) | ~ (cons(all_343_0, v5) = % 146.71/20.30 | | | | | | | | v6) | ~ (app(v4, v6) = nil) | ~ $i(v5) | ? % 146.71/20.30 | | | | | | | | [v7: int] : ( ~ (v7 = 0) & ssList(v5) = v7))))) % 146.71/20.30 | | | | | | | | % 146.71/20.30 | | | | | | | | GROUND_INST: instantiating (32) with all_359_0, all_139_1, % 146.71/20.30 | | | | | | | | simplifying with (98), (100) gives: % 146.71/20.30 | | | | | | | | (115) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 & % 146.71/20.30 | | | | | | | | ssItem(all_359_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 146.71/20.30 | | | | | | | | all_359_0)) % 146.71/20.30 | | | | | | | | % 146.71/20.30 | | | | | | | | GROUND_INST: instantiating (7) with all_359_0, all_139_1, % 146.71/20.30 | | | | | | | | simplifying with (98), (100) gives: % 146.71/20.30 | | | | | | | | (116) ? [v0: any] : ? [v1: any] : (equalelemsP(all_139_1) = % 146.71/20.30 | | | | | | | | v1 & ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 146.71/20.30 | | | | | | | | % 146.71/20.30 | | | | | | | | GROUND_INST: instantiating (4) with all_359_0, all_139_1, % 146.71/20.30 | | | | | | | | simplifying with (98), (100) gives: % 146.71/20.30 | | | | | | | | (117) ? [v0: any] : ? [v1: any] : % 146.71/20.30 | | | | | | | | (strictorderedP(all_139_1) = v1 & ssItem(all_359_0) = % 146.71/20.30 | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 146.71/20.30 | | | | | | | | % 146.71/20.30 | | | | | | | | GROUND_INST: instantiating (3) with all_359_0, all_139_1, % 146.71/20.30 | | | | | | | | simplifying with (98), (100) gives: % 146.71/20.30 | | | | | | | | (118) ? [v0: any] : ? [v1: any] : (strictorderP(all_139_1) % 146.71/20.30 | | | | | | | | = v1 & ssItem(all_359_0) = v0 & ( ~ (v0 = 0) | v1 = % 146.71/20.30 | | | | | | | | 0)) % 146.71/20.30 | | | | | | | | % 146.71/20.30 | | | | | | | | GROUND_INST: instantiating (114) with all_373_0, simplifying % 146.71/20.30 | | | | | | | | with (112), (113) gives: % 146.71/20.30 | | | | | | | | (119) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! % 146.71/20.30 | | | | | | | | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 146.71/20.30 | | | | | | | | (cons(all_343_0, v1) = v2) | ~ (app(v0, v2) = v3) % 146.71/20.30 | | | | | | | | | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 146.71/20.30 | | | | | | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : ( % 146.71/20.30 | | | | | | | | ~ (all_373_0 = all_343_0) | ~ (cons(all_343_0, % 146.71/20.30 | | | | | | | | v4) = v5) | ~ (app(v3, v5) = nil) | ~ % 146.71/20.30 | | | | | | | | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v4) % 146.71/20.30 | | | | | | | | = v6)))) % 146.71/20.30 | | | | | | | | % 146.71/20.30 | | | | | | | | GROUND_INST: instantiating (119) with all_347_0, simplifying % 146.71/20.30 | | | | | | | | with (73), (74) gives: % 146.81/20.30 | | | | | | | | (120) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 146.81/20.30 | | | | | | | | (cons(all_343_0, v0) = v1) | ~ (app(all_347_0, v1) = % 146.81/20.30 | | | | | | | | v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 146.81/20.30 | | | | | | | | ssList(v0) = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 146.81/20.30 | | | | | | | | (all_373_0 = all_343_0) | ~ (cons(all_343_0, v3) = % 146.81/20.30 | | | | | | | | v4) | ~ (app(v2, v4) = nil) | ~ $i(v3) | ? % 146.81/20.30 | | | | | | | | [v5: int] : ( ~ (v5 = 0) & ssList(v3) = v5))) % 146.81/20.30 | | | | | | | | % 146.81/20.30 | | | | | | | | GROUND_INST: instantiating (120) with all_349_2, all_349_1, % 146.81/20.30 | | | | | | | | all_349_0, simplifying with (77), (78), (79) gives: % 146.81/20.30 | | | | | | | | (121) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_349_2) = v0) | % 146.81/20.30 | | | | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (all_373_0 = all_343_0) % 146.81/20.30 | | | | | | | | | ~ (cons(all_343_0, v0) = v1) | ~ (app(all_349_0, % 146.81/20.30 | | | | | | | | v1) = nil) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 146.81/20.30 | | | | | | | | 0) & ssList(v0) = v2)) % 146.81/20.30 | | | | | | | | % 146.81/20.30 | | | | | | | | DELTA: instantiating (116) with fresh symbols all_1603_0, % 146.81/20.30 | | | | | | | | all_1603_1 gives: % 146.81/20.30 | | | | | | | | (122) equalelemsP(all_139_1) = all_1603_0 & ssItem(all_359_0) % 146.81/20.30 | | | | | | | | = all_1603_1 & ( ~ (all_1603_1 = 0) | all_1603_0 = 0) % 146.81/20.30 | | | | | | | | % 146.81/20.30 | | | | | | | | ALPHA: (122) implies: % 146.81/20.30 | | | | | | | | (123) ssItem(all_359_0) = all_1603_1 % 146.81/20.30 | | | | | | | | % 146.81/20.30 | | | | | | | | DELTA: instantiating (117) with fresh symbols all_1607_0, % 146.81/20.30 | | | | | | | | all_1607_1 gives: % 146.81/20.30 | | | | | | | | (124) strictorderedP(all_139_1) = all_1607_0 & % 146.81/20.30 | | | | | | | | ssItem(all_359_0) = all_1607_1 & ( ~ (all_1607_1 = 0) | % 146.81/20.30 | | | | | | | | all_1607_0 = 0) % 146.81/20.30 | | | | | | | | % 146.81/20.30 | | | | | | | | ALPHA: (124) implies: % 146.81/20.30 | | | | | | | | (125) ssItem(all_359_0) = all_1607_1 % 146.81/20.30 | | | | | | | | (126) strictorderedP(all_139_1) = all_1607_0 % 146.81/20.30 | | | | | | | | (127) ~ (all_1607_1 = 0) | all_1607_0 = 0 % 146.81/20.30 | | | | | | | | % 146.81/20.30 | | | | | | | | DELTA: instantiating (118) with fresh symbols all_1609_0, % 146.81/20.30 | | | | | | | | all_1609_1 gives: % 146.81/20.30 | | | | | | | | (128) strictorderP(all_139_1) = all_1609_0 & % 146.81/20.30 | | | | | | | | ssItem(all_359_0) = all_1609_1 & ( ~ (all_1609_1 = 0) | % 146.81/20.30 | | | | | | | | all_1609_0 = 0) % 146.81/20.30 | | | | | | | | % 146.81/20.30 | | | | | | | | ALPHA: (128) implies: % 146.81/20.30 | | | | | | | | (129) ssItem(all_359_0) = all_1609_1 % 146.81/20.30 | | | | | | | | % 146.81/20.30 | | | | | | | | DELTA: instantiating (115) with fresh symbols all_1611_0, % 146.81/20.30 | | | | | | | | all_1611_1 gives: % 146.81/20.31 | | | | | | | | (130) hd(all_139_1) = all_1611_0 & ssItem(all_359_0) = % 146.81/20.31 | | | | | | | | all_1611_1 & $i(all_1611_0) & ( ~ (all_1611_1 = 0) | % 146.81/20.31 | | | | | | | | all_1611_0 = all_359_0) % 146.81/20.31 | | | | | | | | % 146.81/20.31 | | | | | | | | ALPHA: (130) implies: % 146.81/20.31 | | | | | | | | (131) ssItem(all_359_0) = all_1611_1 % 146.81/20.31 | | | | | | | | % 146.81/20.31 | | | | | | | | BETA: splitting (121) gives: % 146.81/20.31 | | | | | | | | % 146.81/20.31 | | | | | | | | Case 1: % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | (132) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_349_2) = v0) % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1708_0 gives: % 146.81/20.31 | | | | | | | | | (133) ~ (all_1708_0 = 0) & ssList(all_349_2) = all_1708_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (133) implies: % 146.81/20.31 | | | | | | | | | (134) ~ (all_1708_0 = 0) % 146.81/20.31 | | | | | | | | | (135) ssList(all_349_2) = all_1708_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1710_0 gives: % 146.81/20.31 | | | | | | | | | (136) ~ (all_1710_0 = 0) & ssList(all_349_2) = all_1710_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (136) implies: % 146.81/20.31 | | | | | | | | | (137) ssList(all_349_2) = all_1710_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1712_0 gives: % 146.81/20.31 | | | | | | | | | (138) ~ (all_1712_0 = 0) & ssList(all_349_2) = all_1712_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (138) implies: % 146.81/20.31 | | | | | | | | | (139) ssList(all_349_2) = all_1712_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1714_0 gives: % 146.81/20.31 | | | | | | | | | (140) ~ (all_1714_0 = 0) & ssList(all_349_2) = all_1714_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (140) implies: % 146.81/20.31 | | | | | | | | | (141) ssList(all_349_2) = all_1714_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1716_0 gives: % 146.81/20.31 | | | | | | | | | (142) ~ (all_1716_0 = 0) & ssList(all_349_2) = all_1716_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (142) implies: % 146.81/20.31 | | | | | | | | | (143) ssList(all_349_2) = all_1716_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1718_0 gives: % 146.81/20.31 | | | | | | | | | (144) ~ (all_1718_0 = 0) & ssList(all_349_2) = all_1718_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (144) implies: % 146.81/20.31 | | | | | | | | | (145) ssList(all_349_2) = all_1718_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1720_0 gives: % 146.81/20.31 | | | | | | | | | (146) ~ (all_1720_0 = 0) & ssList(all_349_2) = all_1720_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (146) implies: % 146.81/20.31 | | | | | | | | | (147) ssList(all_349_2) = all_1720_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1722_0 gives: % 146.81/20.31 | | | | | | | | | (148) ~ (all_1722_0 = 0) & ssList(all_349_2) = all_1722_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (148) implies: % 146.81/20.31 | | | | | | | | | (149) ssList(all_349_2) = all_1722_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | DELTA: instantiating (132) with fresh symbol all_1724_0 gives: % 146.81/20.31 | | | | | | | | | (150) ~ (all_1724_0 = 0) & ssList(all_349_2) = all_1724_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | ALPHA: (150) implies: % 146.81/20.31 | | | | | | | | | (151) ssList(all_349_2) = all_1724_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with all_1712_0, all_1714_0, % 146.81/20.31 | | | | | | | | | all_349_2, simplifying with (139), (141) gives: % 146.81/20.31 | | | | | | | | | (152) all_1714_0 = all_1712_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_1718_0, all_349_2, % 146.81/20.31 | | | | | | | | | simplifying with (80), (145) gives: % 146.81/20.31 | | | | | | | | | (153) all_1718_0 = 0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with all_1712_0, all_1718_0, % 146.81/20.31 | | | | | | | | | all_349_2, simplifying with (139), (145) gives: % 146.81/20.31 | | | | | | | | | (154) all_1718_0 = all_1712_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with all_1708_0, all_1720_0, % 146.81/20.31 | | | | | | | | | all_349_2, simplifying with (135), (147) gives: % 146.81/20.31 | | | | | | | | | (155) all_1720_0 = all_1708_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with all_1720_0, all_1722_0, % 146.81/20.31 | | | | | | | | | all_349_2, simplifying with (147), (149) gives: % 146.81/20.31 | | | | | | | | | (156) all_1722_0 = all_1720_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with all_1716_0, all_1722_0, % 146.81/20.31 | | | | | | | | | all_349_2, simplifying with (143), (149) gives: % 146.81/20.31 | | | | | | | | | (157) all_1722_0 = all_1716_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with all_1714_0, all_1722_0, % 146.81/20.31 | | | | | | | | | all_349_2, simplifying with (141), (149) gives: % 146.81/20.31 | | | | | | | | | (158) all_1722_0 = all_1714_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with all_1714_0, all_1724_0, % 146.81/20.31 | | | | | | | | | all_349_2, simplifying with (141), (151) gives: % 146.81/20.31 | | | | | | | | | (159) all_1724_0 = all_1714_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (11) with all_1710_0, all_1724_0, % 146.81/20.31 | | | | | | | | | all_349_2, simplifying with (137), (151) gives: % 146.81/20.31 | | | | | | | | | (160) all_1724_0 = all_1710_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (159), (160) imply: % 146.81/20.31 | | | | | | | | | (161) all_1714_0 = all_1710_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | SIMP: (161) implies: % 146.81/20.31 | | | | | | | | | (162) all_1714_0 = all_1710_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (157), (158) imply: % 146.81/20.31 | | | | | | | | | (163) all_1716_0 = all_1714_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (156), (157) imply: % 146.81/20.31 | | | | | | | | | (164) all_1720_0 = all_1716_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | SIMP: (164) implies: % 146.81/20.31 | | | | | | | | | (165) all_1720_0 = all_1716_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (155), (165) imply: % 146.81/20.31 | | | | | | | | | (166) all_1716_0 = all_1708_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | SIMP: (166) implies: % 146.81/20.31 | | | | | | | | | (167) all_1716_0 = all_1708_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (153), (154) imply: % 146.81/20.31 | | | | | | | | | (168) all_1712_0 = 0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | SIMP: (168) implies: % 146.81/20.31 | | | | | | | | | (169) all_1712_0 = 0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (163), (167) imply: % 146.81/20.31 | | | | | | | | | (170) all_1714_0 = all_1708_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | SIMP: (170) implies: % 146.81/20.31 | | | | | | | | | (171) all_1714_0 = all_1708_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (152), (162) imply: % 146.81/20.31 | | | | | | | | | (172) all_1712_0 = all_1710_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | SIMP: (172) implies: % 146.81/20.31 | | | | | | | | | (173) all_1712_0 = all_1710_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (162), (171) imply: % 146.81/20.31 | | | | | | | | | (174) all_1710_0 = all_1708_0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (169), (173) imply: % 146.81/20.31 | | | | | | | | | (175) all_1710_0 = 0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | SIMP: (175) implies: % 146.81/20.31 | | | | | | | | | (176) all_1710_0 = 0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | COMBINE_EQS: (174), (176) imply: % 146.81/20.31 | | | | | | | | | (177) all_1708_0 = 0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | SIMP: (177) implies: % 146.81/20.31 | | | | | | | | | (178) all_1708_0 = 0 % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | REDUCE: (134), (178) imply: % 146.81/20.31 | | | | | | | | | (179) $false % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | CLOSE: (179) is inconsistent. % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | Case 2: % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | % 146.81/20.31 | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_1609_1, all_359_0, % 146.81/20.31 | | | | | | | | | simplifying with (99), (129) gives: % 146.81/20.32 | | | | | | | | | (180) all_1609_1 = 0 % 146.81/20.32 | | | | | | | | | % 146.81/20.32 | | | | | | | | | GROUND_INST: instantiating (10) with all_1607_1, all_1609_1, % 146.81/20.32 | | | | | | | | | all_359_0, simplifying with (125), (129) gives: % 146.81/20.32 | | | | | | | | | (181) all_1609_1 = all_1607_1 % 146.81/20.32 | | | | | | | | | % 146.81/20.32 | | | | | | | | | GROUND_INST: instantiating (10) with all_1607_1, all_1611_1, % 146.81/20.32 | | | | | | | | | all_359_0, simplifying with (125), (131) gives: % 146.81/20.32 | | | | | | | | | (182) all_1611_1 = all_1607_1 % 146.81/20.32 | | | | | | | | | % 146.81/20.32 | | | | | | | | | GROUND_INST: instantiating (10) with all_1603_1, all_1611_1, % 146.81/20.32 | | | | | | | | | all_359_0, simplifying with (123), (131) gives: % 146.81/20.32 | | | | | | | | | (183) all_1611_1 = all_1603_1 % 146.81/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | | GROUND_INST: instantiating (12) with all_139_0, all_1607_0, % 146.88/20.32 | | | | | | | | | all_139_1, simplifying with (14), (126) gives: % 146.88/20.32 | | | | | | | | | (184) all_1607_0 = all_139_0 % 146.88/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | | COMBINE_EQS: (182), (183) imply: % 146.88/20.32 | | | | | | | | | (185) all_1607_1 = all_1603_1 % 146.88/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | | SIMP: (185) implies: % 146.88/20.32 | | | | | | | | | (186) all_1607_1 = all_1603_1 % 146.88/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | | COMBINE_EQS: (180), (181) imply: % 146.88/20.32 | | | | | | | | | (187) all_1607_1 = 0 % 146.88/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | | SIMP: (187) implies: % 146.88/20.32 | | | | | | | | | (188) all_1607_1 = 0 % 146.88/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | | COMBINE_EQS: (186), (188) imply: % 146.88/20.32 | | | | | | | | | (189) all_1603_1 = 0 % 146.88/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | | BETA: splitting (127) gives: % 146.88/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | | Case 1: % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | | (190) ~ (all_1607_1 = 0) % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | | REDUCE: (188), (190) imply: % 146.88/20.32 | | | | | | | | | | (191) $false % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | | CLOSE: (191) is inconsistent. % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | Case 2: % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | | (192) all_1607_0 = 0 % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | | COMBINE_EQS: (184), (192) imply: % 146.88/20.32 | | | | | | | | | | (193) all_139_0 = 0 % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | | SIMP: (193) implies: % 146.88/20.32 | | | | | | | | | | (194) all_139_0 = 0 % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | | REDUCE: (26), (194) imply: % 146.88/20.32 | | | | | | | | | | (195) $false % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | | CLOSE: (195) is inconsistent. % 146.88/20.32 | | | | | | | | | | % 146.88/20.32 | | | | | | | | | End of split % 146.88/20.32 | | | | | | | | | % 146.88/20.32 | | | | | | | | End of split % 146.88/20.32 | | | | | | | | % 146.88/20.32 | | | | | | | End of split % 146.88/20.32 | | | | | | | % 146.88/20.32 | | | | | | Case 2: % 146.88/20.32 | | | | | | | % 146.88/20.32 | | | | | | | (196) ~ (all_147_0 = 0) % 146.88/20.32 | | | | | | | % 146.88/20.32 | | | | | | | REDUCE: (95), (196) imply: % 146.88/20.32 | | | | | | | (197) $false % 146.88/20.32 | | | | | | | % 146.88/20.32 | | | | | | | CLOSE: (197) is inconsistent. % 146.88/20.32 | | | | | | | % 146.88/20.32 | | | | | | End of split % 146.88/20.32 | | | | | | % 146.88/20.32 | | | | | End of split % 146.88/20.32 | | | | | % 146.88/20.32 | | | | End of split % 146.88/20.32 | | | | % 146.88/20.32 | | | End of split % 146.88/20.32 | | | % 146.88/20.32 | | End of split % 146.88/20.32 | | % 146.88/20.32 | End of split % 146.88/20.32 | % 146.88/20.32 End of proof % 146.88/20.32 % 146.88/20.32 Sub-proof #1 shows that the following formulas are inconsistent: % 146.88/20.32 ---------------------------------------------------------------- % 146.88/20.32 (1) ~ (all_364_0 = 0) & ssList(nil) = all_364_0 % 146.88/20.32 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 146.88/20.32 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 146.88/20.32 (3) ssList(nil) = 0 % 146.88/20.32 % 146.88/20.32 Begin of proof % 146.88/20.32 | % 146.88/20.32 | ALPHA: (1) implies: % 146.88/20.32 | (4) ~ (all_364_0 = 0) % 146.88/20.32 | (5) ssList(nil) = all_364_0 % 146.88/20.32 | % 146.88/20.32 | GROUND_INST: instantiating (2) with 0, all_364_0, nil, simplifying with (3), % 146.88/20.32 | (5) gives: % 146.88/20.32 | (6) all_364_0 = 0 % 146.88/20.32 | % 146.88/20.32 | REDUCE: (4), (6) imply: % 146.88/20.32 | (7) $false % 146.88/20.32 | % 146.88/20.32 | CLOSE: (7) is inconsistent. % 146.88/20.32 | % 146.88/20.32 End of proof % 146.88/20.32 % SZS output end Proof for theBenchmark % 146.88/20.32 % 146.88/20.32 19711ms %------------------------------------------------------------------------------