%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC294+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 : n028.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 20:50:41 EDT 2023 % Result : Theorem 79.08s 11.06s % Output : Proof 232.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWC294+1 : TPTP v8.1.2. Released v2.4.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Mon Aug 28 15:16:39 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.55/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.55/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.55/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.55/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.55/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.55/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.55/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.88/1.42 Prover 4: Preprocessing ... % 4.88/1.43 Prover 1: Preprocessing ... % 4.88/1.45 Prover 5: Preprocessing ... % 4.88/1.45 Prover 0: Preprocessing ... % 4.88/1.45 Prover 2: Preprocessing ... % 4.88/1.45 Prover 3: Preprocessing ... % 4.88/1.45 Prover 6: Preprocessing ... % 14.74/2.74 Prover 2: Proving ... % 15.66/2.81 Prover 5: Constructing countermodel ... % 15.66/2.82 Prover 6: Proving ... % 15.66/2.82 Prover 1: Constructing countermodel ... % 16.00/2.86 Prover 3: Constructing countermodel ... % 21.74/3.61 Prover 4: Constructing countermodel ... % 22.05/3.71 Prover 0: Proving ... % 73.32/10.31 Prover 2: stopped % 73.32/10.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.37/10.49 Prover 7: Preprocessing ... % 76.01/10.71 Prover 7: Constructing countermodel ... % 79.08/11.06 Prover 3: proved (10435ms) % 79.08/11.06 % 79.08/11.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 79.08/11.06 % 79.08/11.06 Prover 5: stopped % 79.08/11.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 79.08/11.07 Prover 6: stopped % 79.08/11.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 79.08/11.07 Prover 0: stopped % 79.08/11.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 79.57/11.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 80.33/11.25 Prover 8: Preprocessing ... % 80.33/11.26 Prover 11: Preprocessing ... % 80.79/11.28 Prover 10: Preprocessing ... % 81.05/11.33 Prover 13: Preprocessing ... % 81.81/11.41 Prover 10: Constructing countermodel ... % 82.32/11.51 Prover 13: Constructing countermodel ... % 82.32/11.53 Prover 8: Warning: ignoring some quantifiers % 82.32/11.54 Prover 8: Constructing countermodel ... % 87.45/12.22 Prover 11: Constructing countermodel ... % 110.95/15.26 Prover 13: stopped % 110.95/15.26 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 111.98/15.43 Prover 16: Preprocessing ... % 113.64/15.58 Prover 16: Constructing countermodel ... % 116.73/15.97 Prover 1: stopped % 116.73/15.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 117.77/16.06 Prover 19: Preprocessing ... % 120.95/16.50 Prover 19: Warning: ignoring some quantifiers % 121.39/16.54 Prover 19: Constructing countermodel ... % 144.92/19.73 Prover 19: stopped % 148.81/20.32 Prover 16: stopped % 189.87/27.96 Prover 4: stopped % 199.81/30.37 Prover 7: stopped % 230.73/39.36 Prover 8: Found proof (size 319) % 230.73/39.36 Prover 8: proved (28167ms) % 230.73/39.36 Prover 11: stopped % 230.73/39.37 Prover 10: stopped % 230.73/39.37 % 230.73/39.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 230.73/39.37 % 230.73/39.40 % SZS output start Proof for theBenchmark % 230.73/39.41 Assumptions after simplification: % 230.73/39.41 --------------------------------- % 230.73/39.41 % 230.73/39.41 (ax13) % 230.73/39.45 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 230.73/39.45 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 230.73/39.45 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 230.73/39.45 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 230.73/39.45 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 230.73/39.45 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 230.73/39.46 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 230.73/39.46 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 230.73/39.46 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 230.73/39.46 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 230.73/39.46 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 230.73/39.46 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 230.73/39.46 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 230.73/39.46 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 230.73/39.46 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 230.73/39.46 % 230.73/39.46 (ax15) % 230.73/39.46 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 230.73/39.46 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 230.73/39.46 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 230.73/39.46 % 230.73/39.46 (ax17) % 230.73/39.46 ssList(nil) = 0 & $i(nil) % 230.73/39.46 % 230.73/39.46 (ax2) % 230.73/39.46 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 230.73/39.46 ssItem(v1) = 0 & $i(v1))) % 230.73/39.46 % 230.73/39.46 (ax20) % 230.73/39.46 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 230.73/39.46 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 230.73/39.46 ssItem(v2) = 0 & $i(v2)))) % 230.73/39.46 % 230.73/39.46 (ax23) % 230.73/39.46 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 230.73/39.46 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 230.73/39.46 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 230.73/39.46 % 230.73/39.46 (ax25) % 230.73/39.47 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 230.73/39.47 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 230.73/39.47 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 230.73/39.47 % 230.73/39.47 (ax4) % 230.73/39.47 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | % 230.73/39.47 ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: $i] % 230.73/39.47 : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 | ! [v2: % 230.73/39.47 $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 230.73/39.47 0) & ssItem(v2) = v3))))) % 230.73/39.47 % 230.73/39.47 (ax54) % 230.73/39.47 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~ % 230.73/39.47 (segmentP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : % 230.73/39.47 (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 230.73/39.47 % 230.73/39.47 (ax57) % 230.73/39.47 $i(nil) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | % 230.73/39.47 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 230.73/39.47 % 230.73/39.47 (ax59) % 230.73/39.47 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 230.73/39.47 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 230.73/39.47 (v2 = 0) | v3 = 0))) % 230.73/39.47 % 230.73/39.47 (ax61) % 230.73/39.48 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 230.73/39.48 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 230.73/39.48 (v2 = 0) | v3 = 0))) % 230.73/39.48 % 230.73/39.48 (ax63) % 230.73/39.48 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 230.73/39.48 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 230.73/39.48 (v2 = 0) | v3 = 0))) % 230.73/39.48 % 230.73/39.48 (ax65) % 230.73/39.48 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 230.73/39.48 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 230.73/39.48 (v2 = 0) | v3 = 0))) % 230.73/39.48 % 230.73/39.48 (ax68) % 230.73/39.48 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 230.73/39.48 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 230.73/39.48 ~ (v2 = 0) | v3 = 0))) % 230.73/39.48 % 230.73/39.48 (ax69) % 230.73/39.48 strictorderedP(nil) = 0 & $i(nil) % 230.73/39.48 % 230.73/39.48 (ax7) % 230.73/39.48 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 230.73/39.48 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 230.73/39.48 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] : % 230.73/39.48 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] : % 230.73/39.48 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3: % 230.73/39.48 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5: % 230.73/39.48 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~ % 230.73/39.48 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & % 230.73/39.48 ssList(v5) = v6))))))) % 230.73/39.48 % 230.73/39.48 (ax71) % 230.73/39.49 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 230.73/39.49 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 230.73/39.49 ~ (v2 = 0) | v3 = 0))) % 230.73/39.49 % 230.73/39.49 (ax72) % 230.73/39.49 duplicatefreeP(nil) = 0 & $i(nil) % 230.73/39.49 % 230.73/39.49 (ax73) % 230.73/39.49 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 230.73/39.49 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 230.73/39.49 (v2 = 0) | v3 = 0))) % 230.73/39.49 % 230.73/39.49 (co1) % 230.73/39.49 $i(nil) & ? [v0: $i] : ? [v1: any] : (strictorderedP(v0) = v1 & ssList(v0) = % 230.73/39.49 0 & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4: % 230.73/39.49 any] : (singletonP(v3) = v4 & ssList(v3) = 0 & $i(v3) & ? [v5: any] : % 230.73/39.49 (v3 = v0 & ~ (v1 = 0) & segmentP(v2, v0) = 0 & neq(v2, nil) = v5 & ( ~ % 230.73/39.49 (v5 = 0) | v4 = 0))))) % 230.73/39.49 % 230.73/39.49 (function-axioms) % 231.10/39.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 231.10/39.51 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 231.10/39.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 231.10/39.51 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 231.10/39.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 231.10/39.51 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 231.10/39.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 231.10/39.51 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 231.10/39.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 231.10/39.51 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 231.10/39.51 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 231.10/39.51 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 231.10/39.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 231.10/39.51 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 231.10/39.51 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 231.10/39.51 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 231.10/39.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 231.10/39.51 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 231.10/39.51 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 231.10/39.51 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 231.10/39.51 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 231.10/39.51 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 231.10/39.51 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 231.10/39.51 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 231.10/39.51 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 231.10/39.51 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 231.10/39.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 231.10/39.51 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 231.10/39.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 231.10/39.51 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 231.10/39.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 231.10/39.51 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 231.10/39.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 231.10/39.51 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 231.10/39.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 231.10/39.51 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 231.10/39.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 231.10/39.51 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 231.10/39.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 231.10/39.51 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 231.10/39.51 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 231.10/39.51 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 231.10/39.51 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ? % 231.10/39.51 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ? % 231.10/39.51 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ? % 231.10/39.51 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ? % 231.10/39.51 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ? % 231.10/39.51 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2) % 231.10/39.51 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) = % 231.10/39.51 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 231.10/39.51 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 231.10/39.51 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 231.10/39.51 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 231.10/39.51 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 231.10/39.51 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 231.10/39.51 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 231.10/39.51 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 231.10/39.51 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 231.10/39.51 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 231.10/39.51 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 231.10/39.51 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 231.10/39.51 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 231.10/39.51 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0) % 231.10/39.51 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ? % 231.10/39.51 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 231.10/39.51 (hd(v0) = v1 & $i(v1)) % 231.10/39.51 % 231.10/39.51 Further assumptions not needed in the proof: % 231.10/39.51 -------------------------------------------- % 231.10/39.51 ax1, ax10, ax11, ax12, ax14, ax16, ax18, ax19, ax21, ax22, ax24, ax26, ax27, % 231.10/39.51 ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, % 231.10/39.51 ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, % 231.10/39.51 ax52, ax53, ax55, ax56, ax58, ax6, ax60, ax62, ax64, ax66, ax67, ax70, ax74, % 231.10/39.51 ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, ax86, % 231.10/39.51 ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 231.10/39.51 % 231.10/39.51 Those formulas are unsatisfiable: % 231.10/39.51 --------------------------------- % 231.10/39.51 % 231.10/39.51 Begin of proof % 231.10/39.51 | % 231.10/39.51 | ALPHA: (ax4) implies: % 231.10/39.52 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | ? % 231.10/39.52 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: % 231.10/39.52 | $i] : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 % 231.10/39.52 | | ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: % 231.10/39.52 | int] : ( ~ (v3 = 0) & ssItem(v2) = v3))))) % 231.10/39.52 | % 231.10/39.52 | ALPHA: (ax17) implies: % 231.10/39.52 | (2) ssList(nil) = 0 % 231.10/39.52 | % 231.10/39.52 | ALPHA: (ax20) implies: % 231.10/39.52 | (3) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 231.10/39.52 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 231.10/39.52 | ssItem(v2) = 0 & $i(v2)))) % 231.10/39.52 | % 231.10/39.52 | ALPHA: (ax57) implies: % 231.10/39.52 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ~ % 231.10/39.52 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 231.10/39.52 | % 231.10/39.52 | ALPHA: (ax59) implies: % 231.10/39.52 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.52 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 231.10/39.52 | ~ (v2 = 0) | v3 = 0))) % 231.10/39.52 | % 231.10/39.52 | ALPHA: (ax61) implies: % 231.10/39.52 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.52 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 231.10/39.52 | ( ~ (v2 = 0) | v3 = 0))) % 231.10/39.52 | % 231.10/39.52 | ALPHA: (ax63) implies: % 231.10/39.52 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.52 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 231.10/39.52 | ( ~ (v2 = 0) | v3 = 0))) % 231.10/39.52 | % 231.10/39.52 | ALPHA: (ax65) implies: % 231.10/39.53 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.53 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 231.10/39.53 | & ( ~ (v2 = 0) | v3 = 0))) % 231.10/39.53 | % 231.10/39.53 | ALPHA: (ax68) implies: % 231.10/39.53 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.53 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 231.10/39.53 | & ( ~ (v2 = 0) | v3 = 0))) % 231.10/39.53 | % 231.10/39.53 | ALPHA: (ax69) implies: % 231.10/39.53 | (10) strictorderedP(nil) = 0 % 231.10/39.53 | % 231.10/39.53 | ALPHA: (ax71) implies: % 231.10/39.53 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.53 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = % 231.10/39.53 | v2 & ( ~ (v2 = 0) | v3 = 0))) % 231.10/39.53 | % 231.10/39.53 | ALPHA: (ax72) implies: % 231.10/39.53 | (12) duplicatefreeP(nil) = 0 % 231.10/39.53 | % 231.10/39.53 | ALPHA: (ax73) implies: % 231.10/39.53 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.53 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 231.10/39.53 | ( ~ (v2 = 0) | v3 = 0))) % 231.10/39.53 | % 231.10/39.53 | ALPHA: (co1) implies: % 231.10/39.53 | (14) $i(nil) % 231.10/39.53 | (15) ? [v0: $i] : ? [v1: any] : (strictorderedP(v0) = v1 & ssList(v0) = 0 % 231.10/39.53 | & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? % 231.10/39.53 | [v4: any] : (singletonP(v3) = v4 & ssList(v3) = 0 & $i(v3) & ? % 231.10/39.53 | [v5: any] : (v3 = v0 & ~ (v1 = 0) & segmentP(v2, v0) = 0 & % 231.10/39.53 | neq(v2, nil) = v5 & ( ~ (v5 = 0) | v4 = 0))))) % 231.10/39.54 | % 231.10/39.54 | ALPHA: (function-axioms) implies: % 231.10/39.54 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 231.10/39.54 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 231.10/39.54 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 231.10/39.54 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 231.10/39.54 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 231.10/39.54 | : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = % 231.10/39.54 | v0)) % 231.10/39.54 | % 231.10/39.54 | DELTA: instantiating (ax2) with fresh symbol all_137_0 gives: % 231.10/39.54 | (19) ssItem(all_137_0) = 0 & $i(all_137_0) & ? [v0: any] : ( ~ (v0 = % 231.10/39.54 | all_137_0) & ssItem(v0) = 0 & $i(v0)) % 231.10/39.54 | % 231.10/39.54 | ALPHA: (19) implies: % 231.10/39.54 | (20) $i(all_137_0) % 231.10/39.54 | (21) ssItem(all_137_0) = 0 % 231.10/39.54 | % 231.10/39.54 | DELTA: instantiating (15) with fresh symbols all_139_0, all_139_1 gives: % 231.10/39.54 | (22) strictorderedP(all_139_1) = all_139_0 & ssList(all_139_1) = 0 & % 231.10/39.54 | $i(all_139_1) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 231.10/39.54 | ? [v2: any] : (singletonP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? % 231.10/39.54 | [v3: any] : (v1 = all_139_1 & ~ (all_139_0 = 0) & segmentP(v0, % 231.10/39.54 | all_139_1) = 0 & neq(v0, nil) = v3 & ( ~ (v3 = 0) | v2 = 0)))) % 231.10/39.54 | % 231.10/39.54 | ALPHA: (22) implies: % 231.10/39.54 | (23) strictorderedP(all_139_1) = all_139_0 % 231.10/39.54 | (24) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 231.10/39.54 | (singletonP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? [v3: any] : (v1 % 231.10/39.54 | = all_139_1 & ~ (all_139_0 = 0) & segmentP(v0, all_139_1) = 0 & % 231.10/39.54 | neq(v0, nil) = v3 & ( ~ (v3 = 0) | v2 = 0)))) % 231.10/39.54 | % 231.10/39.54 | DELTA: instantiating (24) with fresh symbol all_143_0 gives: % 231.10/39.54 | (25) ssList(all_143_0) = 0 & $i(all_143_0) & ? [v0: $i] : ? [v1: any] : % 231.10/39.54 | (singletonP(v0) = v1 & ssList(v0) = 0 & $i(v0) & ? [v2: any] : (v0 = % 231.10/39.54 | all_139_1 & ~ (all_139_0 = 0) & segmentP(all_143_0, all_139_1) = % 231.10/39.54 | 0 & neq(all_143_0, nil) = v2 & ( ~ (v2 = 0) | v1 = 0))) % 231.10/39.54 | % 231.10/39.54 | ALPHA: (25) implies: % 231.10/39.54 | (26) $i(all_143_0) % 231.10/39.54 | (27) ssList(all_143_0) = 0 % 231.10/39.54 | (28) ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 & % 231.10/39.54 | $i(v0) & ? [v2: any] : (v0 = all_139_1 & ~ (all_139_0 = 0) & % 231.10/39.54 | segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) = v2 & ( % 231.10/39.54 | ~ (v2 = 0) | v1 = 0))) % 231.10/39.54 | % 231.10/39.54 | DELTA: instantiating (28) with fresh symbols all_145_0, all_145_1 gives: % 231.10/39.54 | (29) singletonP(all_145_1) = all_145_0 & ssList(all_145_1) = 0 & % 231.10/39.54 | $i(all_145_1) & ? [v0: any] : (all_145_1 = all_139_1 & ~ (all_139_0 % 231.10/39.54 | = 0) & segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) = % 231.10/39.54 | v0 & ( ~ (v0 = 0) | all_145_0 = 0)) % 231.10/39.54 | % 231.10/39.54 | ALPHA: (29) implies: % 231.10/39.54 | (30) $i(all_145_1) % 231.10/39.54 | (31) ssList(all_145_1) = 0 % 231.10/39.55 | (32) singletonP(all_145_1) = all_145_0 % 231.10/39.55 | (33) ? [v0: any] : (all_145_1 = all_139_1 & ~ (all_139_0 = 0) & % 231.10/39.55 | segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) = v0 & ( ~ % 231.10/39.55 | (v0 = 0) | all_145_0 = 0)) % 231.10/39.55 | % 231.10/39.55 | DELTA: instantiating (33) with fresh symbol all_147_0 gives: % 231.10/39.55 | (34) all_145_1 = all_139_1 & ~ (all_139_0 = 0) & segmentP(all_143_0, % 231.10/39.55 | all_139_1) = 0 & neq(all_143_0, nil) = all_147_0 & ( ~ (all_147_0 = % 231.10/39.55 | 0) | all_145_0 = 0) % 231.10/39.55 | % 231.10/39.55 | ALPHA: (34) implies: % 231.10/39.55 | (35) all_145_1 = all_139_1 % 231.10/39.55 | (36) ~ (all_139_0 = 0) % 231.10/39.55 | (37) neq(all_143_0, nil) = all_147_0 % 231.10/39.55 | (38) segmentP(all_143_0, all_139_1) = 0 % 231.10/39.55 | (39) ~ (all_147_0 = 0) | all_145_0 = 0 % 231.10/39.55 | % 231.10/39.55 | REDUCE: (32), (35) imply: % 231.10/39.55 | (40) singletonP(all_139_1) = all_145_0 % 231.10/39.55 | % 231.10/39.55 | REDUCE: (31), (35) imply: % 231.10/39.55 | (41) ssList(all_139_1) = 0 % 231.10/39.55 | % 231.10/39.55 | REDUCE: (30), (35) imply: % 231.10/39.55 | (42) $i(all_139_1) % 231.10/39.55 | % 231.10/39.55 | GROUND_INST: instantiating (ax25) with nil, simplifying with (2), (14) gives: % 231.10/39.55 | (43) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.55 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 231.10/39.55 | ( ~ (v2 = 0) | v3 = nil))) % 231.10/39.55 | % 231.10/39.55 | GROUND_INST: instantiating (ax23) with nil, simplifying with (2), (14) gives: % 231.10/39.55 | (44) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 231.10/39.55 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 231.10/39.55 | ( ~ (v2 = 0) | v3 = v0))) % 231.10/39.55 | % 231.10/39.55 | GROUND_INST: instantiating (3) with all_139_1, simplifying with (41), (42) % 231.10/39.55 | gives: % 231.10/39.55 | (45) all_139_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 231.10/39.55 | : (cons(v1, v0) = all_139_1 & ssItem(v1) = 0 & $i(v1))) % 231.10/39.55 | % 231.10/39.55 | GROUND_INST: instantiating (3) with all_143_0, simplifying with (26), (27) % 231.10/39.55 | gives: % 231.10/39.55 | (46) all_143_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 231.10/39.55 | : (cons(v1, v0) = all_143_0 & ssItem(v1) = 0 & $i(v1))) % 231.10/39.55 | % 231.10/39.55 | GROUND_INST: instantiating (ax7) with all_143_0, simplifying with (26), (27) % 231.10/39.55 | gives: % 231.10/39.55 | (47) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_143_0, v0) = v1) | ~ % 231.10/39.55 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 231.10/39.55 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0) % 231.10/39.55 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 & % 231.10/39.55 | app(v3, v4) = all_143_0 & $i(v4)))) & (v1 = 0 | ! [v2: $i] % 231.10/39.55 | : ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: % 231.10/39.55 | int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ % 231.10/39.55 | (app(v3, v4) = all_143_0) | ~ $i(v4) | ? [v5: int] : ( ~ % 231.10/39.55 | (v5 = 0) & ssList(v4) = v5)))))) % 231.10/39.55 | % 231.10/39.55 | GROUND_INST: instantiating (ax15) with all_143_0, simplifying with (26), (27) % 231.10/39.55 | gives: % 231.10/39.55 | (48) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_143_0, v0) = v1) | ~ $i(v0) % 231.10/39.55 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 231.10/39.55 | ~ (v0 = all_143_0)) & (v1 = 0 | v0 = all_143_0))) % 231.10/39.55 | % 231.10/39.55 | GROUND_INST: instantiating (ax54) with all_143_0, simplifying with (26), (27) % 231.10/39.55 | gives: % 231.10/39.56 | (49) ! [v0: any] : (v0 = all_143_0 | ~ (segmentP(all_143_0, v0) = 0) | ~ % 231.10/39.56 | $i(v0) | ? [v1: any] : ? [v2: any] : (segmentP(v0, all_143_0) = v2 % 231.10/39.56 | & ssList(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 231.10/39.56 | % 231.10/39.56 | GROUND_INST: instantiating (1) with all_139_1, all_145_0, simplifying with % 231.10/39.56 | (40), (42) gives: % 231.10/39.56 | (50) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) | (( ~ % 231.10/39.56 | (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_139_1 & % 231.10/39.56 | ssItem(v0) = 0 & $i(v0))) & (all_145_0 = 0 | ! [v0: $i] : ( ~ % 231.10/39.56 | (cons(v0, nil) = all_139_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 231.10/39.56 | = 0) & ssItem(v0) = v1)))) % 231.10/39.56 | % 231.10/39.56 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (12), (14) % 231.10/39.56 | gives: % 231.10/39.56 | (51) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 231.10/39.56 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 231.10/39.56 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 231.10/39.56 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 231.10/39.56 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 231.10/39.56 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 231.10/39.56 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 231.10/39.56 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 231.10/39.56 | v8)))))) % 231.10/39.56 | % 231.10/39.56 | GROUND_INST: instantiating (49) with all_139_1, simplifying with (38), (42) % 231.10/39.56 | gives: % 231.10/39.56 | (52) all_143_0 = all_139_1 | ? [v0: any] : ? [v1: any] : % 231.10/39.56 | (segmentP(all_139_1, all_143_0) = v1 & ssList(all_139_1) = v0 & ( ~ % 231.10/39.56 | (v1 = 0) | ~ (v0 = 0))) % 231.10/39.56 | % 231.10/39.56 | GROUND_INST: instantiating (48) with nil, all_147_0, simplifying with (14), % 231.10/39.56 | (37) gives: % 231.10/39.56 | (53) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_147_0 = 0) % 231.10/39.56 | | ~ (all_143_0 = nil)) & (all_147_0 = 0 | all_143_0 = nil)) % 231.10/39.56 | % 231.10/39.56 | GROUND_INST: instantiating (47) with all_139_1, 0, simplifying with (38), (42) % 231.10/39.56 | gives: % 231.10/39.56 | (54) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_139_1) = v1 % 231.10/39.56 | & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & app(v1, v2) = % 231.10/39.56 | all_143_0 & $i(v2))) | ? [v0: int] : ( ~ (v0 = 0) & % 231.10/39.56 | ssList(all_139_1) = v0) % 231.10/39.56 | % 231.10/39.56 | BETA: splitting (51) gives: % 231.10/39.56 | % 231.10/39.56 | Case 1: % 231.10/39.56 | | % 231.10/39.56 | | (55) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 231.10/39.56 | | % 231.10/39.56 | | DELTA: instantiating (55) with fresh symbol all_380_0 gives: % 231.10/39.56 | | (56) ~ (all_380_0 = 0) & ssList(nil) = all_380_0 % 231.10/39.56 | | % 231.10/39.56 | | REF_CLOSE: (2), (17), (56) are inconsistent by sub-proof #3. % 231.10/39.56 | | % 231.10/39.56 | Case 2: % 231.10/39.56 | | % 231.10/39.56 | | (57) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 231.10/39.56 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 231.10/39.56 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 231.10/39.56 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 231.10/39.56 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 231.10/39.56 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 231.10/39.56 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 231.10/39.56 | | 0) & ssList(v6) = v8)))))) % 231.10/39.56 | | % 231.10/39.56 | | BETA: splitting (54) gives: % 231.10/39.56 | | % 231.10/39.56 | | Case 1: % 231.10/39.56 | | | % 231.10/39.56 | | | (58) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_139_1) = % 231.10/39.56 | | | v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & app(v1, % 231.10/39.56 | | | v2) = all_143_0 & $i(v2))) % 231.10/39.56 | | | % 231.10/39.56 | | | DELTA: instantiating (58) with fresh symbols all_341_0, all_341_1 gives: % 231.10/39.56 | | | (59) ssList(all_341_1) = 0 & app(all_341_1, all_139_1) = all_341_0 & % 231.10/39.56 | | | $i(all_341_0) & $i(all_341_1) & ? [v0: $i] : (ssList(v0) = 0 & % 231.10/39.56 | | | app(all_341_0, v0) = all_143_0 & $i(v0)) % 231.10/39.56 | | | % 231.10/39.56 | | | ALPHA: (59) implies: % 231.10/39.56 | | | (60) $i(all_341_1) % 231.10/39.57 | | | (61) app(all_341_1, all_139_1) = all_341_0 % 231.10/39.57 | | | (62) ssList(all_341_1) = 0 % 231.10/39.57 | | | % 231.10/39.57 | | | BETA: splitting (39) gives: % 231.10/39.57 | | | % 231.10/39.57 | | | Case 1: % 231.10/39.57 | | | | % 231.10/39.57 | | | | (63) ~ (all_147_0 = 0) % 231.10/39.57 | | | | % 231.10/39.57 | | | | BETA: splitting (53) gives: % 231.10/39.57 | | | | % 231.10/39.57 | | | | Case 1: % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | (64) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | DELTA: instantiating (64) with fresh symbol all_380_0 gives: % 231.10/39.57 | | | | | (65) ~ (all_380_0 = 0) & ssList(nil) = all_380_0 % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | REF_CLOSE: (2), (17), (65) are inconsistent by sub-proof #3. % 231.10/39.57 | | | | | % 231.10/39.57 | | | | Case 2: % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | (66) ( ~ (all_147_0 = 0) | ~ (all_143_0 = nil)) & (all_147_0 = 0 | % 231.10/39.57 | | | | | all_143_0 = nil) % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | ALPHA: (66) implies: % 231.10/39.57 | | | | | (67) all_147_0 = 0 | all_143_0 = nil % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | BETA: splitting (67) gives: % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | Case 1: % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | (68) all_143_0 = nil % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | REF_CLOSE: (4), (10), (17), (18), (23), (36), (41), (42), (45), % 231.10/39.57 | | | | | | (52), (68) are inconsistent by sub-proof #1. % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | Case 2: % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | (69) all_147_0 = 0 % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | REDUCE: (63), (69) imply: % 231.10/39.57 | | | | | | (70) $false % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | CLOSE: (70) is inconsistent. % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | End of split % 231.10/39.57 | | | | | % 231.10/39.57 | | | | End of split % 231.10/39.57 | | | | % 231.10/39.57 | | | Case 2: % 231.10/39.57 | | | | % 231.10/39.57 | | | | (71) all_145_0 = 0 % 231.10/39.57 | | | | % 231.10/39.57 | | | | BETA: splitting (50) gives: % 231.10/39.57 | | | | % 231.10/39.57 | | | | Case 1: % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | (72) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | REF_CLOSE: (17), (41), (72) are inconsistent by sub-proof #2. % 231.10/39.57 | | | | | % 231.10/39.57 | | | | Case 2: % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | (73) ( ~ (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_139_1 % 231.10/39.57 | | | | | & ssItem(v0) = 0 & $i(v0))) & (all_145_0 = 0 | ! [v0: $i] % 231.10/39.57 | | | | | : ( ~ (cons(v0, nil) = all_139_1) | ~ $i(v0) | ? [v1: int] % 231.10/39.57 | | | | | : ( ~ (v1 = 0) & ssItem(v0) = v1))) % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | ALPHA: (73) implies: % 231.10/39.57 | | | | | (74) ~ (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_139_1 % 231.10/39.57 | | | | | & ssItem(v0) = 0 & $i(v0)) % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | BETA: splitting (46) gives: % 231.10/39.57 | | | | | % 231.10/39.57 | | | | | Case 1: % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | (75) all_143_0 = nil % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | REF_CLOSE: (4), (10), (17), (18), (23), (36), (41), (42), (45), % 231.10/39.57 | | | | | | (52), (75) are inconsistent by sub-proof #1. % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | Case 2: % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | (76) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 231.10/39.57 | | | | | | (cons(v1, v0) = all_143_0 & ssItem(v1) = 0 & $i(v1))) % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | DELTA: instantiating (76) with fresh symbol all_388_0 gives: % 231.10/39.57 | | | | | | (77) ssList(all_388_0) = 0 & $i(all_388_0) & ? [v0: $i] : % 231.10/39.57 | | | | | | (cons(v0, all_388_0) = all_143_0 & ssItem(v0) = 0 & $i(v0)) % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | ALPHA: (77) implies: % 231.10/39.57 | | | | | | (78) $i(all_388_0) % 231.10/39.57 | | | | | | (79) ssList(all_388_0) = 0 % 231.10/39.57 | | | | | | (80) ? [v0: $i] : (cons(v0, all_388_0) = all_143_0 & ssItem(v0) % 231.10/39.57 | | | | | | = 0 & $i(v0)) % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | DELTA: instantiating (80) with fresh symbol all_390_0 gives: % 231.10/39.57 | | | | | | (81) cons(all_390_0, all_388_0) = all_143_0 & ssItem(all_390_0) = % 231.10/39.57 | | | | | | 0 & $i(all_390_0) % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | ALPHA: (81) implies: % 231.10/39.57 | | | | | | (82) $i(all_390_0) % 231.10/39.57 | | | | | | (83) ssItem(all_390_0) = 0 % 231.10/39.57 | | | | | | (84) cons(all_390_0, all_388_0) = all_143_0 % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | BETA: splitting (74) gives: % 231.10/39.57 | | | | | | % 231.10/39.57 | | | | | | Case 1: % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | | (85) ~ (all_145_0 = 0) % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | | REDUCE: (71), (85) imply: % 231.10/39.57 | | | | | | | (86) $false % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | | CLOSE: (86) is inconsistent. % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | Case 2: % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | | (87) ? [v0: $i] : (cons(v0, nil) = all_139_1 & ssItem(v0) = 0 % 231.10/39.57 | | | | | | | & $i(v0)) % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | | DELTA: instantiating (87) with fresh symbol all_395_0 gives: % 231.10/39.57 | | | | | | | (88) cons(all_395_0, nil) = all_139_1 & ssItem(all_395_0) = 0 & % 231.10/39.57 | | | | | | | $i(all_395_0) % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | | ALPHA: (88) implies: % 231.10/39.57 | | | | | | | (89) $i(all_395_0) % 231.10/39.57 | | | | | | | (90) ssItem(all_395_0) = 0 % 231.10/39.57 | | | | | | | (91) cons(all_395_0, nil) = all_139_1 % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | | BETA: splitting (52) gives: % 231.10/39.57 | | | | | | | % 231.10/39.57 | | | | | | | Case 1: % 231.10/39.57 | | | | | | | | % 231.10/39.57 | | | | | | | | (92) all_143_0 = all_139_1 % 231.10/39.57 | | | | | | | | % 231.10/39.57 | | | | | | | | REDUCE: (84), (92) imply: % 231.10/39.57 | | | | | | | | (93) cons(all_390_0, all_388_0) = all_139_1 % 231.10/39.57 | | | | | | | | % 231.10/39.57 | | | | | | | | GROUND_INST: instantiating (57) with all_390_0, simplifying with % 231.10/39.57 | | | | | | | | (82), (83) gives: % 231.10/39.58 | | | | | | | | (94) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: % 231.10/39.58 | | | | | | | | $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ! [v2: $i] % 231.10/39.58 | | | | | | | | : ! [v3: $i] : ! [v4: $i] : ( ~ (cons(all_390_0, % 231.10/39.58 | | | | | | | | v2) = v3) | ~ (app(v1, v3) = v4) | ~ $i(v2) % 231.10/39.58 | | | | | | | | | ? [v5: int] : ( ~ (v5 = 0) & ssList(v2) = v5) | % 231.10/39.58 | | | | | | | | ! [v5: $i] : ! [v6: $i] : ( ~ (v0 = all_390_0) | % 231.10/39.58 | | | | | | | | ~ (cons(all_390_0, v5) = v6) | ~ (app(v4, v6) % 231.10/39.58 | | | | | | | | = nil) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = % 231.10/39.58 | | | | | | | | 0) & ssList(v5) = v7))))) % 231.10/39.58 | | | | | | | | % 231.10/39.58 | | | | | | | | GROUND_INST: instantiating (43) with all_395_0, all_139_1, % 231.10/39.58 | | | | | | | | simplifying with (89), (91) gives: % 231.86/39.58 | | | | | | | | (95) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 & % 231.86/39.58 | | | | | | | | ssItem(all_395_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 231.86/39.58 | | | | | | | | nil)) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (44) with all_395_0, all_139_1, % 231.86/39.58 | | | | | | | | simplifying with (89), (91) gives: % 231.86/39.58 | | | | | | | | (96) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 & % 231.86/39.58 | | | | | | | | ssItem(all_395_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 231.86/39.58 | | | | | | | | all_395_0)) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (13) with all_395_0, all_139_1, % 231.86/39.58 | | | | | | | | simplifying with (89), (91) gives: % 231.86/39.58 | | | | | | | | (97) ? [v0: any] : ? [v1: any] : (equalelemsP(all_139_1) = % 231.86/39.58 | | | | | | | | v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (9) with all_395_0, all_139_1, % 231.86/39.58 | | | | | | | | simplifying with (89), (91) gives: % 231.86/39.58 | | | | | | | | (98) ? [v0: any] : ? [v1: any] : (strictorderedP(all_139_1) % 231.86/39.58 | | | | | | | | = v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = % 231.86/39.58 | | | | | | | | 0)) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (8) with all_395_0, all_139_1, % 231.86/39.58 | | | | | | | | simplifying with (89), (91) gives: % 231.86/39.58 | | | | | | | | (99) ? [v0: any] : ? [v1: any] : (totalorderedP(all_139_1) % 231.86/39.58 | | | | | | | | = v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = % 231.86/39.58 | | | | | | | | 0)) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (7) with all_395_0, all_139_1, % 231.86/39.58 | | | | | | | | simplifying with (89), (91) gives: % 231.86/39.58 | | | | | | | | (100) ? [v0: any] : ? [v1: any] : (strictorderP(all_139_1) % 231.86/39.58 | | | | | | | | = v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = % 231.86/39.58 | | | | | | | | 0)) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (6) with all_395_0, all_139_1, % 231.86/39.58 | | | | | | | | simplifying with (89), (91) gives: % 231.86/39.58 | | | | | | | | (101) ? [v0: any] : ? [v1: any] : (totalorderP(all_139_1) = % 231.86/39.58 | | | | | | | | v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (5) with all_395_0, all_139_1, % 231.86/39.58 | | | | | | | | simplifying with (89), (91) gives: % 231.86/39.58 | | | | | | | | (102) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_139_1) = % 231.86/39.58 | | | | | | | | v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (94) with all_137_0, simplifying with % 231.86/39.58 | | | | | | | | (20), (21) gives: % 231.86/39.58 | | | | | | | | (103) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! % 231.86/39.58 | | | | | | | | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 231.86/39.58 | | | | | | | | (cons(all_390_0, v1) = v2) | ~ (app(v0, v2) = v3) % 231.86/39.58 | | | | | | | | | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 231.86/39.58 | | | | | | | | ssList(v1) = v4) | ! [v4: $i] : ! [v5: $i] : ( % 231.86/39.58 | | | | | | | | ~ (all_390_0 = all_137_0) | ~ (cons(all_137_0, % 231.86/39.58 | | | | | | | | v4) = v5) | ~ (app(v3, v5) = nil) | ~ % 231.86/39.58 | | | | | | | | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v4) % 231.86/39.58 | | | | | | | | = v6)))) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (103) with all_341_1, simplifying % 231.86/39.58 | | | | | | | | with (60), (62) gives: % 231.86/39.58 | | | | | | | | (104) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 231.86/39.58 | | | | | | | | (cons(all_390_0, v0) = v1) | ~ (app(all_341_1, v1) = % 231.86/39.58 | | | | | | | | v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 231.86/39.58 | | | | | | | | ssList(v0) = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 231.86/39.58 | | | | | | | | (all_390_0 = all_137_0) | ~ (cons(all_137_0, v3) = % 231.86/39.58 | | | | | | | | v4) | ~ (app(v2, v4) = nil) | ~ $i(v3) | ? % 231.86/39.58 | | | | | | | | [v5: int] : ( ~ (v5 = 0) & ssList(v3) = v5))) % 231.86/39.58 | | | | | | | | % 231.86/39.58 | | | | | | | | GROUND_INST: instantiating (104) with all_388_0, all_139_1, % 231.86/39.58 | | | | | | | | all_341_0, simplifying with (61), (78), (93) gives: % 231.89/39.58 | | | | | | | | (105) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_388_0) = v0) | % 231.89/39.58 | | | | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (all_390_0 = all_137_0) % 231.89/39.58 | | | | | | | | | ~ (cons(all_137_0, v0) = v1) | ~ (app(all_341_0, % 231.89/39.58 | | | | | | | | v1) = nil) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 231.89/39.58 | | | | | | | | 0) & ssList(v0) = v2)) % 231.89/39.58 | | | | | | | | % 231.89/39.58 | | | | | | | | DELTA: instantiating (97) with fresh symbols all_1827_0, % 231.89/39.58 | | | | | | | | all_1827_1 gives: % 231.89/39.58 | | | | | | | | (106) equalelemsP(all_139_1) = all_1827_0 & ssItem(all_395_0) % 231.89/39.58 | | | | | | | | = all_1827_1 & ( ~ (all_1827_1 = 0) | all_1827_0 = 0) % 231.89/39.58 | | | | | | | | % 231.89/39.58 | | | | | | | | ALPHA: (106) implies: % 231.89/39.58 | | | | | | | | (107) ssItem(all_395_0) = all_1827_1 % 231.89/39.58 | | | | | | | | % 231.89/39.58 | | | | | | | | DELTA: instantiating (102) with fresh symbols all_1829_0, % 231.89/39.58 | | | | | | | | all_1829_1 gives: % 231.89/39.58 | | | | | | | | (108) cyclefreeP(all_139_1) = all_1829_0 & ssItem(all_395_0) % 231.89/39.58 | | | | | | | | = all_1829_1 & ( ~ (all_1829_1 = 0) | all_1829_0 = 0) % 231.89/39.58 | | | | | | | | % 231.89/39.58 | | | | | | | | ALPHA: (108) implies: % 231.89/39.58 | | | | | | | | (109) ssItem(all_395_0) = all_1829_1 % 231.89/39.58 | | | | | | | | % 231.89/39.58 | | | | | | | | DELTA: instantiating (101) with fresh symbols all_1831_0, % 231.89/39.58 | | | | | | | | all_1831_1 gives: % 231.89/39.58 | | | | | | | | (110) totalorderP(all_139_1) = all_1831_0 & ssItem(all_395_0) % 231.89/39.58 | | | | | | | | = all_1831_1 & ( ~ (all_1831_1 = 0) | all_1831_0 = 0) % 231.89/39.58 | | | | | | | | % 231.89/39.58 | | | | | | | | ALPHA: (110) implies: % 231.89/39.59 | | | | | | | | (111) ssItem(all_395_0) = all_1831_1 % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | DELTA: instantiating (100) with fresh symbols all_1833_0, % 231.89/39.59 | | | | | | | | all_1833_1 gives: % 231.89/39.59 | | | | | | | | (112) strictorderP(all_139_1) = all_1833_0 & % 231.89/39.59 | | | | | | | | ssItem(all_395_0) = all_1833_1 & ( ~ (all_1833_1 = 0) | % 231.89/39.59 | | | | | | | | all_1833_0 = 0) % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | ALPHA: (112) implies: % 231.89/39.59 | | | | | | | | (113) ssItem(all_395_0) = all_1833_1 % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | DELTA: instantiating (99) with fresh symbols all_1835_0, % 231.89/39.59 | | | | | | | | all_1835_1 gives: % 231.89/39.59 | | | | | | | | (114) totalorderedP(all_139_1) = all_1835_0 & % 231.89/39.59 | | | | | | | | ssItem(all_395_0) = all_1835_1 & ( ~ (all_1835_1 = 0) | % 231.89/39.59 | | | | | | | | all_1835_0 = 0) % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | ALPHA: (114) implies: % 231.89/39.59 | | | | | | | | (115) ssItem(all_395_0) = all_1835_1 % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | DELTA: instantiating (98) with fresh symbols all_1837_0, % 231.89/39.59 | | | | | | | | all_1837_1 gives: % 231.89/39.59 | | | | | | | | (116) strictorderedP(all_139_1) = all_1837_0 & % 231.89/39.59 | | | | | | | | ssItem(all_395_0) = all_1837_1 & ( ~ (all_1837_1 = 0) | % 231.89/39.59 | | | | | | | | all_1837_0 = 0) % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | ALPHA: (116) implies: % 231.89/39.59 | | | | | | | | (117) ssItem(all_395_0) = all_1837_1 % 231.89/39.59 | | | | | | | | (118) strictorderedP(all_139_1) = all_1837_0 % 231.89/39.59 | | | | | | | | (119) ~ (all_1837_1 = 0) | all_1837_0 = 0 % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | DELTA: instantiating (96) with fresh symbols all_1839_0, % 231.89/39.59 | | | | | | | | all_1839_1 gives: % 231.89/39.59 | | | | | | | | (120) hd(all_139_1) = all_1839_0 & ssItem(all_395_0) = % 231.89/39.59 | | | | | | | | all_1839_1 & $i(all_1839_0) & ( ~ (all_1839_1 = 0) | % 231.89/39.59 | | | | | | | | all_1839_0 = all_395_0) % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | ALPHA: (120) implies: % 231.89/39.59 | | | | | | | | (121) ssItem(all_395_0) = all_1839_1 % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | DELTA: instantiating (95) with fresh symbols all_1841_0, % 231.89/39.59 | | | | | | | | all_1841_1 gives: % 231.89/39.59 | | | | | | | | (122) tl(all_139_1) = all_1841_0 & ssItem(all_395_0) = % 231.89/39.59 | | | | | | | | all_1841_1 & $i(all_1841_0) & ( ~ (all_1841_1 = 0) | % 231.89/39.59 | | | | | | | | all_1841_0 = nil) % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | ALPHA: (122) implies: % 231.89/39.59 | | | | | | | | (123) ssItem(all_395_0) = all_1841_1 % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | BETA: splitting (105) gives: % 231.89/39.59 | | | | | | | | % 231.89/39.59 | | | | | | | | Case 1: % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | (124) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_388_0) = v0) % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | DELTA: instantiating (124) with fresh symbol all_1996_0 gives: % 231.89/39.59 | | | | | | | | | (125) ~ (all_1996_0 = 0) & ssList(all_388_0) = all_1996_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | ALPHA: (125) implies: % 231.89/39.59 | | | | | | | | | (126) ~ (all_1996_0 = 0) % 231.89/39.59 | | | | | | | | | (127) ssList(all_388_0) = all_1996_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | DELTA: instantiating (124) with fresh symbol all_1998_0 gives: % 231.89/39.59 | | | | | | | | | (128) ~ (all_1998_0 = 0) & ssList(all_388_0) = all_1998_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | ALPHA: (128) implies: % 231.89/39.59 | | | | | | | | | (129) ssList(all_388_0) = all_1998_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | DELTA: instantiating (124) with fresh symbol all_2000_0 gives: % 231.89/39.59 | | | | | | | | | (130) ~ (all_2000_0 = 0) & ssList(all_388_0) = all_2000_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | ALPHA: (130) implies: % 231.89/39.59 | | | | | | | | | (131) ssList(all_388_0) = all_2000_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | DELTA: instantiating (124) with fresh symbol all_2002_0 gives: % 231.89/39.59 | | | | | | | | | (132) ~ (all_2002_0 = 0) & ssList(all_388_0) = all_2002_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | ALPHA: (132) implies: % 231.89/39.59 | | | | | | | | | (133) ssList(all_388_0) = all_2002_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | DELTA: instantiating (124) with fresh symbol all_2004_0 gives: % 231.89/39.59 | | | | | | | | | (134) ~ (all_2004_0 = 0) & ssList(all_388_0) = all_2004_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | ALPHA: (134) implies: % 231.89/39.59 | | | | | | | | | (135) ssList(all_388_0) = all_2004_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | DELTA: instantiating (124) with fresh symbol all_2006_0 gives: % 231.89/39.59 | | | | | | | | | (136) ~ (all_2006_0 = 0) & ssList(all_388_0) = all_2006_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | ALPHA: (136) implies: % 231.89/39.59 | | | | | | | | | (137) ssList(all_388_0) = all_2006_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | DELTA: instantiating (124) with fresh symbol all_2008_0 gives: % 231.89/39.59 | | | | | | | | | (138) ~ (all_2008_0 = 0) & ssList(all_388_0) = all_2008_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | ALPHA: (138) implies: % 231.89/39.59 | | | | | | | | | (139) ssList(all_388_0) = all_2008_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_2002_0, all_388_0, % 231.89/39.59 | | | | | | | | | simplifying with (79), (133) gives: % 231.89/39.59 | | | | | | | | | (140) all_2002_0 = 0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | GROUND_INST: instantiating (17) with all_2002_0, all_2004_0, % 231.89/39.59 | | | | | | | | | all_388_0, simplifying with (133), (135) gives: % 231.89/39.59 | | | | | | | | | (141) all_2004_0 = all_2002_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | GROUND_INST: instantiating (17) with all_1996_0, all_2004_0, % 231.89/39.59 | | | | | | | | | all_388_0, simplifying with (127), (135) gives: % 231.89/39.59 | | | | | | | | | (142) all_2004_0 = all_1996_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | GROUND_INST: instantiating (17) with all_2002_0, all_2006_0, % 231.89/39.59 | | | | | | | | | all_388_0, simplifying with (133), (137) gives: % 231.89/39.59 | | | | | | | | | (143) all_2006_0 = all_2002_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | GROUND_INST: instantiating (17) with all_1998_0, all_2006_0, % 231.89/39.59 | | | | | | | | | all_388_0, simplifying with (129), (137) gives: % 231.89/39.59 | | | | | | | | | (144) all_2006_0 = all_1998_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | GROUND_INST: instantiating (17) with all_2002_0, all_2008_0, % 231.89/39.59 | | | | | | | | | all_388_0, simplifying with (133), (139) gives: % 231.89/39.59 | | | | | | | | | (145) all_2008_0 = all_2002_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | GROUND_INST: instantiating (17) with all_2000_0, all_2008_0, % 231.89/39.59 | | | | | | | | | all_388_0, simplifying with (131), (139) gives: % 231.89/39.59 | | | | | | | | | (146) all_2008_0 = all_2000_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (145), (146) imply: % 231.89/39.59 | | | | | | | | | (147) all_2002_0 = all_2000_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | SIMP: (147) implies: % 231.89/39.59 | | | | | | | | | (148) all_2002_0 = all_2000_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (143), (144) imply: % 231.89/39.59 | | | | | | | | | (149) all_2002_0 = all_1998_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | SIMP: (149) implies: % 231.89/39.59 | | | | | | | | | (150) all_2002_0 = all_1998_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (141), (142) imply: % 231.89/39.59 | | | | | | | | | (151) all_2002_0 = all_1996_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | SIMP: (151) implies: % 231.89/39.59 | | | | | | | | | (152) all_2002_0 = all_1996_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (148), (152) imply: % 231.89/39.59 | | | | | | | | | (153) all_2000_0 = all_1996_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (140), (148) imply: % 231.89/39.59 | | | | | | | | | (154) all_2000_0 = 0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (148), (150) imply: % 231.89/39.59 | | | | | | | | | (155) all_2000_0 = all_1998_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (154), (155) imply: % 231.89/39.59 | | | | | | | | | (156) all_1998_0 = 0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (153), (155) imply: % 231.89/39.59 | | | | | | | | | (157) all_1998_0 = all_1996_0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | COMBINE_EQS: (156), (157) imply: % 231.89/39.59 | | | | | | | | | (158) all_1996_0 = 0 % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | REDUCE: (126), (158) imply: % 231.89/39.59 | | | | | | | | | (159) $false % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | CLOSE: (159) is inconsistent. % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | Case 2: % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | % 231.89/39.59 | | | | | | | | | GROUND_INST: instantiating (16) with all_1829_1, all_1831_1, % 231.89/39.59 | | | | | | | | | all_395_0, simplifying with (109), (111) gives: % 231.89/39.59 | | | | | | | | | (160) all_1831_1 = all_1829_1 % 231.89/39.59 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_1835_1, all_395_0, % 231.89/39.60 | | | | | | | | | simplifying with (90), (115) gives: % 231.89/39.60 | | | | | | | | | (161) all_1835_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (16) with all_1829_1, all_1837_1, % 231.89/39.60 | | | | | | | | | all_395_0, simplifying with (109), (117) gives: % 231.89/39.60 | | | | | | | | | (162) all_1837_1 = all_1829_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (16) with all_1837_1, all_1839_1, % 231.89/39.60 | | | | | | | | | all_395_0, simplifying with (117), (121) gives: % 231.89/39.60 | | | | | | | | | (163) all_1839_1 = all_1837_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (16) with all_1827_1, all_1839_1, % 231.89/39.60 | | | | | | | | | all_395_0, simplifying with (107), (121) gives: % 231.89/39.60 | | | | | | | | | (164) all_1839_1 = all_1827_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (16) with all_1835_1, all_1841_1, % 231.89/39.60 | | | | | | | | | all_395_0, simplifying with (115), (123) gives: % 231.89/39.60 | | | | | | | | | (165) all_1841_1 = all_1835_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (16) with all_1833_1, all_1841_1, % 231.89/39.60 | | | | | | | | | all_395_0, simplifying with (113), (123) gives: % 231.89/39.60 | | | | | | | | | (166) all_1841_1 = all_1833_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (16) with all_1831_1, all_1841_1, % 231.89/39.60 | | | | | | | | | all_395_0, simplifying with (111), (123) gives: % 231.89/39.60 | | | | | | | | | (167) all_1841_1 = all_1831_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (18) with all_139_0, all_1837_0, % 231.89/39.60 | | | | | | | | | all_139_1, simplifying with (23), (118) gives: % 231.89/39.60 | | | | | | | | | (168) all_1837_0 = all_139_0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (165), (166) imply: % 231.89/39.60 | | | | | | | | | (169) all_1835_1 = all_1833_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | SIMP: (169) implies: % 231.89/39.60 | | | | | | | | | (170) all_1835_1 = all_1833_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (166), (167) imply: % 231.89/39.60 | | | | | | | | | (171) all_1833_1 = all_1831_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (163), (164) imply: % 231.89/39.60 | | | | | | | | | (172) all_1837_1 = all_1827_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | SIMP: (172) implies: % 231.89/39.60 | | | | | | | | | (173) all_1837_1 = all_1827_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (162), (173) imply: % 231.89/39.60 | | | | | | | | | (174) all_1829_1 = all_1827_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | SIMP: (174) implies: % 231.89/39.60 | | | | | | | | | (175) all_1829_1 = all_1827_1 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (161), (170) imply: % 231.89/39.60 | | | | | | | | | (176) all_1833_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | SIMP: (176) implies: % 231.89/39.60 | | | | | | | | | (177) all_1833_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (171), (177) imply: % 231.89/39.60 | | | | | | | | | (178) all_1831_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | SIMP: (178) implies: % 231.89/39.60 | | | | | | | | | (179) all_1831_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (160), (179) imply: % 231.89/39.60 | | | | | | | | | (180) all_1829_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | SIMP: (180) implies: % 231.89/39.60 | | | | | | | | | (181) all_1829_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (175), (181) imply: % 231.89/39.60 | | | | | | | | | (182) all_1827_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | SIMP: (182) implies: % 231.89/39.60 | | | | | | | | | (183) all_1827_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | COMBINE_EQS: (173), (183) imply: % 231.89/39.60 | | | | | | | | | (184) all_1837_1 = 0 % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | BETA: splitting (119) gives: % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | Case 1: % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | | (185) ~ (all_1837_1 = 0) % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | | REDUCE: (184), (185) imply: % 231.89/39.60 | | | | | | | | | | (186) $false % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | | CLOSE: (186) is inconsistent. % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | Case 2: % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | | (187) all_1837_0 = 0 % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | | COMBINE_EQS: (168), (187) imply: % 231.89/39.60 | | | | | | | | | | (188) all_139_0 = 0 % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | | SIMP: (188) implies: % 231.89/39.60 | | | | | | | | | | (189) all_139_0 = 0 % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | | REDUCE: (36), (189) imply: % 231.89/39.60 | | | | | | | | | | (190) $false % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | | CLOSE: (190) is inconsistent. % 231.89/39.60 | | | | | | | | | | % 231.89/39.60 | | | | | | | | | End of split % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | End of split % 231.89/39.60 | | | | | | | | % 231.89/39.60 | | | | | | | Case 2: % 231.89/39.60 | | | | | | | | % 231.89/39.60 | | | | | | | | (191) ? [v0: any] : ? [v1: any] : (segmentP(all_139_1, % 231.89/39.60 | | | | | | | | all_143_0) = v1 & ssList(all_139_1) = v0 & ( ~ (v1 % 231.89/39.60 | | | | | | | | = 0) | ~ (v0 = 0))) % 231.89/39.60 | | | | | | | | % 231.89/39.60 | | | | | | | | DELTA: instantiating (191) with fresh symbols all_449_0, % 231.89/39.60 | | | | | | | | all_449_1 gives: % 231.89/39.60 | | | | | | | | (192) segmentP(all_139_1, all_143_0) = all_449_0 & % 231.89/39.60 | | | | | | | | ssList(all_139_1) = all_449_1 & ( ~ (all_449_0 = 0) | % 231.89/39.60 | | | | | | | | ~ (all_449_1 = 0)) % 231.89/39.60 | | | | | | | | % 231.89/39.60 | | | | | | | | ALPHA: (192) implies: % 231.89/39.60 | | | | | | | | (193) ssList(all_139_1) = all_449_1 % 231.89/39.60 | | | | | | | | (194) ~ (all_449_0 = 0) | ~ (all_449_1 = 0) % 231.89/39.60 | | | | | | | | % 231.89/39.60 | | | | | | | | GROUND_INST: instantiating (17) with 0, all_449_1, all_139_1, % 231.89/39.60 | | | | | | | | simplifying with (41), (193) gives: % 231.89/39.60 | | | | | | | | (195) all_449_1 = 0 % 231.89/39.60 | | | | | | | | % 231.89/39.60 | | | | | | | | BETA: splitting (194) gives: % 231.89/39.60 | | | | | | | | % 231.89/39.60 | | | | | | | | Case 1: % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (43) with all_395_0, all_139_1, % 231.89/39.60 | | | | | | | | | simplifying with (89), (91) gives: % 231.89/39.60 | | | | | | | | | (196) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 & % 231.89/39.60 | | | | | | | | | ssItem(all_395_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 % 231.89/39.60 | | | | | | | | | = nil)) % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (44) with all_395_0, all_139_1, % 231.89/39.60 | | | | | | | | | simplifying with (89), (91) gives: % 231.89/39.60 | | | | | | | | | (197) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 & % 231.89/39.60 | | | | | | | | | ssItem(all_395_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 % 231.89/39.60 | | | | | | | | | = all_395_0)) % 231.89/39.60 | | | | | | | | | % 231.89/39.60 | | | | | | | | | GROUND_INST: instantiating (13) with all_395_0, all_139_1, % 231.89/39.60 | | | | | | | | | simplifying with (89), (91) gives: % 231.98/39.60 | | | | | | | | | (198) ? [v0: any] : ? [v1: any] : (equalelemsP(all_139_1) % 231.98/39.60 | | | | | | | | | = v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = % 231.98/39.60 | | | | | | | | | 0)) % 231.98/39.60 | | | | | | | | | % 231.98/39.60 | | | | | | | | | GROUND_INST: instantiating (11) with all_395_0, all_139_1, % 231.98/39.60 | | | | | | | | | simplifying with (89), (91) gives: % 231.98/39.60 | | | | | | | | | (199) ? [v0: any] : ? [v1: any] : % 231.98/39.60 | | | | | | | | | (duplicatefreeP(all_139_1) = v1 & ssItem(all_395_0) = % 231.98/39.60 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 231.98/39.60 | | | | | | | | | % 231.98/39.60 | | | | | | | | | GROUND_INST: instantiating (9) with all_395_0, all_139_1, % 231.98/39.60 | | | | | | | | | simplifying with (89), (91) gives: % 231.98/39.60 | | | | | | | | | (200) ? [v0: any] : ? [v1: any] : % 231.98/39.60 | | | | | | | | | (strictorderedP(all_139_1) = v1 & ssItem(all_395_0) = % 231.98/39.60 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 231.98/39.60 | | | | | | | | | % 231.98/39.60 | | | | | | | | | GROUND_INST: instantiating (8) with all_395_0, all_139_1, % 231.98/39.60 | | | | | | | | | simplifying with (89), (91) gives: % 231.98/39.61 | | | | | | | | | (201) ? [v0: any] : ? [v1: any] : % 231.98/39.61 | | | | | | | | | (totalorderedP(all_139_1) = v1 & ssItem(all_395_0) = % 231.98/39.61 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (7) with all_395_0, all_139_1, % 231.98/39.61 | | | | | | | | | simplifying with (89), (91) gives: % 231.98/39.61 | | | | | | | | | (202) ? [v0: any] : ? [v1: any] : % 231.98/39.61 | | | | | | | | | (strictorderP(all_139_1) = v1 & ssItem(all_395_0) = % 231.98/39.61 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (6) with all_395_0, all_139_1, % 231.98/39.61 | | | | | | | | | simplifying with (89), (91) gives: % 231.98/39.61 | | | | | | | | | (203) ? [v0: any] : ? [v1: any] : (totalorderP(all_139_1) % 231.98/39.61 | | | | | | | | | = v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = % 231.98/39.61 | | | | | | | | | 0)) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (5) with all_395_0, all_139_1, % 231.98/39.61 | | | | | | | | | simplifying with (89), (91) gives: % 231.98/39.61 | | | | | | | | | (204) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_139_1) % 231.98/39.61 | | | | | | | | | = v1 & ssItem(all_395_0) = v0 & ( ~ (v0 = 0) | v1 = % 231.98/39.61 | | | | | | | | | 0)) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (199) with fresh symbols all_1927_0, % 231.98/39.61 | | | | | | | | | all_1927_1 gives: % 231.98/39.61 | | | | | | | | | (205) duplicatefreeP(all_139_1) = all_1927_0 & % 231.98/39.61 | | | | | | | | | ssItem(all_395_0) = all_1927_1 & ( ~ (all_1927_1 = 0) % 231.98/39.61 | | | | | | | | | | all_1927_0 = 0) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (205) implies: % 231.98/39.61 | | | | | | | | | (206) ssItem(all_395_0) = all_1927_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (198) with fresh symbols all_1929_0, % 231.98/39.61 | | | | | | | | | all_1929_1 gives: % 231.98/39.61 | | | | | | | | | (207) equalelemsP(all_139_1) = all_1929_0 & % 231.98/39.61 | | | | | | | | | ssItem(all_395_0) = all_1929_1 & ( ~ (all_1929_1 = 0) % 231.98/39.61 | | | | | | | | | | all_1929_0 = 0) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (207) implies: % 231.98/39.61 | | | | | | | | | (208) ssItem(all_395_0) = all_1929_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (204) with fresh symbols all_1931_0, % 231.98/39.61 | | | | | | | | | all_1931_1 gives: % 231.98/39.61 | | | | | | | | | (209) cyclefreeP(all_139_1) = all_1931_0 & % 231.98/39.61 | | | | | | | | | ssItem(all_395_0) = all_1931_1 & ( ~ (all_1931_1 = 0) % 231.98/39.61 | | | | | | | | | | all_1931_0 = 0) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (209) implies: % 231.98/39.61 | | | | | | | | | (210) ssItem(all_395_0) = all_1931_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (203) with fresh symbols all_1933_0, % 231.98/39.61 | | | | | | | | | all_1933_1 gives: % 231.98/39.61 | | | | | | | | | (211) totalorderP(all_139_1) = all_1933_0 & % 231.98/39.61 | | | | | | | | | ssItem(all_395_0) = all_1933_1 & ( ~ (all_1933_1 = 0) % 231.98/39.61 | | | | | | | | | | all_1933_0 = 0) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (211) implies: % 231.98/39.61 | | | | | | | | | (212) ssItem(all_395_0) = all_1933_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (202) with fresh symbols all_1935_0, % 231.98/39.61 | | | | | | | | | all_1935_1 gives: % 231.98/39.61 | | | | | | | | | (213) strictorderP(all_139_1) = all_1935_0 & % 231.98/39.61 | | | | | | | | | ssItem(all_395_0) = all_1935_1 & ( ~ (all_1935_1 = 0) % 231.98/39.61 | | | | | | | | | | all_1935_0 = 0) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (213) implies: % 231.98/39.61 | | | | | | | | | (214) ssItem(all_395_0) = all_1935_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (201) with fresh symbols all_1937_0, % 231.98/39.61 | | | | | | | | | all_1937_1 gives: % 231.98/39.61 | | | | | | | | | (215) totalorderedP(all_139_1) = all_1937_0 & % 231.98/39.61 | | | | | | | | | ssItem(all_395_0) = all_1937_1 & ( ~ (all_1937_1 = 0) % 231.98/39.61 | | | | | | | | | | all_1937_0 = 0) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (215) implies: % 231.98/39.61 | | | | | | | | | (216) ssItem(all_395_0) = all_1937_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (200) with fresh symbols all_1939_0, % 231.98/39.61 | | | | | | | | | all_1939_1 gives: % 231.98/39.61 | | | | | | | | | (217) strictorderedP(all_139_1) = all_1939_0 & % 231.98/39.61 | | | | | | | | | ssItem(all_395_0) = all_1939_1 & ( ~ (all_1939_1 = 0) % 231.98/39.61 | | | | | | | | | | all_1939_0 = 0) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (217) implies: % 231.98/39.61 | | | | | | | | | (218) ssItem(all_395_0) = all_1939_1 % 231.98/39.61 | | | | | | | | | (219) strictorderedP(all_139_1) = all_1939_0 % 231.98/39.61 | | | | | | | | | (220) ~ (all_1939_1 = 0) | all_1939_0 = 0 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_1941_0, % 231.98/39.61 | | | | | | | | | all_1941_1 gives: % 231.98/39.61 | | | | | | | | | (221) hd(all_139_1) = all_1941_0 & ssItem(all_395_0) = % 231.98/39.61 | | | | | | | | | all_1941_1 & $i(all_1941_0) & ( ~ (all_1941_1 = 0) | % 231.98/39.61 | | | | | | | | | all_1941_0 = all_395_0) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (221) implies: % 231.98/39.61 | | | | | | | | | (222) ssItem(all_395_0) = all_1941_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | DELTA: instantiating (196) with fresh symbols all_1943_0, % 231.98/39.61 | | | | | | | | | all_1943_1 gives: % 231.98/39.61 | | | | | | | | | (223) tl(all_139_1) = all_1943_0 & ssItem(all_395_0) = % 231.98/39.61 | | | | | | | | | all_1943_1 & $i(all_1943_0) & ( ~ (all_1943_1 = 0) | % 231.98/39.61 | | | | | | | | | all_1943_0 = nil) % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | ALPHA: (223) implies: % 231.98/39.61 | | | | | | | | | (224) ssItem(all_395_0) = all_1943_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_1937_1, all_395_0, % 231.98/39.61 | | | | | | | | | simplifying with (90), (216) gives: % 231.98/39.61 | | | | | | | | | (225) all_1937_1 = 0 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with all_1935_1, all_1937_1, % 231.98/39.61 | | | | | | | | | all_395_0, simplifying with (214), (216) gives: % 231.98/39.61 | | | | | | | | | (226) all_1937_1 = all_1935_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with all_1931_1, all_1937_1, % 231.98/39.61 | | | | | | | | | all_395_0, simplifying with (210), (216) gives: % 231.98/39.61 | | | | | | | | | (227) all_1937_1 = all_1931_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with all_1929_1, all_1937_1, % 231.98/39.61 | | | | | | | | | all_395_0, simplifying with (208), (216) gives: % 231.98/39.61 | | | | | | | | | (228) all_1937_1 = all_1929_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with all_1939_1, all_1941_1, % 231.98/39.61 | | | | | | | | | all_395_0, simplifying with (218), (222) gives: % 231.98/39.61 | | | | | | | | | (229) all_1941_1 = all_1939_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with all_1933_1, all_1941_1, % 231.98/39.61 | | | | | | | | | all_395_0, simplifying with (212), (222) gives: % 231.98/39.61 | | | | | | | | | (230) all_1941_1 = all_1933_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with all_1929_1, all_1941_1, % 231.98/39.61 | | | | | | | | | all_395_0, simplifying with (208), (222) gives: % 231.98/39.61 | | | | | | | | | (231) all_1941_1 = all_1929_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with all_1941_1, all_1943_1, % 231.98/39.61 | | | | | | | | | all_395_0, simplifying with (222), (224) gives: % 231.98/39.61 | | | | | | | | | (232) all_1943_1 = all_1941_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (16) with all_1927_1, all_1943_1, % 231.98/39.61 | | | | | | | | | all_395_0, simplifying with (206), (224) gives: % 231.98/39.61 | | | | | | | | | (233) all_1943_1 = all_1927_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | GROUND_INST: instantiating (18) with all_139_0, all_1939_0, % 231.98/39.61 | | | | | | | | | all_139_1, simplifying with (23), (219) gives: % 231.98/39.61 | | | | | | | | | (234) all_1939_0 = all_139_0 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (232), (233) imply: % 231.98/39.61 | | | | | | | | | (235) all_1941_1 = all_1927_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | SIMP: (235) implies: % 231.98/39.61 | | | | | | | | | (236) all_1941_1 = all_1927_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (229), (236) imply: % 231.98/39.61 | | | | | | | | | (237) all_1939_1 = all_1927_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (229), (230) imply: % 231.98/39.61 | | | | | | | | | (238) all_1939_1 = all_1933_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (229), (231) imply: % 231.98/39.61 | | | | | | | | | (239) all_1939_1 = all_1929_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (238), (239) imply: % 231.98/39.61 | | | | | | | | | (240) all_1933_1 = all_1929_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (237), (238) imply: % 231.98/39.61 | | | | | | | | | (241) all_1933_1 = all_1927_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (226), (227) imply: % 231.98/39.61 | | | | | | | | | (242) all_1935_1 = all_1931_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (225), (226) imply: % 231.98/39.61 | | | | | | | | | (243) all_1935_1 = 0 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (226), (228) imply: % 231.98/39.61 | | | | | | | | | (244) all_1935_1 = all_1929_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (242), (243) imply: % 231.98/39.61 | | | | | | | | | (245) all_1931_1 = 0 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (242), (244) imply: % 231.98/39.61 | | | | | | | | | (246) all_1931_1 = all_1929_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (240), (241) imply: % 231.98/39.61 | | | | | | | | | (247) all_1929_1 = all_1927_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | SIMP: (247) implies: % 231.98/39.61 | | | | | | | | | (248) all_1929_1 = all_1927_1 % 231.98/39.61 | | | | | | | | | % 231.98/39.61 | | | | | | | | | COMBINE_EQS: (245), (246) imply: % 231.98/39.61 | | | | | | | | | (249) all_1929_1 = 0 % 231.98/39.61 | | | | | | | | | % 231.98/39.62 | | | | | | | | | SIMP: (249) implies: % 231.98/39.62 | | | | | | | | | (250) all_1929_1 = 0 % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | | COMBINE_EQS: (248), (250) imply: % 231.98/39.62 | | | | | | | | | (251) all_1927_1 = 0 % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | | COMBINE_EQS: (241), (251) imply: % 231.98/39.62 | | | | | | | | | (252) all_1933_1 = 0 % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | | COMBINE_EQS: (238), (252) imply: % 231.98/39.62 | | | | | | | | | (253) all_1939_1 = 0 % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | | BETA: splitting (220) gives: % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | | Case 1: % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | | (254) ~ (all_1939_1 = 0) % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | | REDUCE: (253), (254) imply: % 231.98/39.62 | | | | | | | | | | (255) $false % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | | CLOSE: (255) is inconsistent. % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | Case 2: % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | | (256) all_1939_0 = 0 % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | | COMBINE_EQS: (234), (256) imply: % 231.98/39.62 | | | | | | | | | | (257) all_139_0 = 0 % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | | REDUCE: (36), (257) imply: % 231.98/39.62 | | | | | | | | | | (258) $false % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | | CLOSE: (258) is inconsistent. % 231.98/39.62 | | | | | | | | | | % 231.98/39.62 | | | | | | | | | End of split % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | Case 2: % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | | (259) ~ (all_449_1 = 0) % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | | REDUCE: (195), (259) imply: % 231.98/39.62 | | | | | | | | | (260) $false % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | | CLOSE: (260) is inconsistent. % 231.98/39.62 | | | | | | | | | % 231.98/39.62 | | | | | | | | End of split % 231.98/39.62 | | | | | | | | % 231.98/39.62 | | | | | | | End of split % 231.98/39.62 | | | | | | | % 231.98/39.62 | | | | | | End of split % 231.98/39.62 | | | | | | % 231.98/39.62 | | | | | End of split % 231.98/39.62 | | | | | % 231.98/39.62 | | | | End of split % 231.98/39.62 | | | | % 231.98/39.62 | | | End of split % 231.98/39.62 | | | % 231.98/39.62 | | Case 2: % 231.98/39.62 | | | % 231.98/39.62 | | | (261) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 231.98/39.62 | | | % 231.98/39.62 | | | DELTA: instantiating (261) with fresh symbol all_341_0 gives: % 231.98/39.62 | | | (262) ~ (all_341_0 = 0) & ssList(all_139_1) = all_341_0 % 231.98/39.62 | | | % 231.98/39.62 | | | ALPHA: (262) implies: % 231.98/39.62 | | | (263) ~ (all_341_0 = 0) % 231.98/39.62 | | | (264) ssList(all_139_1) = all_341_0 % 231.98/39.62 | | | % 232.05/39.62 | | | GROUND_INST: instantiating (17) with 0, all_341_0, all_139_1, simplifying % 232.05/39.62 | | | with (41), (264) gives: % 232.05/39.62 | | | (265) all_341_0 = 0 % 232.05/39.62 | | | % 232.05/39.62 | | | REDUCE: (263), (265) imply: % 232.05/39.62 | | | (266) $false % 232.05/39.62 | | | % 232.05/39.62 | | | CLOSE: (266) is inconsistent. % 232.05/39.62 | | | % 232.05/39.62 | | End of split % 232.05/39.62 | | % 232.05/39.62 | End of split % 232.05/39.62 | % 232.05/39.62 End of proof % 232.05/39.62 % 232.05/39.62 Sub-proof #1 shows that the following formulas are inconsistent: % 232.05/39.62 ---------------------------------------------------------------- % 232.05/39.62 (1) strictorderedP(nil) = 0 % 232.05/39.62 (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ~ % 232.05/39.62 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 232.05/39.62 (3) all_143_0 = nil % 232.05/39.62 (4) all_139_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 232.05/39.62 (cons(v1, v0) = all_139_1 & ssItem(v1) = 0 & $i(v1))) % 232.05/39.62 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 232.05/39.62 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 232.05/39.62 (6) ssList(all_139_1) = 0 % 232.05/39.62 (7) strictorderedP(all_139_1) = all_139_0 % 232.05/39.62 (8) ~ (all_139_0 = 0) % 232.05/39.62 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 232.05/39.62 (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0)) % 232.05/39.62 (10) all_143_0 = all_139_1 | ? [v0: any] : ? [v1: any] : % 232.05/39.62 (segmentP(all_139_1, all_143_0) = v1 & ssList(all_139_1) = v0 & ( ~ (v1 % 232.05/39.62 = 0) | ~ (v0 = 0))) % 232.05/39.62 (11) $i(all_139_1) % 232.05/39.62 % 232.05/39.62 Begin of proof % 232.05/39.62 | % 232.05/39.62 | BETA: splitting (4) gives: % 232.05/39.62 | % 232.05/39.62 | Case 1: % 232.05/39.62 | | % 232.05/39.62 | | (12) all_139_1 = nil % 232.05/39.62 | | % 232.05/39.62 | | REDUCE: (7), (12) imply: % 232.05/39.62 | | (13) strictorderedP(nil) = all_139_0 % 232.05/39.62 | | % 232.05/39.62 | | GROUND_INST: instantiating (9) with 0, all_139_0, nil, simplifying with (1), % 232.05/39.62 | | (13) gives: % 232.05/39.62 | | (14) all_139_0 = 0 % 232.05/39.62 | | % 232.05/39.62 | | REDUCE: (8), (14) imply: % 232.05/39.62 | | (15) $false % 232.05/39.62 | | % 232.05/39.62 | | CLOSE: (15) is inconsistent. % 232.05/39.62 | | % 232.05/39.62 | Case 2: % 232.05/39.62 | | % 232.05/39.62 | | (16) ~ (all_139_1 = nil) % 232.05/39.62 | | % 232.05/39.62 | | BETA: splitting (10) gives: % 232.05/39.62 | | % 232.05/39.62 | | Case 1: % 232.05/39.62 | | | % 232.05/39.62 | | | (17) all_143_0 = all_139_1 % 232.05/39.62 | | | % 232.05/39.62 | | | COMBINE_EQS: (3), (17) imply: % 232.05/39.62 | | | (18) all_139_1 = nil % 232.05/39.62 | | | % 232.05/39.62 | | | SIMP: (18) implies: % 232.05/39.62 | | | (19) all_139_1 = nil % 232.05/39.62 | | | % 232.05/39.62 | | | REDUCE: (16), (19) imply: % 232.05/39.62 | | | (20) $false % 232.05/39.62 | | | % 232.05/39.62 | | | CLOSE: (20) is inconsistent. % 232.05/39.62 | | | % 232.05/39.62 | | Case 2: % 232.05/39.62 | | | % 232.05/39.62 | | | (21) ? [v0: any] : ? [v1: any] : (segmentP(all_139_1, all_143_0) = v1 % 232.05/39.62 | | | & ssList(all_139_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 232.05/39.62 | | | % 232.05/39.62 | | | DELTA: instantiating (21) with fresh symbols all_397_0, all_397_1 gives: % 232.05/39.62 | | | (22) segmentP(all_139_1, all_143_0) = all_397_0 & ssList(all_139_1) = % 232.05/39.62 | | | all_397_1 & ( ~ (all_397_0 = 0) | ~ (all_397_1 = 0)) % 232.05/39.62 | | | % 232.05/39.62 | | | ALPHA: (22) implies: % 232.05/39.62 | | | (23) ssList(all_139_1) = all_397_1 % 232.05/39.62 | | | (24) segmentP(all_139_1, all_143_0) = all_397_0 % 232.05/39.62 | | | (25) ~ (all_397_0 = 0) | ~ (all_397_1 = 0) % 232.05/39.62 | | | % 232.05/39.62 | | | REDUCE: (3), (24) imply: % 232.05/39.62 | | | (26) segmentP(all_139_1, nil) = all_397_0 % 232.05/39.62 | | | % 232.05/39.62 | | | GROUND_INST: instantiating (5) with 0, all_397_1, all_139_1, simplifying % 232.05/39.62 | | | with (6), (23) gives: % 232.05/39.62 | | | (27) all_397_1 = 0 % 232.05/39.62 | | | % 232.05/39.62 | | | BETA: splitting (25) gives: % 232.05/39.62 | | | % 232.05/39.62 | | | Case 1: % 232.05/39.62 | | | | % 232.05/39.62 | | | | (28) ~ (all_397_0 = 0) % 232.05/39.62 | | | | % 232.05/39.62 | | | | GROUND_INST: instantiating (2) with all_139_1, all_397_0, simplifying % 232.05/39.62 | | | | with (11), (26) gives: % 232.05/39.62 | | | | (29) all_397_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) % 232.05/39.62 | | | | = v0) % 232.05/39.62 | | | | % 232.05/39.62 | | | | BETA: splitting (29) gives: % 232.05/39.62 | | | | % 232.05/39.62 | | | | Case 1: % 232.05/39.62 | | | | | % 232.05/39.62 | | | | | (30) all_397_0 = 0 % 232.05/39.62 | | | | | % 232.05/39.62 | | | | | REDUCE: (28), (30) imply: % 232.05/39.62 | | | | | (31) $false % 232.05/39.62 | | | | | % 232.05/39.62 | | | | | CLOSE: (31) is inconsistent. % 232.05/39.62 | | | | | % 232.05/39.62 | | | | Case 2: % 232.05/39.62 | | | | | % 232.05/39.62 | | | | | (32) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 232.05/39.62 | | | | | % 232.05/39.63 | | | | | REF_CLOSE: (5), (6), (32) are inconsistent by sub-proof #2. % 232.05/39.63 | | | | | % 232.05/39.63 | | | | End of split % 232.05/39.63 | | | | % 232.05/39.63 | | | Case 2: % 232.05/39.63 | | | | % 232.05/39.63 | | | | (33) ~ (all_397_1 = 0) % 232.05/39.63 | | | | % 232.05/39.63 | | | | REDUCE: (27), (33) imply: % 232.05/39.63 | | | | (34) $false % 232.05/39.63 | | | | % 232.05/39.63 | | | | CLOSE: (34) is inconsistent. % 232.05/39.63 | | | | % 232.05/39.63 | | | End of split % 232.05/39.63 | | | % 232.05/39.63 | | End of split % 232.05/39.63 | | % 232.05/39.63 | End of split % 232.05/39.63 | % 232.05/39.63 End of proof % 232.05/39.63 % 232.05/39.63 Sub-proof #2 shows that the following formulas are inconsistent: % 232.05/39.63 ---------------------------------------------------------------- % 232.05/39.63 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) % 232.05/39.63 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 232.05/39.63 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 232.05/39.63 (3) ssList(all_139_1) = 0 % 232.05/39.63 % 232.05/39.63 Begin of proof % 232.05/39.63 | % 232.05/39.63 | DELTA: instantiating (1) with fresh symbol all_448_0 gives: % 232.05/39.63 | (4) ~ (all_448_0 = 0) & ssList(all_139_1) = all_448_0 % 232.05/39.63 | % 232.05/39.63 | ALPHA: (4) implies: % 232.05/39.63 | (5) ~ (all_448_0 = 0) % 232.05/39.63 | (6) ssList(all_139_1) = all_448_0 % 232.05/39.63 | % 232.05/39.63 | GROUND_INST: instantiating (2) with 0, all_448_0, all_139_1, simplifying with % 232.05/39.63 | (3), (6) gives: % 232.05/39.63 | (7) all_448_0 = 0 % 232.05/39.63 | % 232.05/39.63 | REDUCE: (5), (7) imply: % 232.05/39.63 | (8) $false % 232.05/39.63 | % 232.05/39.63 | CLOSE: (8) is inconsistent. % 232.05/39.63 | % 232.05/39.63 End of proof % 232.05/39.63 % 232.05/39.63 Sub-proof #3 shows that the following formulas are inconsistent: % 232.05/39.63 ---------------------------------------------------------------- % 232.05/39.63 (1) ~ (all_380_0 = 0) & ssList(nil) = all_380_0 % 232.05/39.63 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 232.05/39.63 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 232.05/39.63 (3) ssList(nil) = 0 % 232.05/39.63 % 232.05/39.63 Begin of proof % 232.05/39.63 | % 232.05/39.63 | ALPHA: (1) implies: % 232.05/39.63 | (4) ~ (all_380_0 = 0) % 232.05/39.63 | (5) ssList(nil) = all_380_0 % 232.05/39.63 | % 232.05/39.63 | GROUND_INST: instantiating (2) with 0, all_380_0, nil, simplifying with (3), % 232.05/39.63 | (5) gives: % 232.05/39.63 | (6) all_380_0 = 0 % 232.05/39.63 | % 232.05/39.63 | REDUCE: (4), (6) imply: % 232.05/39.63 | (7) $false % 232.05/39.63 | % 232.05/39.63 | CLOSE: (7) is inconsistent. % 232.05/39.63 | % 232.05/39.63 End of proof % 232.05/39.63 % SZS output end Proof for theBenchmark % 232.05/39.63 % 232.05/39.63 39028ms %------------------------------------------------------------------------------