%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC386+1 : TPTP v8.1.2. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 20:51:10 EDT 2023 % Result : Theorem 24.57s 3.98s % Output : Proof 74.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC386+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 18:36:32 EDT 2023 % 0.13/0.34 % CPUTime : % 0.52/0.61 ________ _____ % 0.52/0.61 ___ __ \_________(_)________________________________ % 0.52/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.61 % 0.52/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.61 (2023-06-19) % 0.52/0.61 % 0.52/0.61 (c) Philipp Rümmer, 2009-2023 % 0.52/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.61 Amanda Stjerna. % 0.52/0.61 Free software under BSD-3-Clause. % 0.52/0.61 % 0.52/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.61 % 0.52/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.52/0.63 Running up to 7 provers in parallel. % 0.52/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.51/1.42 Prover 4: Preprocessing ... % 5.51/1.42 Prover 1: Preprocessing ... % 5.51/1.45 Prover 5: Preprocessing ... % 5.51/1.45 Prover 0: Preprocessing ... % 5.51/1.45 Prover 6: Preprocessing ... % 5.51/1.45 Prover 3: Preprocessing ... % 5.51/1.45 Prover 2: Preprocessing ... % 13.94/2.56 Prover 2: Proving ... % 14.76/2.70 Prover 5: Constructing countermodel ... % 15.40/2.75 Prover 1: Constructing countermodel ... % 15.40/2.77 Prover 3: Constructing countermodel ... % 15.66/2.81 Prover 6: Proving ... % 19.11/3.28 Prover 4: Constructing countermodel ... % 20.83/3.49 Prover 0: Proving ... % 24.57/3.98 Prover 3: proved (3347ms) % 24.57/3.98 % 24.57/3.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.57/3.98 % 24.57/3.98 Prover 5: stopped % 24.93/4.00 Prover 2: stopped % 24.93/4.00 Prover 6: stopped % 24.93/4.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.93/4.00 Prover 0: stopped % 24.93/4.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.93/4.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 24.93/4.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.93/4.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.85/4.26 Prover 13: Preprocessing ... % 26.85/4.28 Prover 11: Preprocessing ... % 26.85/4.29 Prover 8: Preprocessing ... % 26.85/4.30 Prover 7: Preprocessing ... % 26.85/4.30 Prover 10: Preprocessing ... % 28.23/4.46 Prover 10: Constructing countermodel ... % 28.79/4.54 Prover 7: Constructing countermodel ... % 29.25/4.61 Prover 13: Constructing countermodel ... % 30.59/4.78 Prover 8: Warning: ignoring some quantifiers % 30.59/4.79 Prover 8: Constructing countermodel ... % 35.45/5.38 Prover 11: Constructing countermodel ... % 66.38/9.47 Prover 13: stopped % 66.38/9.48 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 67.90/9.62 Prover 16: Preprocessing ... % 69.36/9.74 Prover 16: Constructing countermodel ... % 71.63/10.12 Prover 1: Found proof (size 239) % 71.63/10.12 Prover 1: proved (9485ms) % 71.63/10.12 Prover 16: stopped % 71.63/10.12 Prover 8: stopped % 71.63/10.12 Prover 7: stopped % 71.63/10.12 Prover 10: stopped % 71.63/10.12 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 71.63/10.12 Prover 11: stopped % 71.90/10.13 Prover 4: stopped % 71.90/10.18 Prover 19: Preprocessing ... % 73.66/10.46 Prover 19: Warning: ignoring some quantifiers % 73.66/10.48 Prover 19: Constructing countermodel ... % 73.86/10.49 Prover 19: stopped % 73.86/10.49 % 73.86/10.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 73.86/10.49 % 73.86/10.54 % SZS output start Proof for theBenchmark % 74.09/10.54 Assumptions after simplification: % 74.09/10.54 --------------------------------- % 74.09/10.54 % 74.09/10.54 (ax15) % 74.13/10.59 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 74.13/10.59 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 74.13/10.59 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 74.13/10.59 % 74.13/10.59 (ax17) % 74.13/10.59 ssList(nil) = 0 & $i(nil) % 74.13/10.59 % 74.13/10.59 (ax18) % 74.13/10.60 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1, % 74.13/10.60 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) = % 74.13/10.60 v2))) % 74.13/10.60 % 74.13/10.60 (ax2) % 74.13/10.60 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 74.13/10.60 ssItem(v1) = 0 & $i(v1))) % 74.13/10.60 % 74.13/10.60 (ax20) % 74.13/10.60 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 74.13/10.60 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 74.13/10.60 ssItem(v2) = 0 & $i(v2)))) % 74.13/10.60 % 74.13/10.60 (ax23) % 74.13/10.60 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 74.13/10.60 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 74.13/10.60 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 74.13/10.60 % 74.13/10.60 (ax25) % 74.13/10.60 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 74.13/10.60 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 74.13/10.60 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 74.13/10.60 % 74.13/10.60 (ax38) % 74.13/10.60 $i(nil) & ! [v0: $i] : ( ~ (memberP(nil, v0) = 0) | ~ $i(v0) | ? [v1: int] % 74.13/10.60 : ( ~ (v1 = 0) & ssItem(v0) = v1)) % 74.13/10.60 % 74.13/10.60 (ax44) % 74.39/10.61 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) % 74.39/10.61 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) | % 74.39/10.61 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] % 74.39/10.61 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~ % 74.39/10.61 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] : % 74.39/10.61 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = % 74.39/10.61 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = % 74.39/10.61 v0))))))))) % 74.39/10.61 % 74.39/10.61 (ax59) % 74.39/10.61 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 74.39/10.61 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 74.39/10.61 (v2 = 0) | v3 = 0))) % 74.39/10.61 % 74.39/10.61 (ax61) % 74.39/10.61 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 74.39/10.61 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 74.39/10.61 (v2 = 0) | v3 = 0))) % 74.39/10.61 % 74.39/10.61 (ax63) % 74.39/10.61 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 74.39/10.61 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 74.39/10.61 (v2 = 0) | v3 = 0))) % 74.39/10.61 % 74.39/10.61 (ax65) % 74.39/10.61 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 74.39/10.61 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 74.39/10.61 (v2 = 0) | v3 = 0))) % 74.39/10.61 % 74.39/10.61 (ax68) % 74.39/10.61 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 74.39/10.61 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 74.39/10.61 ~ (v2 = 0) | v3 = 0))) % 74.39/10.61 % 74.39/10.61 (ax71) % 74.39/10.62 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 74.39/10.62 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 74.39/10.62 ~ (v2 = 0) | v3 = 0))) % 74.39/10.62 % 74.39/10.62 (ax73) % 74.39/10.62 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 74.39/10.62 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 74.39/10.62 (v2 = 0) | v3 = 0))) % 74.39/10.62 % 74.39/10.62 (co1) % 74.39/10.62 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] % 74.39/10.62 : (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ( ? [v3: $i] : (memberP(v1, % 74.39/10.62 v3) = 0 & cons(v3, nil) = v0 & ssItem(v3) = 0 & $i(v3)) | (v1 = nil % 74.39/10.62 & v0 = nil)) & ((v2 = 0 & ! [v3: $i] : ( ~ (cons(v3, nil) = v0) | ~ % 74.39/10.62 $i(v3) | ? [v4: any] : ? [v5: any] : (memberP(v1, v3) = v5 & % 74.39/10.62 ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) | (v1 = nil & ~ % 74.39/10.62 (v0 = nil))))) % 74.39/10.62 % 74.39/10.62 (function-axioms) % 74.39/10.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 74.39/10.63 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 74.39/10.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.39/10.63 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 74.39/10.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.39/10.63 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 74.39/10.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.39/10.63 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 74.39/10.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.39/10.63 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 74.39/10.63 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 74.39/10.63 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 74.39/10.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 74.39/10.63 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 74.39/10.63 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 74.39/10.63 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 74.39/10.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.39/10.63 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 74.39/10.63 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 74.39/10.63 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 74.39/10.63 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 74.39/10.63 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 74.39/10.63 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 74.39/10.63 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 74.39/10.63 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 74.39/10.63 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.39/10.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 74.39/10.63 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.39/10.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 74.39/10.63 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.39/10.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 74.39/10.63 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.39/10.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 74.39/10.63 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.39/10.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 74.39/10.63 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.39/10.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 74.39/10.63 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.39/10.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 74.39/10.63 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.39/10.63 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 74.39/10.63 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 74.39/10.63 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 74.39/10.63 % 74.39/10.63 Further assumptions not needed in the proof: % 74.39/10.63 -------------------------------------------- % 74.39/10.63 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax19, ax21, ax22, ax24, ax26, ax27, % 74.39/10.63 ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax39, ax4, % 74.39/10.63 ax40, ax41, ax42, ax43, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, % 74.39/10.63 ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, ax66, ax67, ax69, % 74.39/10.63 ax7, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, % 74.39/10.63 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, % 74.39/10.63 ax95 % 74.39/10.63 % 74.39/10.63 Those formulas are unsatisfiable: % 74.39/10.63 --------------------------------- % 74.39/10.63 % 74.39/10.63 Begin of proof % 74.39/10.63 | % 74.39/10.63 | ALPHA: (ax17) implies: % 74.39/10.63 | (1) ssList(nil) = 0 % 74.39/10.63 | % 74.39/10.63 | ALPHA: (ax20) implies: % 74.39/10.63 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 74.39/10.63 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 74.39/10.63 | ssItem(v2) = 0 & $i(v2)))) % 74.39/10.63 | % 74.39/10.63 | ALPHA: (ax38) implies: % 74.39/10.63 | (3) ! [v0: $i] : ( ~ (memberP(nil, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( % 74.39/10.63 | ~ (v1 = 0) & ssItem(v0) = v1)) % 74.39/10.63 | % 74.39/10.63 | ALPHA: (ax59) implies: % 74.39/10.63 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.63 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 74.39/10.63 | ~ (v2 = 0) | v3 = 0))) % 74.39/10.63 | % 74.39/10.63 | ALPHA: (ax61) implies: % 74.39/10.63 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.63 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 74.39/10.63 | ( ~ (v2 = 0) | v3 = 0))) % 74.39/10.63 | % 74.39/10.63 | ALPHA: (ax63) implies: % 74.39/10.64 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.64 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 74.39/10.64 | ( ~ (v2 = 0) | v3 = 0))) % 74.39/10.64 | % 74.39/10.64 | ALPHA: (ax65) implies: % 74.39/10.64 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.64 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 74.39/10.64 | & ( ~ (v2 = 0) | v3 = 0))) % 74.39/10.64 | % 74.39/10.64 | ALPHA: (ax68) implies: % 74.39/10.64 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.64 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 74.39/10.64 | & ( ~ (v2 = 0) | v3 = 0))) % 74.39/10.64 | % 74.39/10.64 | ALPHA: (ax71) implies: % 74.39/10.64 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.64 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 74.39/10.64 | & ( ~ (v2 = 0) | v3 = 0))) % 74.39/10.64 | % 74.39/10.64 | ALPHA: (ax73) implies: % 74.39/10.64 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.64 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 74.39/10.64 | ( ~ (v2 = 0) | v3 = 0))) % 74.39/10.64 | % 74.39/10.64 | ALPHA: (co1) implies: % 74.39/10.64 | (11) $i(nil) % 74.39/10.64 | (12) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 74.39/10.64 | (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ( ? [v3: $i] : % 74.39/10.64 | (memberP(v1, v3) = 0 & cons(v3, nil) = v0 & ssItem(v3) = 0 & % 74.39/10.64 | $i(v3)) | (v1 = nil & v0 = nil)) & ((v2 = 0 & ! [v3: $i] : ( % 74.39/10.64 | ~ (cons(v3, nil) = v0) | ~ $i(v3) | ? [v4: any] : ? [v5: % 74.39/10.64 | any] : (memberP(v1, v3) = v5 & ssItem(v3) = v4 & ( ~ (v5 = % 74.39/10.64 | 0) | ~ (v4 = 0))))) | (v1 = nil & ~ (v0 = nil))))) % 74.39/10.64 | % 74.39/10.64 | ALPHA: (function-axioms) implies: % 74.39/10.64 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 74.39/10.64 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 74.39/10.64 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 74.39/10.64 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 74.39/10.64 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 74.39/10.64 | : ! [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, % 74.39/10.64 | v2) = v0)) % 74.39/10.64 | % 74.39/10.64 | DELTA: instantiating (ax2) with fresh symbol all_91_0 gives: % 74.39/10.64 | (16) ssItem(all_91_0) = 0 & $i(all_91_0) & ? [v0: any] : ( ~ (v0 = % 74.39/10.64 | all_91_0) & ssItem(v0) = 0 & $i(v0)) % 74.39/10.64 | % 74.39/10.64 | ALPHA: (16) implies: % 74.39/10.65 | (17) ? [v0: any] : ( ~ (v0 = all_91_0) & ssItem(v0) = 0 & $i(v0)) % 74.39/10.65 | % 74.39/10.65 | DELTA: instantiating (12) with fresh symbol all_93_0 gives: % 74.39/10.65 | (18) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : ? [v1: any] : % 74.39/10.65 | (ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ( ? [v2: $i] : % 74.39/10.65 | (memberP(v0, v2) = 0 & cons(v2, nil) = all_93_0 & ssItem(v2) = 0 & % 74.39/10.65 | $i(v2)) | (v0 = nil & all_93_0 = nil)) & ((v1 = 0 & ! [v2: $i] % 74.39/10.65 | : ( ~ (cons(v2, nil) = all_93_0) | ~ $i(v2) | ? [v3: any] : ? % 74.39/10.65 | [v4: any] : (memberP(v0, v2) = v4 & ssItem(v2) = v3 & ( ~ (v4 % 74.39/10.65 | = 0) | ~ (v3 = 0))))) | (v0 = nil & ~ (all_93_0 = % 74.39/10.65 | nil)))) % 74.39/10.65 | % 74.39/10.65 | ALPHA: (18) implies: % 74.39/10.65 | (19) $i(all_93_0) % 74.39/10.65 | (20) ssList(all_93_0) = 0 % 74.39/10.65 | (21) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 74.39/10.65 | $i(v0) & ( ? [v2: $i] : (memberP(v0, v2) = 0 & cons(v2, nil) = % 74.39/10.65 | all_93_0 & ssItem(v2) = 0 & $i(v2)) | (v0 = nil & all_93_0 = % 74.39/10.65 | nil)) & ((v1 = 0 & ! [v2: $i] : ( ~ (cons(v2, nil) = all_93_0) % 74.39/10.65 | | ~ $i(v2) | ? [v3: any] : ? [v4: any] : (memberP(v0, v2) = % 74.39/10.65 | v4 & ssItem(v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) | (v0 % 74.39/10.65 | = nil & ~ (all_93_0 = nil)))) % 74.39/10.65 | % 74.39/10.65 | DELTA: instantiating (17) with fresh symbol all_95_0 gives: % 74.39/10.65 | (22) ~ (all_95_0 = all_91_0) & ssItem(all_95_0) = 0 & $i(all_95_0) % 74.39/10.65 | % 74.39/10.65 | ALPHA: (22) implies: % 74.39/10.65 | (23) $i(all_95_0) % 74.39/10.65 | (24) ssItem(all_95_0) = 0 % 74.39/10.65 | % 74.39/10.65 | DELTA: instantiating (21) with fresh symbols all_97_0, all_97_1 gives: % 74.39/10.65 | (25) ssList(all_97_1) = 0 & neq(all_97_1, nil) = all_97_0 & $i(all_97_1) & % 74.39/10.65 | ( ? [v0: $i] : (memberP(all_97_1, v0) = 0 & cons(v0, nil) = all_93_0 & % 74.39/10.65 | ssItem(v0) = 0 & $i(v0)) | (all_97_1 = nil & all_93_0 = nil)) & % 74.39/10.65 | ((all_97_0 = 0 & ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_0) | ~ % 74.39/10.65 | $i(v0) | ? [v1: any] : ? [v2: any] : (memberP(all_97_1, v0) = % 74.39/10.65 | v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))) | % 74.39/10.65 | (all_97_1 = nil & ~ (all_93_0 = nil))) % 74.39/10.65 | % 74.39/10.65 | ALPHA: (25) implies: % 74.39/10.65 | (26) $i(all_97_1) % 74.39/10.65 | (27) neq(all_97_1, nil) = all_97_0 % 74.39/10.65 | (28) ssList(all_97_1) = 0 % 74.39/10.65 | (29) (all_97_0 = 0 & ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_0) | ~ % 74.39/10.65 | $i(v0) | ? [v1: any] : ? [v2: any] : (memberP(all_97_1, v0) = v2 % 74.39/10.65 | & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))) | (all_97_1 = % 74.39/10.65 | nil & ~ (all_93_0 = nil)) % 74.39/10.66 | (30) ? [v0: $i] : (memberP(all_97_1, v0) = 0 & cons(v0, nil) = all_93_0 & % 74.39/10.66 | ssItem(v0) = 0 & $i(v0)) | (all_97_1 = nil & all_93_0 = nil) % 74.39/10.66 | % 74.39/10.66 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (11) gives: % 74.39/10.66 | (31) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.66 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 74.39/10.66 | ( ~ (v2 = 0) | v3 = nil))) % 74.39/10.66 | % 74.39/10.66 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (11) gives: % 74.39/10.66 | (32) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 74.39/10.66 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 74.39/10.66 | ( ~ (v2 = 0) | v3 = v0))) % 74.39/10.66 | % 74.39/10.66 | GROUND_INST: instantiating (ax18) with nil, simplifying with (1), (11) gives: % 74.39/10.66 | (33) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : ( % 74.39/10.66 | ~ (v1 = 0) & ssItem(v0) = v1)) % 74.39/10.66 | % 74.39/10.66 | GROUND_INST: instantiating (2) with all_93_0, simplifying with (19), (20) % 74.39/10.66 | gives: % 74.39/10.66 | (34) all_93_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 74.39/10.66 | : (cons(v1, v0) = all_93_0 & ssItem(v1) = 0 & $i(v1))) % 74.39/10.66 | % 74.39/10.66 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (26), (28) % 74.39/10.66 | gives: % 74.39/10.66 | (35) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0) % 74.39/10.66 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 74.39/10.66 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1))) % 74.39/10.66 | % 74.39/10.66 | GROUND_INST: instantiating (35) with nil, all_97_0, simplifying with (11), % 74.39/10.66 | (27) gives: % 74.39/10.66 | (36) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_0 = 0) % 74.39/10.66 | | ~ (all_97_1 = nil)) & (all_97_0 = 0 | all_97_1 = nil)) % 74.39/10.66 | % 74.39/10.66 | BETA: splitting (30) gives: % 74.39/10.66 | % 74.39/10.66 | Case 1: % 74.39/10.66 | | % 74.39/10.66 | | (37) ? [v0: $i] : (memberP(all_97_1, v0) = 0 & cons(v0, nil) = all_93_0 % 74.39/10.66 | | & ssItem(v0) = 0 & $i(v0)) % 74.39/10.66 | | % 74.39/10.66 | | DELTA: instantiating (37) with fresh symbol all_294_0 gives: % 74.39/10.66 | | (38) memberP(all_97_1, all_294_0) = 0 & cons(all_294_0, nil) = all_93_0 & % 74.39/10.66 | | ssItem(all_294_0) = 0 & $i(all_294_0) % 74.39/10.66 | | % 74.39/10.66 | | ALPHA: (38) implies: % 74.39/10.66 | | (39) $i(all_294_0) % 74.39/10.66 | | (40) ssItem(all_294_0) = 0 % 74.39/10.66 | | (41) cons(all_294_0, nil) = all_93_0 % 74.39/10.66 | | (42) memberP(all_97_1, all_294_0) = 0 % 74.39/10.66 | | % 74.39/10.66 | | BETA: splitting (29) gives: % 74.39/10.66 | | % 74.39/10.66 | | Case 1: % 74.39/10.66 | | | % 74.39/10.67 | | | (43) all_97_0 = 0 & ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_0) | ~ % 74.39/10.67 | | | $i(v0) | ? [v1: any] : ? [v2: any] : (memberP(all_97_1, v0) = % 74.39/10.67 | | | v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 74.39/10.67 | | | % 74.39/10.67 | | | ALPHA: (43) implies: % 74.39/10.67 | | | (44) ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_0) | ~ $i(v0) | ? [v1: % 74.39/10.67 | | | any] : ? [v2: any] : (memberP(all_97_1, v0) = v2 & ssItem(v0) % 74.39/10.67 | | | = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 74.39/10.67 | | | % 74.39/10.67 | | | BETA: splitting (34) gives: % 74.39/10.67 | | | % 74.39/10.67 | | | Case 1: % 74.39/10.67 | | | | % 74.39/10.67 | | | | (45) all_93_0 = nil % 74.39/10.67 | | | | % 74.39/10.67 | | | | REDUCE: (41), (45) imply: % 74.39/10.67 | | | | (46) cons(all_294_0, nil) = nil % 74.39/10.67 | | | | % 74.39/10.67 | | | | GROUND_INST: instantiating (33) with all_294_0, simplifying with (39), % 74.39/10.67 | | | | (46) gives: % 74.39/10.67 | | | | (47) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_294_0) = v0) % 74.39/10.67 | | | | % 74.39/10.67 | | | | GROUND_INST: instantiating (31) with all_294_0, nil, simplifying with % 74.39/10.67 | | | | (39), (46) gives: % 74.39/10.67 | | | | (48) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 & ssItem(all_294_0) = % 74.39/10.67 | | | | v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 74.39/10.67 | | | | % 74.39/10.67 | | | | GROUND_INST: instantiating (32) with all_294_0, nil, simplifying with % 74.39/10.67 | | | | (39), (46) gives: % 74.39/10.67 | | | | (49) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 & ssItem(all_294_0) = % 74.39/10.67 | | | | v0 & $i(v1) & ( ~ (v0 = 0) | v1 = all_294_0)) % 74.39/10.67 | | | | % 74.39/10.67 | | | | DELTA: instantiating (47) with fresh symbol all_529_0 gives: % 74.39/10.67 | | | | (50) ~ (all_529_0 = 0) & ssItem(all_294_0) = all_529_0 % 74.39/10.67 | | | | % 74.39/10.67 | | | | ALPHA: (50) implies: % 74.39/10.67 | | | | (51) ~ (all_529_0 = 0) % 74.39/10.67 | | | | (52) ssItem(all_294_0) = all_529_0 % 74.39/10.67 | | | | % 74.39/10.67 | | | | DELTA: instantiating (48) with fresh symbols all_531_0, all_531_1 gives: % 74.39/10.67 | | | | (53) tl(nil) = all_531_0 & ssItem(all_294_0) = all_531_1 & % 74.39/10.67 | | | | $i(all_531_0) & ( ~ (all_531_1 = 0) | all_531_0 = nil) % 74.39/10.67 | | | | % 74.39/10.67 | | | | ALPHA: (53) implies: % 74.39/10.67 | | | | (54) ssItem(all_294_0) = all_531_1 % 74.39/10.67 | | | | % 74.39/10.67 | | | | DELTA: instantiating (49) with fresh symbols all_533_0, all_533_1 gives: % 74.39/10.67 | | | | (55) hd(nil) = all_533_0 & ssItem(all_294_0) = all_533_1 & % 74.39/10.67 | | | | $i(all_533_0) & ( ~ (all_533_1 = 0) | all_533_0 = all_294_0) % 74.39/10.67 | | | | % 74.39/10.67 | | | | ALPHA: (55) implies: % 74.39/10.67 | | | | (56) ssItem(all_294_0) = all_533_1 % 74.39/10.67 | | | | % 74.39/10.67 | | | | GROUND_INST: instantiating (13) with all_529_0, all_531_1, all_294_0, % 74.39/10.67 | | | | simplifying with (52), (54) gives: % 74.39/10.67 | | | | (57) all_531_1 = all_529_0 % 74.39/10.67 | | | | % 74.39/10.67 | | | | GROUND_INST: instantiating (13) with 0, all_533_1, all_294_0, % 74.39/10.67 | | | | simplifying with (40), (56) gives: % 74.39/10.67 | | | | (58) all_533_1 = 0 % 74.39/10.67 | | | | % 74.39/10.67 | | | | GROUND_INST: instantiating (13) with all_531_1, all_533_1, all_294_0, % 74.39/10.67 | | | | simplifying with (54), (56) gives: % 74.39/10.67 | | | | (59) all_533_1 = all_531_1 % 74.39/10.67 | | | | % 74.39/10.67 | | | | COMBINE_EQS: (58), (59) imply: % 74.39/10.67 | | | | (60) all_531_1 = 0 % 74.39/10.67 | | | | % 74.39/10.67 | | | | SIMP: (60) implies: % 74.39/10.67 | | | | (61) all_531_1 = 0 % 74.39/10.67 | | | | % 74.39/10.67 | | | | COMBINE_EQS: (57), (61) imply: % 74.39/10.67 | | | | (62) all_529_0 = 0 % 74.39/10.67 | | | | % 74.39/10.67 | | | | SIMP: (62) implies: % 74.39/10.67 | | | | (63) all_529_0 = 0 % 74.39/10.67 | | | | % 74.39/10.67 | | | | REDUCE: (51), (63) imply: % 74.39/10.67 | | | | (64) $false % 74.39/10.67 | | | | % 74.39/10.67 | | | | CLOSE: (64) is inconsistent. % 74.39/10.67 | | | | % 74.39/10.67 | | | Case 2: % 74.39/10.67 | | | | % 74.39/10.68 | | | | (65) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (cons(v1, % 74.39/10.68 | | | | v0) = all_93_0 & ssItem(v1) = 0 & $i(v1))) % 74.39/10.68 | | | | % 74.39/10.68 | | | | DELTA: instantiating (65) with fresh symbol all_323_0 gives: % 74.39/10.68 | | | | (66) ssList(all_323_0) = 0 & $i(all_323_0) & ? [v0: $i] : (cons(v0, % 74.39/10.68 | | | | all_323_0) = all_93_0 & ssItem(v0) = 0 & $i(v0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | ALPHA: (66) implies: % 74.39/10.68 | | | | (67) $i(all_323_0) % 74.39/10.68 | | | | (68) ssList(all_323_0) = 0 % 74.39/10.68 | | | | (69) ? [v0: $i] : (cons(v0, all_323_0) = all_93_0 & ssItem(v0) = 0 & % 74.39/10.68 | | | | $i(v0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | DELTA: instantiating (69) with fresh symbol all_325_0 gives: % 74.39/10.68 | | | | (70) cons(all_325_0, all_323_0) = all_93_0 & ssItem(all_325_0) = 0 & % 74.39/10.68 | | | | $i(all_325_0) % 74.39/10.68 | | | | % 74.39/10.68 | | | | ALPHA: (70) implies: % 74.39/10.68 | | | | (71) $i(all_325_0) % 74.39/10.68 | | | | (72) ssItem(all_325_0) = 0 % 74.39/10.68 | | | | (73) cons(all_325_0, all_323_0) = all_93_0 % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (ax44) with all_325_0, simplifying with (71), % 74.39/10.68 | | | | (72) gives: % 74.39/10.68 | | | | (74) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : % 74.39/10.68 | | | | ! [v2: $i] : ( ~ (cons(all_325_0, v1) = v2) | ~ $i(v1) | ? % 74.39/10.68 | | | | [v3: int] : ( ~ (v3 = 0) & ssList(v1) = v3) | ! [v3: $i] : % 74.39/10.68 | | | | ! [v4: $i] : ! [v5: any] : ( ~ (frontsegP(v2, v4) = v5) | % 74.39/10.68 | | | | ~ (cons(v0, v3) = v4) | ~ $i(v3) | ? [v6: any] : ? [v7: % 74.39/10.68 | | | | any] : (frontsegP(v1, v3) = v7 & ssList(v3) = v6 & ( ~ % 74.39/10.68 | | | | (v6 = 0) | (( ~ (v7 = 0) | ~ (v0 = all_325_0) | v5 = % 74.39/10.68 | | | | 0) & ( ~ (v5 = 0) | (v7 = 0 & v0 = % 74.39/10.68 | | | | all_325_0)))))))) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (44) with all_294_0, simplifying with (39), % 74.39/10.68 | | | | (41) gives: % 74.39/10.68 | | | | (75) ? [v0: any] : ? [v1: any] : (memberP(all_97_1, all_294_0) = v1 % 74.39/10.68 | | | | & ssItem(all_294_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (31) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (76) ? [v0: any] : ? [v1: $i] : (tl(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (32) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (77) ? [v0: any] : ? [v1: $i] : (hd(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 74.39/10.68 | | | | all_294_0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (10) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (78) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (9) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (79) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (8) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (80) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (7) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (81) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (6) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (82) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (5) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (83) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (4) with all_294_0, all_93_0, simplifying % 74.39/10.68 | | | | with (39), (41) gives: % 74.39/10.68 | | | | (84) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_0) = v1 & % 74.39/10.68 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.68 | | | | % 74.39/10.68 | | | | GROUND_INST: instantiating (74) with all_95_0, simplifying with (23), % 74.39/10.68 | | | | (24) gives: % 74.39/10.69 | | | | (85) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_325_0, v0) = v1) | ~ % 74.39/10.69 | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! % 74.39/10.69 | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (frontsegP(v1, v3) % 74.39/10.69 | | | | = v4) | ~ (cons(all_95_0, v2) = v3) | ~ $i(v2) | ? [v5: % 74.39/10.69 | | | | any] : ? [v6: any] : (frontsegP(v0, v2) = v6 & ssList(v2) % 74.39/10.69 | | | | = v5 & ( ~ (v5 = 0) | (( ~ (v6 = 0) | ~ (all_325_0 = % 74.39/10.69 | | | | all_95_0) | v4 = 0) & ( ~ (v4 = 0) | (v6 = 0 & % 74.39/10.69 | | | | all_325_0 = all_95_0))))))) % 74.39/10.69 | | | | % 74.39/10.69 | | | | GROUND_INST: instantiating (85) with all_323_0, all_93_0, simplifying % 74.39/10.69 | | | | with (67), (73) gives: % 74.39/10.69 | | | | (86) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_323_0) = v0) | ! [v0: % 74.39/10.69 | | | | $i] : ! [v1: $i] : ! [v2: any] : ( ~ (frontsegP(all_93_0, % 74.39/10.69 | | | | v1) = v2) | ~ (cons(all_95_0, v0) = v1) | ~ $i(v0) | ? % 74.39/10.69 | | | | [v3: any] : ? [v4: any] : (frontsegP(all_323_0, v0) = v4 & % 74.39/10.69 | | | | ssList(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | ~ % 74.39/10.69 | | | | (all_325_0 = all_95_0) | v2 = 0) & ( ~ (v2 = 0) | (v4 % 74.39/10.69 | | | | = 0 & all_325_0 = all_95_0)))))) % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (84) with fresh symbols all_764_0, all_764_1 gives: % 74.39/10.69 | | | | (87) cyclefreeP(all_93_0) = all_764_0 & ssItem(all_294_0) = all_764_1 % 74.39/10.69 | | | | & ( ~ (all_764_1 = 0) | all_764_0 = 0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (87) implies: % 74.39/10.69 | | | | (88) ssItem(all_294_0) = all_764_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (83) with fresh symbols all_766_0, all_766_1 gives: % 74.39/10.69 | | | | (89) totalorderP(all_93_0) = all_766_0 & ssItem(all_294_0) = % 74.39/10.69 | | | | all_766_1 & ( ~ (all_766_1 = 0) | all_766_0 = 0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (89) implies: % 74.39/10.69 | | | | (90) ssItem(all_294_0) = all_766_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (80) with fresh symbols all_768_0, all_768_1 gives: % 74.39/10.69 | | | | (91) strictorderedP(all_93_0) = all_768_0 & ssItem(all_294_0) = % 74.39/10.69 | | | | all_768_1 & ( ~ (all_768_1 = 0) | all_768_0 = 0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (91) implies: % 74.39/10.69 | | | | (92) ssItem(all_294_0) = all_768_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (79) with fresh symbols all_770_0, all_770_1 gives: % 74.39/10.69 | | | | (93) duplicatefreeP(all_93_0) = all_770_0 & ssItem(all_294_0) = % 74.39/10.69 | | | | all_770_1 & ( ~ (all_770_1 = 0) | all_770_0 = 0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (93) implies: % 74.39/10.69 | | | | (94) ssItem(all_294_0) = all_770_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (78) with fresh symbols all_772_0, all_772_1 gives: % 74.39/10.69 | | | | (95) equalelemsP(all_93_0) = all_772_0 & ssItem(all_294_0) = % 74.39/10.69 | | | | all_772_1 & ( ~ (all_772_1 = 0) | all_772_0 = 0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (95) implies: % 74.39/10.69 | | | | (96) ssItem(all_294_0) = all_772_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (82) with fresh symbols all_774_0, all_774_1 gives: % 74.39/10.69 | | | | (97) strictorderP(all_93_0) = all_774_0 & ssItem(all_294_0) = % 74.39/10.69 | | | | all_774_1 & ( ~ (all_774_1 = 0) | all_774_0 = 0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (97) implies: % 74.39/10.69 | | | | (98) ssItem(all_294_0) = all_774_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (75) with fresh symbols all_776_0, all_776_1 gives: % 74.39/10.69 | | | | (99) memberP(all_97_1, all_294_0) = all_776_0 & ssItem(all_294_0) = % 74.39/10.69 | | | | all_776_1 & ( ~ (all_776_0 = 0) | ~ (all_776_1 = 0)) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (99) implies: % 74.39/10.69 | | | | (100) ssItem(all_294_0) = all_776_1 % 74.39/10.69 | | | | (101) memberP(all_97_1, all_294_0) = all_776_0 % 74.39/10.69 | | | | (102) ~ (all_776_0 = 0) | ~ (all_776_1 = 0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (81) with fresh symbols all_778_0, all_778_1 gives: % 74.39/10.69 | | | | (103) totalorderedP(all_93_0) = all_778_0 & ssItem(all_294_0) = % 74.39/10.69 | | | | all_778_1 & ( ~ (all_778_1 = 0) | all_778_0 = 0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (103) implies: % 74.39/10.69 | | | | (104) ssItem(all_294_0) = all_778_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (76) with fresh symbols all_780_0, all_780_1 gives: % 74.39/10.69 | | | | (105) tl(all_93_0) = all_780_0 & ssItem(all_294_0) = all_780_1 & % 74.39/10.69 | | | | $i(all_780_0) & ( ~ (all_780_1 = 0) | all_780_0 = nil) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (105) implies: % 74.39/10.69 | | | | (106) ssItem(all_294_0) = all_780_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | DELTA: instantiating (77) with fresh symbols all_782_0, all_782_1 gives: % 74.39/10.69 | | | | (107) hd(all_93_0) = all_782_0 & ssItem(all_294_0) = all_782_1 & % 74.39/10.69 | | | | $i(all_782_0) & ( ~ (all_782_1 = 0) | all_782_0 = all_294_0) % 74.39/10.69 | | | | % 74.39/10.69 | | | | ALPHA: (107) implies: % 74.39/10.69 | | | | (108) ssItem(all_294_0) = all_782_1 % 74.39/10.69 | | | | % 74.39/10.69 | | | | BETA: splitting (86) gives: % 74.39/10.69 | | | | % 74.39/10.69 | | | | Case 1: % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | (109) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_323_0) = v0) % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | DELTA: instantiating (109) with fresh symbol all_816_0 gives: % 74.39/10.69 | | | | | (110) ~ (all_816_0 = 0) & ssList(all_323_0) = all_816_0 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | ALPHA: (110) implies: % 74.39/10.69 | | | | | (111) ~ (all_816_0 = 0) % 74.39/10.69 | | | | | (112) ssList(all_323_0) = all_816_0 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | DELTA: instantiating (109) with fresh symbol all_818_0 gives: % 74.39/10.69 | | | | | (113) ~ (all_818_0 = 0) & ssList(all_323_0) = all_818_0 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | ALPHA: (113) implies: % 74.39/10.69 | | | | | (114) ssList(all_323_0) = all_818_0 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | GROUND_INST: instantiating (14) with 0, all_818_0, all_323_0, % 74.39/10.69 | | | | | simplifying with (68), (114) gives: % 74.39/10.69 | | | | | (115) all_818_0 = 0 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | GROUND_INST: instantiating (14) with all_816_0, all_818_0, all_323_0, % 74.39/10.69 | | | | | simplifying with (112), (114) gives: % 74.39/10.69 | | | | | (116) all_818_0 = all_816_0 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | COMBINE_EQS: (115), (116) imply: % 74.39/10.69 | | | | | (117) all_816_0 = 0 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | SIMP: (117) implies: % 74.39/10.69 | | | | | (118) all_816_0 = 0 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | REDUCE: (111), (118) imply: % 74.39/10.69 | | | | | (119) $false % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | CLOSE: (119) is inconsistent. % 74.39/10.69 | | | | | % 74.39/10.69 | | | | Case 2: % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | GROUND_INST: instantiating (13) with all_768_1, all_770_1, all_294_0, % 74.39/10.69 | | | | | simplifying with (92), (94) gives: % 74.39/10.69 | | | | | (120) all_770_1 = all_768_1 % 74.39/10.69 | | | | | % 74.39/10.69 | | | | | GROUND_INST: instantiating (13) with 0, all_774_1, all_294_0, % 74.39/10.69 | | | | | simplifying with (40), (98) gives: % 74.39/10.69 | | | | | (121) all_774_1 = 0 % 74.39/10.69 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (13) with all_768_1, all_774_1, all_294_0, % 74.39/10.70 | | | | | simplifying with (92), (98) gives: % 74.39/10.70 | | | | | (122) all_774_1 = all_768_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (13) with all_768_1, all_776_1, all_294_0, % 74.39/10.70 | | | | | simplifying with (92), (100) gives: % 74.39/10.70 | | | | | (123) all_776_1 = all_768_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (13) with all_764_1, all_776_1, all_294_0, % 74.39/10.70 | | | | | simplifying with (88), (100) gives: % 74.39/10.70 | | | | | (124) all_776_1 = all_764_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (13) with all_778_1, all_780_1, all_294_0, % 74.39/10.70 | | | | | simplifying with (104), (106) gives: % 74.39/10.70 | | | | | (125) all_780_1 = all_778_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (13) with all_772_1, all_780_1, all_294_0, % 74.39/10.70 | | | | | simplifying with (96), (106) gives: % 74.39/10.70 | | | | | (126) all_780_1 = all_772_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (13) with all_770_1, all_780_1, all_294_0, % 74.39/10.70 | | | | | simplifying with (94), (106) gives: % 74.39/10.70 | | | | | (127) all_780_1 = all_770_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (13) with all_778_1, all_782_1, all_294_0, % 74.39/10.70 | | | | | simplifying with (104), (108) gives: % 74.39/10.70 | | | | | (128) all_782_1 = all_778_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (13) with all_766_1, all_782_1, all_294_0, % 74.39/10.70 | | | | | simplifying with (90), (108) gives: % 74.39/10.70 | | | | | (129) all_782_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (15) with 0, all_776_0, all_294_0, % 74.39/10.70 | | | | | all_97_1, simplifying with (42), (101) gives: % 74.39/10.70 | | | | | (130) all_776_0 = 0 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (128), (129) imply: % 74.39/10.70 | | | | | (131) all_778_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | SIMP: (131) implies: % 74.39/10.70 | | | | | (132) all_778_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (125), (126) imply: % 74.39/10.70 | | | | | (133) all_778_1 = all_772_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | SIMP: (133) implies: % 74.39/10.70 | | | | | (134) all_778_1 = all_772_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (126), (127) imply: % 74.39/10.70 | | | | | (135) all_772_1 = all_770_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (132), (134) imply: % 74.39/10.70 | | | | | (136) all_772_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | SIMP: (136) implies: % 74.39/10.70 | | | | | (137) all_772_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (123), (124) imply: % 74.39/10.70 | | | | | (138) all_768_1 = all_764_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | SIMP: (138) implies: % 74.39/10.70 | | | | | (139) all_768_1 = all_764_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (121), (122) imply: % 74.39/10.70 | | | | | (140) all_768_1 = 0 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | SIMP: (140) implies: % 74.39/10.70 | | | | | (141) all_768_1 = 0 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (135), (137) imply: % 74.39/10.70 | | | | | (142) all_770_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | SIMP: (142) implies: % 74.39/10.70 | | | | | (143) all_770_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (120), (143) imply: % 74.39/10.70 | | | | | (144) all_768_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | SIMP: (144) implies: % 74.39/10.70 | | | | | (145) all_768_1 = all_766_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (141), (145) imply: % 74.39/10.70 | | | | | (146) all_766_1 = 0 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (139), (145) imply: % 74.39/10.70 | | | | | (147) all_766_1 = all_764_1 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (146), (147) imply: % 74.39/10.70 | | | | | (148) all_764_1 = 0 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | SIMP: (148) implies: % 74.39/10.70 | | | | | (149) all_764_1 = 0 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | COMBINE_EQS: (124), (149) imply: % 74.39/10.70 | | | | | (150) all_776_1 = 0 % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | BETA: splitting (102) gives: % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | Case 1: % 74.39/10.70 | | | | | | % 74.39/10.70 | | | | | | (151) ~ (all_776_0 = 0) % 74.39/10.70 | | | | | | % 74.39/10.70 | | | | | | REDUCE: (130), (151) imply: % 74.39/10.70 | | | | | | (152) $false % 74.39/10.70 | | | | | | % 74.39/10.70 | | | | | | CLOSE: (152) is inconsistent. % 74.39/10.70 | | | | | | % 74.39/10.70 | | | | | Case 2: % 74.39/10.70 | | | | | | % 74.39/10.70 | | | | | | (153) ~ (all_776_1 = 0) % 74.39/10.70 | | | | | | % 74.39/10.70 | | | | | | REDUCE: (150), (153) imply: % 74.39/10.70 | | | | | | (154) $false % 74.39/10.70 | | | | | | % 74.39/10.70 | | | | | | CLOSE: (154) is inconsistent. % 74.39/10.70 | | | | | | % 74.39/10.70 | | | | | End of split % 74.39/10.70 | | | | | % 74.39/10.70 | | | | End of split % 74.39/10.70 | | | | % 74.39/10.70 | | | End of split % 74.39/10.70 | | | % 74.39/10.70 | | Case 2: % 74.39/10.70 | | | % 74.39/10.70 | | | (155) all_97_1 = nil & ~ (all_93_0 = nil) % 74.39/10.70 | | | % 74.39/10.70 | | | ALPHA: (155) implies: % 74.39/10.70 | | | (156) all_97_1 = nil % 74.39/10.70 | | | % 74.39/10.70 | | | REDUCE: (42), (156) imply: % 74.39/10.70 | | | (157) memberP(nil, all_294_0) = 0 % 74.39/10.70 | | | % 74.39/10.70 | | | BETA: splitting (36) gives: % 74.39/10.70 | | | % 74.39/10.70 | | | Case 1: % 74.39/10.70 | | | | % 74.39/10.70 | | | | (158) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 74.39/10.70 | | | | % 74.39/10.70 | | | | DELTA: instantiating (158) with fresh symbol all_303_0 gives: % 74.39/10.70 | | | | (159) ~ (all_303_0 = 0) & ssList(nil) = all_303_0 % 74.39/10.70 | | | | % 74.39/10.70 | | | | REF_CLOSE: (1), (14), (159) are inconsistent by sub-proof #1. % 74.39/10.70 | | | | % 74.39/10.70 | | | Case 2: % 74.39/10.70 | | | | % 74.39/10.70 | | | | (160) ( ~ (all_97_0 = 0) | ~ (all_97_1 = nil)) & (all_97_0 = 0 | % 74.39/10.70 | | | | all_97_1 = nil) % 74.39/10.70 | | | | % 74.39/10.70 | | | | ALPHA: (160) implies: % 74.39/10.70 | | | | (161) ~ (all_97_0 = 0) | ~ (all_97_1 = nil) % 74.39/10.70 | | | | % 74.39/10.70 | | | | BETA: splitting (161) gives: % 74.39/10.70 | | | | % 74.39/10.70 | | | | Case 1: % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | (162) ~ (all_97_1 = nil) % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | REDUCE: (156), (162) imply: % 74.39/10.70 | | | | | (163) $false % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | CLOSE: (163) is inconsistent. % 74.39/10.70 | | | | | % 74.39/10.70 | | | | Case 2: % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (31) with all_294_0, all_93_0, simplifying % 74.39/10.70 | | | | | with (39), (41) gives: % 74.39/10.70 | | | | | (164) ? [v0: any] : ? [v1: $i] : (tl(all_93_0) = v1 & % 74.39/10.70 | | | | | ssItem(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (32) with all_294_0, all_93_0, simplifying % 74.39/10.70 | | | | | with (39), (41) gives: % 74.39/10.70 | | | | | (165) ? [v0: any] : ? [v1: $i] : (hd(all_93_0) = v1 & % 74.39/10.70 | | | | | ssItem(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 74.39/10.70 | | | | | all_294_0)) % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (10) with all_294_0, all_93_0, simplifying % 74.39/10.70 | | | | | with (39), (41) gives: % 74.39/10.70 | | | | | (166) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_0) = v1 & % 74.39/10.70 | | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.70 | | | | | % 74.39/10.70 | | | | | GROUND_INST: instantiating (9) with all_294_0, all_93_0, simplifying % 74.39/10.70 | | | | | with (39), (41) gives: % 74.39/10.71 | | | | | (167) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_0) = v1 % 74.39/10.71 | | | | | & ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (8) with all_294_0, all_93_0, simplifying % 74.39/10.71 | | | | | with (39), (41) gives: % 74.39/10.71 | | | | | (168) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_0) = v1 % 74.39/10.71 | | | | | & ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (7) with all_294_0, all_93_0, simplifying % 74.39/10.71 | | | | | with (39), (41) gives: % 74.39/10.71 | | | | | (169) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_0) = v1 & % 74.39/10.71 | | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (6) with all_294_0, all_93_0, simplifying % 74.39/10.71 | | | | | with (39), (41) gives: % 74.39/10.71 | | | | | (170) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_0) = v1 & % 74.39/10.71 | | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (5) with all_294_0, all_93_0, simplifying % 74.39/10.71 | | | | | with (39), (41) gives: % 74.39/10.71 | | | | | (171) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_0) = v1 & % 74.39/10.71 | | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (4) with all_294_0, all_93_0, simplifying % 74.39/10.71 | | | | | with (39), (41) gives: % 74.39/10.71 | | | | | (172) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_0) = v1 & % 74.39/10.71 | | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (3) with all_294_0, simplifying with (39), % 74.39/10.71 | | | | | (157) gives: % 74.39/10.71 | | | | | (173) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_294_0) = v0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (173) with fresh symbol all_521_0 gives: % 74.39/10.71 | | | | | (174) ~ (all_521_0 = 0) & ssItem(all_294_0) = all_521_0 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (174) implies: % 74.39/10.71 | | | | | (175) ~ (all_521_0 = 0) % 74.39/10.71 | | | | | (176) ssItem(all_294_0) = all_521_0 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (167) with fresh symbols all_523_0, all_523_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (177) duplicatefreeP(all_93_0) = all_523_0 & ssItem(all_294_0) = % 74.39/10.71 | | | | | all_523_1 & ( ~ (all_523_1 = 0) | all_523_0 = 0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (177) implies: % 74.39/10.71 | | | | | (178) ssItem(all_294_0) = all_523_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (172) with fresh symbols all_525_0, all_525_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (179) cyclefreeP(all_93_0) = all_525_0 & ssItem(all_294_0) = % 74.39/10.71 | | | | | all_525_1 & ( ~ (all_525_1 = 0) | all_525_0 = 0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (179) implies: % 74.39/10.71 | | | | | (180) ssItem(all_294_0) = all_525_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (171) with fresh symbols all_527_0, all_527_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (181) totalorderP(all_93_0) = all_527_0 & ssItem(all_294_0) = % 74.39/10.71 | | | | | all_527_1 & ( ~ (all_527_1 = 0) | all_527_0 = 0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (181) implies: % 74.39/10.71 | | | | | (182) ssItem(all_294_0) = all_527_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (170) with fresh symbols all_529_0, all_529_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (183) strictorderP(all_93_0) = all_529_0 & ssItem(all_294_0) = % 74.39/10.71 | | | | | all_529_1 & ( ~ (all_529_1 = 0) | all_529_0 = 0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (183) implies: % 74.39/10.71 | | | | | (184) ssItem(all_294_0) = all_529_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (166) with fresh symbols all_531_0, all_531_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (185) equalelemsP(all_93_0) = all_531_0 & ssItem(all_294_0) = % 74.39/10.71 | | | | | all_531_1 & ( ~ (all_531_1 = 0) | all_531_0 = 0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (185) implies: % 74.39/10.71 | | | | | (186) ssItem(all_294_0) = all_531_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (169) with fresh symbols all_533_0, all_533_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (187) totalorderedP(all_93_0) = all_533_0 & ssItem(all_294_0) = % 74.39/10.71 | | | | | all_533_1 & ( ~ (all_533_1 = 0) | all_533_0 = 0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (187) implies: % 74.39/10.71 | | | | | (188) ssItem(all_294_0) = all_533_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (168) with fresh symbols all_535_0, all_535_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (189) strictorderedP(all_93_0) = all_535_0 & ssItem(all_294_0) = % 74.39/10.71 | | | | | all_535_1 & ( ~ (all_535_1 = 0) | all_535_0 = 0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (189) implies: % 74.39/10.71 | | | | | (190) ssItem(all_294_0) = all_535_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (165) with fresh symbols all_537_0, all_537_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (191) hd(all_93_0) = all_537_0 & ssItem(all_294_0) = all_537_1 & % 74.39/10.71 | | | | | $i(all_537_0) & ( ~ (all_537_1 = 0) | all_537_0 = all_294_0) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (191) implies: % 74.39/10.71 | | | | | (192) ssItem(all_294_0) = all_537_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | DELTA: instantiating (164) with fresh symbols all_539_0, all_539_1 % 74.39/10.71 | | | | | gives: % 74.39/10.71 | | | | | (193) tl(all_93_0) = all_539_0 & ssItem(all_294_0) = all_539_1 & % 74.39/10.71 | | | | | $i(all_539_0) & ( ~ (all_539_1 = 0) | all_539_0 = nil) % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | ALPHA: (193) implies: % 74.39/10.71 | | | | | (194) ssItem(all_294_0) = all_539_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_527_1, all_529_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (182), (184) gives: % 74.39/10.71 | | | | | (195) all_529_1 = all_527_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_529_1, all_533_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (184), (188) gives: % 74.39/10.71 | | | | | (196) all_533_1 = all_529_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_521_0, all_533_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (176), (188) gives: % 74.39/10.71 | | | | | (197) all_533_1 = all_521_0 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with 0, all_535_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (40), (190) gives: % 74.39/10.71 | | | | | (198) all_535_1 = 0 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_531_1, all_535_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (186), (190) gives: % 74.39/10.71 | | | | | (199) all_535_1 = all_531_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_535_1, all_537_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (190), (192) gives: % 74.39/10.71 | | | | | (200) all_537_1 = all_535_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_529_1, all_537_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (184), (192) gives: % 74.39/10.71 | | | | | (201) all_537_1 = all_529_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_523_1, all_537_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (178), (192) gives: % 74.39/10.71 | | | | | (202) all_537_1 = all_523_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_529_1, all_539_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (184), (194) gives: % 74.39/10.71 | | | | | (203) all_539_1 = all_529_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | GROUND_INST: instantiating (13) with all_525_1, all_539_1, all_294_0, % 74.39/10.71 | | | | | simplifying with (180), (194) gives: % 74.39/10.71 | | | | | (204) all_539_1 = all_525_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | COMBINE_EQS: (203), (204) imply: % 74.39/10.71 | | | | | (205) all_529_1 = all_525_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | SIMP: (205) implies: % 74.39/10.71 | | | | | (206) all_529_1 = all_525_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | COMBINE_EQS: (200), (202) imply: % 74.39/10.71 | | | | | (207) all_535_1 = all_523_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | SIMP: (207) implies: % 74.39/10.71 | | | | | (208) all_535_1 = all_523_1 % 74.39/10.71 | | | | | % 74.39/10.71 | | | | | COMBINE_EQS: (201), (202) imply: % 74.39/10.72 | | | | | (209) all_529_1 = all_523_1 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | SIMP: (209) implies: % 74.39/10.72 | | | | | (210) all_529_1 = all_523_1 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (198), (199) imply: % 74.39/10.72 | | | | | (211) all_531_1 = 0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (199), (208) imply: % 74.39/10.72 | | | | | (212) all_531_1 = all_523_1 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (196), (197) imply: % 74.39/10.72 | | | | | (213) all_529_1 = all_521_0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | SIMP: (213) implies: % 74.39/10.72 | | | | | (214) all_529_1 = all_521_0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (211), (212) imply: % 74.39/10.72 | | | | | (215) all_523_1 = 0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | SIMP: (215) implies: % 74.39/10.72 | | | | | (216) all_523_1 = 0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (195), (210) imply: % 74.39/10.72 | | | | | (217) all_527_1 = all_523_1 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (195), (206) imply: % 74.39/10.72 | | | | | (218) all_527_1 = all_525_1 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (195), (214) imply: % 74.39/10.72 | | | | | (219) all_527_1 = all_521_0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (218), (219) imply: % 74.39/10.72 | | | | | (220) all_525_1 = all_521_0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (217), (218) imply: % 74.39/10.72 | | | | | (221) all_525_1 = all_523_1 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (220), (221) imply: % 74.39/10.72 | | | | | (222) all_523_1 = all_521_0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | SIMP: (222) implies: % 74.39/10.72 | | | | | (223) all_523_1 = all_521_0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | COMBINE_EQS: (216), (223) imply: % 74.39/10.72 | | | | | (224) all_521_0 = 0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | SIMP: (224) implies: % 74.39/10.72 | | | | | (225) all_521_0 = 0 % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | REDUCE: (175), (225) imply: % 74.39/10.72 | | | | | (226) $false % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | CLOSE: (226) is inconsistent. % 74.39/10.72 | | | | | % 74.39/10.72 | | | | End of split % 74.39/10.72 | | | | % 74.39/10.72 | | | End of split % 74.39/10.72 | | | % 74.39/10.72 | | End of split % 74.39/10.72 | | % 74.39/10.72 | Case 2: % 74.39/10.72 | | % 74.39/10.72 | | (227) all_97_1 = nil & all_93_0 = nil % 74.39/10.72 | | % 74.39/10.72 | | ALPHA: (227) implies: % 74.39/10.72 | | (228) all_93_0 = nil % 74.39/10.72 | | (229) all_97_1 = nil % 74.39/10.72 | | % 74.39/10.72 | | BETA: splitting (29) gives: % 74.39/10.72 | | % 74.39/10.72 | | Case 1: % 74.39/10.72 | | | % 74.39/10.72 | | | (230) all_97_0 = 0 & ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_0) | ~ % 74.39/10.72 | | | $i(v0) | ? [v1: any] : ? [v2: any] : (memberP(all_97_1, v0) = % 74.39/10.72 | | | v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 74.39/10.72 | | | % 74.39/10.72 | | | ALPHA: (230) implies: % 74.39/10.72 | | | (231) all_97_0 = 0 % 74.39/10.72 | | | % 74.39/10.72 | | | BETA: splitting (36) gives: % 74.39/10.72 | | | % 74.39/10.72 | | | Case 1: % 74.39/10.72 | | | | % 74.39/10.72 | | | | (232) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 74.39/10.72 | | | | % 74.39/10.72 | | | | DELTA: instantiating (232) with fresh symbol all_303_0 gives: % 74.39/10.72 | | | | (233) ~ (all_303_0 = 0) & ssList(nil) = all_303_0 % 74.39/10.72 | | | | % 74.39/10.72 | | | | REF_CLOSE: (1), (14), (233) are inconsistent by sub-proof #1. % 74.39/10.72 | | | | % 74.39/10.72 | | | Case 2: % 74.39/10.72 | | | | % 74.39/10.72 | | | | (234) ( ~ (all_97_0 = 0) | ~ (all_97_1 = nil)) & (all_97_0 = 0 | % 74.39/10.72 | | | | all_97_1 = nil) % 74.39/10.72 | | | | % 74.39/10.72 | | | | ALPHA: (234) implies: % 74.39/10.72 | | | | (235) ~ (all_97_0 = 0) | ~ (all_97_1 = nil) % 74.39/10.72 | | | | % 74.39/10.72 | | | | BETA: splitting (235) gives: % 74.39/10.72 | | | | % 74.39/10.72 | | | | Case 1: % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | (236) ~ (all_97_1 = nil) % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | REDUCE: (229), (236) imply: % 74.39/10.72 | | | | | (237) $false % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | CLOSE: (237) is inconsistent. % 74.39/10.72 | | | | | % 74.39/10.72 | | | | Case 2: % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | (238) ~ (all_97_0 = 0) % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | REDUCE: (231), (238) imply: % 74.39/10.72 | | | | | (239) $false % 74.39/10.72 | | | | | % 74.39/10.72 | | | | | CLOSE: (239) is inconsistent. % 74.39/10.72 | | | | | % 74.39/10.72 | | | | End of split % 74.39/10.72 | | | | % 74.39/10.72 | | | End of split % 74.39/10.72 | | | % 74.39/10.72 | | Case 2: % 74.39/10.72 | | | % 74.39/10.72 | | | (240) all_97_1 = nil & ~ (all_93_0 = nil) % 74.39/10.72 | | | % 74.39/10.72 | | | ALPHA: (240) implies: % 74.39/10.72 | | | (241) ~ (all_93_0 = nil) % 74.39/10.72 | | | % 74.39/10.72 | | | REDUCE: (228), (241) imply: % 74.39/10.72 | | | (242) $false % 74.39/10.72 | | | % 74.39/10.72 | | | CLOSE: (242) is inconsistent. % 74.39/10.72 | | | % 74.39/10.72 | | End of split % 74.39/10.72 | | % 74.39/10.72 | End of split % 74.39/10.72 | % 74.39/10.72 End of proof % 74.39/10.72 % 74.39/10.72 Sub-proof #1 shows that the following formulas are inconsistent: % 74.39/10.72 ---------------------------------------------------------------- % 74.39/10.72 (1) ~ (all_303_0 = 0) & ssList(nil) = all_303_0 % 74.39/10.72 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 74.39/10.72 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 74.39/10.72 (3) ssList(nil) = 0 % 74.39/10.72 % 74.39/10.72 Begin of proof % 74.39/10.72 | % 74.39/10.72 | ALPHA: (1) implies: % 74.39/10.72 | (4) ~ (all_303_0 = 0) % 74.39/10.72 | (5) ssList(nil) = all_303_0 % 74.39/10.72 | % 74.39/10.72 | GROUND_INST: instantiating (2) with 0, all_303_0, nil, simplifying with (3), % 74.39/10.72 | (5) gives: % 74.39/10.72 | (6) all_303_0 = 0 % 74.39/10.72 | % 74.39/10.72 | REDUCE: (4), (6) imply: % 74.39/10.72 | (7) $false % 74.39/10.72 | % 74.39/10.72 | CLOSE: (7) is inconsistent. % 74.39/10.72 | % 74.39/10.72 End of proof % 74.39/10.72 % SZS output end Proof for theBenchmark % 74.39/10.72 % 74.39/10.72 10107ms %------------------------------------------------------------------------------