%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC048+1 : TPTP v8.1.2. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 20:49:23 EDT 2023 % Result : Theorem 48.05s 7.42s % Output : Proof 198.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SWC048+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n015.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Mon Aug 28 19:16:40 EDT 2023 % 0.11/0.31 % CPUTime : % 0.17/0.60 ________ _____ % 0.17/0.60 ___ __ \_________(_)________________________________ % 0.17/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.61 % 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.61 (2023-06-19) % 0.17/0.61 % 0.17/0.61 (c) Philipp Rümmer, 2009-2023 % 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.61 Amanda Stjerna. % 0.17/0.61 Free software under BSD-3-Clause. % 0.17/0.61 % 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.61 % 0.17/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.62 Running up to 7 provers in parallel. % 0.17/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.16/1.64 Prover 4: Preprocessing ... % 6.28/1.69 Prover 1: Preprocessing ... % 6.71/1.72 Prover 6: Preprocessing ... % 6.71/1.72 Prover 0: Preprocessing ... % 6.71/1.72 Prover 5: Preprocessing ... % 6.71/1.72 Prover 2: Preprocessing ... % 6.71/1.73 Prover 3: Preprocessing ... % 20.01/3.57 Prover 2: Proving ... % 21.04/3.72 Prover 5: Constructing countermodel ... % 21.04/3.86 Prover 1: Constructing countermodel ... % 23.13/4.04 Prover 6: Proving ... % 23.57/4.07 Prover 3: Constructing countermodel ... % 32.50/5.26 Prover 4: Constructing countermodel ... % 32.77/5.32 Prover 0: Proving ... % 48.05/7.42 Prover 3: proved (6784ms) % 48.05/7.42 % 48.05/7.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 48.05/7.42 % 48.83/7.44 Prover 5: stopped % 48.83/7.44 Prover 6: stopped % 48.83/7.45 Prover 2: stopped % 48.83/7.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 48.83/7.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 48.83/7.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 48.83/7.47 Prover 0: stopped % 48.83/7.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 48.83/7.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 50.44/7.72 Prover 8: Preprocessing ... % 51.22/7.74 Prover 7: Preprocessing ... % 51.22/7.75 Prover 13: Preprocessing ... % 51.69/7.84 Prover 10: Preprocessing ... % 51.69/7.87 Prover 11: Preprocessing ... % 53.50/8.08 Prover 7: Constructing countermodel ... % 55.02/8.30 Prover 10: Constructing countermodel ... % 56.53/8.45 Prover 13: Constructing countermodel ... % 56.64/8.74 Prover 8: Warning: ignoring some quantifiers % 56.64/8.76 Prover 8: Constructing countermodel ... % 66.44/9.82 Prover 11: Constructing countermodel ... % 81.42/12.02 Prover 13: stopped % 81.42/12.03 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 84.51/12.17 Prover 16: Preprocessing ... % 87.13/12.48 Prover 16: Constructing countermodel ... % 113.74/15.97 Prover 1: stopped % 113.74/15.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 114.32/16.21 Prover 19: Preprocessing ... % 119.53/16.82 Prover 19: Warning: ignoring some quantifiers % 120.29/16.87 Prover 19: Constructing countermodel ... % 123.90/17.33 Prover 16: stopped % 140.61/19.60 Prover 19: stopped % 196.62/27.97 Prover 4: stopped % 197.47/28.16 Prover 8: Found proof (size 373) % 197.47/28.16 Prover 8: proved (20457ms) % 197.47/28.16 Prover 10: stopped % 197.47/28.16 Prover 7: stopped % 197.47/28.17 Prover 11: stopped % 197.47/28.17 % 197.47/28.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 197.47/28.17 % 197.47/28.18 % SZS output start Proof for theBenchmark % 197.47/28.19 Assumptions after simplification: % 197.47/28.19 --------------------------------- % 197.47/28.19 % 197.47/28.19 (ax13) % 197.47/28.22 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 197.47/28.22 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 197.47/28.22 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 197.47/28.22 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 197.47/28.22 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 197.47/28.22 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 197.47/28.22 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 197.47/28.22 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 197.47/28.22 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 197.47/28.22 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 197.47/28.22 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 197.47/28.22 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 197.47/28.22 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 197.47/28.22 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 197.47/28.22 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 197.47/28.22 % 197.47/28.22 (ax15) % 197.47/28.23 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 197.47/28.23 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 197.47/28.23 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 197.47/28.23 % 197.47/28.23 (ax17) % 197.47/28.23 ssList(nil) = 0 & $i(nil) % 197.47/28.23 % 197.47/28.23 (ax20) % 197.47/28.23 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 197.47/28.23 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 197.47/28.23 ssItem(v2) = 0 & $i(v2)))) % 197.47/28.23 % 197.47/28.23 (ax48) % 197.47/28.23 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~ % 197.47/28.23 (rearsegP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : % 197.47/28.23 (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 197.47/28.23 % 197.47/28.23 (ax49) % 197.47/28.23 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ~ $i(v0) % 197.47/28.23 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 197.47/28.23 % 197.47/28.23 (ax6) % 197.47/28.24 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 197.47/28.24 ( ~ (rearsegP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 197.47/28.24 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : (ssList(v3) = 0 & % 197.47/28.24 app(v3, v1) = v0 & $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (app(v3, % 197.47/28.24 v1) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) % 197.47/28.24 = v4)))))) % 197.47/28.24 % 197.47/28.24 (ax72) % 197.47/28.24 duplicatefreeP(nil) = 0 & $i(nil) % 197.47/28.24 % 197.47/28.24 (ax75) % 197.47/28.24 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (hd(v0) = v1) | ~ $i(v0) % 197.47/28.24 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (ssItem(v1) = 0 & % 197.47/28.24 $i(v1))) % 197.47/28.24 % 197.47/28.24 (ax83) % 197.47/28.24 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 197.47/28.24 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 197.47/28.24 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1 % 197.47/28.24 = nil) | ~ (v0 = nil) | v2 = nil)))) % 197.47/28.24 % 197.87/28.24 (ax85) % 197.87/28.24 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (hd(v0) = v1) | ~ $i(v0) | ? [v2: % 197.87/28.24 int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ! [v3: $i] : (v0 = % 197.87/28.24 nil | ~ (app(v0, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : % 197.87/28.24 (hd(v3) = v5 & ssList(v2) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v1)))) % 197.87/28.24 % 197.87/28.24 (co1) % 197.87/28.24 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] % 197.87/28.24 : (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ? [v3: $i] : ? [v4: any] % 197.87/28.24 : (ssList(v3) = 0 & neq(v3, nil) = v4 & $i(v3) & ? [v5: any] : (v3 = v0 & % 197.87/28.24 rearsegP(v1, v0) = v5 & ((v5 = 0 & v4 = 0) | (v1 = nil & v0 = nil)) & % 197.87/28.24 ((v2 = 0 & ! [v6: $i] : ( ~ (neq(v6, nil) = 0) | ~ $i(v6) | ? [v7: % 197.87/28.24 any] : ? [v8: any] : ? [v9: any] : (rearsegP(v1, v6) = v8 & % 197.87/28.24 rearsegP(v0, v6) = v9 & ssList(v6) = v7 & ( ~ (v9 = 0) | ~ % 197.87/28.24 (v8 = 0) | ~ (v7 = 0))))) | (v1 = nil & ~ (v0 = nil))))))) % 197.87/28.24 % 197.87/28.24 (function-axioms) % 197.87/28.26 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 197.87/28.26 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 197.87/28.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 197.87/28.26 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 197.87/28.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 197.87/28.26 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 197.87/28.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 197.87/28.26 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 197.87/28.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 197.87/28.26 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 197.87/28.26 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 197.87/28.26 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 197.87/28.26 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 197.87/28.26 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 197.87/28.26 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 197.87/28.26 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 197.87/28.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 197.87/28.26 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 197.87/28.26 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 197.87/28.26 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 197.87/28.26 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 197.87/28.26 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 197.87/28.26 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 197.87/28.26 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 197.87/28.26 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 197.87/28.26 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 197.87/28.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 197.87/28.26 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 197.87/28.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 197.87/28.26 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 197.87/28.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 197.87/28.26 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 197.87/28.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 197.87/28.26 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 197.87/28.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 197.87/28.26 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 197.87/28.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 197.87/28.26 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 197.87/28.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 197.87/28.26 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 197.87/28.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 197.87/28.26 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 197.87/28.26 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ? % 197.87/28.26 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ? % 197.87/28.26 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ? % 197.87/28.26 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ? % 197.87/28.26 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ? % 197.87/28.26 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2) % 197.87/28.26 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) = % 197.87/28.26 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 197.87/28.26 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 197.87/28.26 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 197.87/28.26 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? % 197.87/28.26 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 197.87/28.26 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 197.87/28.26 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 197.87/28.26 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 197.87/28.26 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 197.87/28.26 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 197.87/28.26 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 197.87/28.26 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 197.87/28.26 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 197.87/28.26 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0) % 197.87/28.26 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ? % 197.87/28.26 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 197.87/28.26 (hd(v0) = v1 & $i(v1)) % 197.87/28.26 % 197.87/28.26 Further assumptions not needed in the proof: % 197.87/28.26 -------------------------------------------- % 197.87/28.26 ax1, ax10, ax11, ax12, ax14, ax16, ax18, ax19, ax2, ax21, ax22, ax23, ax24, % 197.87/28.26 ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 197.87/28.26 ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax5, % 197.87/28.26 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax60, ax61, ax62, % 197.87/28.26 ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax73, ax74, ax76, % 197.87/28.26 ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax84, ax86, ax87, ax88, ax89, ax9, % 197.87/28.26 ax90, ax91, ax92, ax93, ax94, ax95 % 197.87/28.26 % 197.87/28.26 Those formulas are unsatisfiable: % 197.87/28.26 --------------------------------- % 197.87/28.26 % 197.87/28.26 Begin of proof % 197.87/28.26 | % 197.87/28.26 | ALPHA: (ax17) implies: % 197.87/28.26 | (1) ssList(nil) = 0 % 197.87/28.26 | % 197.87/28.26 | ALPHA: (ax20) implies: % 197.87/28.26 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 197.87/28.26 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 197.87/28.26 | ssItem(v2) = 0 & $i(v2)))) % 197.87/28.26 | % 197.87/28.26 | ALPHA: (ax72) implies: % 197.87/28.26 | (3) duplicatefreeP(nil) = 0 % 197.87/28.26 | % 197.87/28.26 | ALPHA: (ax75) implies: % 197.87/28.26 | (4) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (hd(v0) = v1) | ~ $i(v0) | % 197.87/28.26 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (ssItem(v1) = 0 & % 197.87/28.26 | $i(v1))) % 197.87/28.26 | % 197.87/28.26 | ALPHA: (ax83) implies: % 197.87/28.26 | (5) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 197.87/28.26 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 197.87/28.26 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = % 197.87/28.26 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil)))) % 197.87/28.26 | % 197.87/28.26 | ALPHA: (ax85) implies: % 197.87/28.27 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (hd(v0) = v1) | ~ $i(v0) | ? [v2: % 197.87/28.27 | int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] : ! [v3: $i] % 197.87/28.27 | : (v0 = nil | ~ (app(v0, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 197.87/28.27 | [v5: $i] : (hd(v3) = v5 & ssList(v2) = v4 & $i(v5) & ( ~ (v4 = 0) | % 197.87/28.27 | v5 = v1)))) % 197.87/28.27 | % 197.87/28.27 | ALPHA: (co1) implies: % 197.87/28.27 | (7) $i(nil) % 197.87/28.27 | (8) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 197.87/28.27 | (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ? [v3: $i] : ? [v4: % 197.87/28.27 | any] : (ssList(v3) = 0 & neq(v3, nil) = v4 & $i(v3) & ? [v5: % 197.87/28.27 | any] : (v3 = v0 & rearsegP(v1, v0) = v5 & ((v5 = 0 & v4 = 0) | % 197.87/28.27 | (v1 = nil & v0 = nil)) & ((v2 = 0 & ! [v6: $i] : ( ~ % 197.87/28.27 | (neq(v6, nil) = 0) | ~ $i(v6) | ? [v7: any] : ? [v8: % 197.87/28.27 | any] : ? [v9: any] : (rearsegP(v1, v6) = v8 & % 197.87/28.27 | rearsegP(v0, v6) = v9 & ssList(v6) = v7 & ( ~ (v9 = 0) % 197.87/28.27 | | ~ (v8 = 0) | ~ (v7 = 0))))) | (v1 = nil & ~ (v0 % 197.87/28.27 | = nil))))))) % 197.87/28.27 | % 197.87/28.27 | ALPHA: (function-axioms) implies: % 197.87/28.27 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 197.87/28.27 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 197.87/28.27 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 197.87/28.27 | : ! [v3: $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ % 197.87/28.27 | (rearsegP(v3, v2) = v0)) % 197.87/28.27 | (11) ? [v0: $i] : ? [v1: $i] : (hd(v0) = v1 & $i(v1)) % 197.87/28.27 | % 197.87/28.27 | DELTA: instantiating (11) with fresh symbols all_129_0, all_129_1 gives: % 197.87/28.27 | (12) hd(all_129_1) = all_129_0 & $i(all_129_0) % 197.87/28.27 | % 197.87/28.27 | ALPHA: (12) implies: % 197.87/28.27 | (13) hd(all_129_1) = all_129_0 % 197.87/28.27 | % 197.87/28.27 | DELTA: instantiating (8) with fresh symbol all_139_0 gives: % 197.87/28.27 | (14) ssList(all_139_0) = 0 & $i(all_139_0) & ? [v0: $i] : ? [v1: any] : % 197.87/28.27 | (ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v2: $i] : ? [v3: % 197.87/28.27 | any] : (ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ? [v4: any] % 197.87/28.27 | : (v2 = all_139_0 & rearsegP(v0, all_139_0) = v4 & ((v4 = 0 & v3 = % 197.87/28.27 | 0) | (v0 = nil & all_139_0 = nil)) & ((v1 = 0 & ! [v5: $i] % 197.87/28.27 | : ( ~ (neq(v5, nil) = 0) | ~ $i(v5) | ? [v6: any] : ? % 197.87/28.27 | [v7: any] : ? [v8: any] : (rearsegP(v0, v5) = v7 & % 197.87/28.27 | rearsegP(all_139_0, v5) = v8 & ssList(v5) = v6 & ( ~ (v8 % 197.87/28.27 | = 0) | ~ (v7 = 0) | ~ (v6 = 0))))) | (v0 = nil & % 197.87/28.27 | ~ (all_139_0 = nil)))))) % 197.87/28.27 | % 197.87/28.27 | ALPHA: (14) implies: % 197.87/28.28 | (15) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 197.87/28.28 | $i(v0) & ? [v2: $i] : ? [v3: any] : (ssList(v2) = 0 & neq(v2, nil) % 197.87/28.28 | = v3 & $i(v2) & ? [v4: any] : (v2 = all_139_0 & rearsegP(v0, % 197.87/28.28 | all_139_0) = v4 & ((v4 = 0 & v3 = 0) | (v0 = nil & all_139_0 = % 197.87/28.28 | nil)) & ((v1 = 0 & ! [v5: $i] : ( ~ (neq(v5, nil) = 0) | ~ % 197.87/28.28 | $i(v5) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 197.87/28.28 | (rearsegP(v0, v5) = v7 & rearsegP(all_139_0, v5) = v8 & % 197.87/28.28 | ssList(v5) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 197.87/28.28 | 0))))) | (v0 = nil & ~ (all_139_0 = nil)))))) % 197.87/28.28 | % 197.87/28.28 | DELTA: instantiating (15) with fresh symbols all_143_0, all_143_1 gives: % 197.87/28.28 | (16) ssList(all_143_1) = 0 & neq(all_143_1, nil) = all_143_0 & % 197.87/28.28 | $i(all_143_1) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, % 197.87/28.28 | nil) = v1 & $i(v0) & ? [v2: any] : (v0 = all_139_0 & % 197.87/28.28 | rearsegP(all_143_1, all_139_0) = v2 & ((v2 = 0 & v1 = 0) | % 197.87/28.28 | (all_143_1 = nil & all_139_0 = nil)) & ((all_143_0 = 0 & ! [v3: % 197.87/28.28 | $i] : ( ~ (neq(v3, nil) = 0) | ~ $i(v3) | ? [v4: any] : ? % 197.87/28.28 | [v5: any] : ? [v6: any] : (rearsegP(all_143_1, v3) = v5 & % 197.87/28.28 | rearsegP(all_139_0, v3) = v6 & ssList(v3) = v4 & ( ~ (v6 = % 197.87/28.28 | 0) | ~ (v5 = 0) | ~ (v4 = 0))))) | (all_143_1 = nil % 197.87/28.28 | & ~ (all_139_0 = nil))))) % 197.87/28.28 | % 197.87/28.28 | ALPHA: (16) implies: % 197.87/28.28 | (17) $i(all_143_1) % 197.87/28.28 | (18) neq(all_143_1, nil) = all_143_0 % 197.87/28.28 | (19) ssList(all_143_1) = 0 % 197.87/28.28 | (20) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 197.87/28.28 | $i(v0) & ? [v2: any] : (v0 = all_139_0 & rearsegP(all_143_1, % 197.87/28.28 | all_139_0) = v2 & ((v2 = 0 & v1 = 0) | (all_143_1 = nil & % 197.87/28.28 | all_139_0 = nil)) & ((all_143_0 = 0 & ! [v3: $i] : ( ~ % 197.87/28.28 | (neq(v3, nil) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] % 197.87/28.28 | : ? [v6: any] : (rearsegP(all_143_1, v3) = v5 & % 197.87/28.28 | rearsegP(all_139_0, v3) = v6 & ssList(v3) = v4 & ( ~ (v6 = % 197.87/28.28 | 0) | ~ (v5 = 0) | ~ (v4 = 0))))) | (all_143_1 = nil % 197.87/28.28 | & ~ (all_139_0 = nil))))) % 197.87/28.28 | % 197.87/28.28 | DELTA: instantiating (20) with fresh symbols all_145_0, all_145_1 gives: % 197.87/28.28 | (21) ssList(all_145_1) = 0 & neq(all_145_1, nil) = all_145_0 & % 197.87/28.28 | $i(all_145_1) & ? [v0: any] : (all_145_1 = all_139_0 & % 197.87/28.28 | rearsegP(all_143_1, all_139_0) = v0 & ((v0 = 0 & all_145_0 = 0) | % 197.87/28.28 | (all_143_1 = nil & all_139_0 = nil)) & ((all_143_0 = 0 & ! [v1: % 197.87/28.28 | $i] : ( ~ (neq(v1, nil) = 0) | ~ $i(v1) | ? [v2: any] : ? % 197.87/28.28 | [v3: any] : ? [v4: any] : (rearsegP(all_143_1, v1) = v3 & % 197.87/28.28 | rearsegP(all_139_0, v1) = v4 & ssList(v1) = v2 & ( ~ (v4 = % 197.87/28.28 | 0) | ~ (v3 = 0) | ~ (v2 = 0))))) | (all_143_1 = nil & % 197.87/28.28 | ~ (all_139_0 = nil)))) % 197.87/28.28 | % 197.87/28.28 | ALPHA: (21) implies: % 197.87/28.29 | (22) $i(all_145_1) % 197.87/28.29 | (23) neq(all_145_1, nil) = all_145_0 % 197.87/28.29 | (24) ssList(all_145_1) = 0 % 197.87/28.29 | (25) ? [v0: any] : (all_145_1 = all_139_0 & rearsegP(all_143_1, all_139_0) % 197.87/28.29 | = v0 & ((v0 = 0 & all_145_0 = 0) | (all_143_1 = nil & all_139_0 = % 197.87/28.29 | nil)) & ((all_143_0 = 0 & ! [v1: $i] : ( ~ (neq(v1, nil) = 0) | % 197.87/28.29 | ~ $i(v1) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 197.87/28.29 | (rearsegP(all_143_1, v1) = v3 & rearsegP(all_139_0, v1) = v4 & % 197.87/28.29 | ssList(v1) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = % 197.87/28.29 | 0))))) | (all_143_1 = nil & ~ (all_139_0 = nil)))) % 197.87/28.29 | % 197.87/28.29 | DELTA: instantiating (25) with fresh symbol all_147_0 gives: % 198.11/28.29 | (26) all_145_1 = all_139_0 & rearsegP(all_143_1, all_139_0) = all_147_0 & % 198.11/28.29 | ((all_147_0 = 0 & all_145_0 = 0) | (all_143_1 = nil & all_139_0 = % 198.11/28.29 | nil)) & ((all_143_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | % 198.11/28.29 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : % 198.11/28.29 | (rearsegP(all_143_1, v0) = v2 & rearsegP(all_139_0, v0) = v3 & % 198.11/28.29 | ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) % 198.11/28.29 | | (all_143_1 = nil & ~ (all_139_0 = nil))) % 198.11/28.29 | % 198.11/28.29 | ALPHA: (26) implies: % 198.11/28.29 | (27) all_145_1 = all_139_0 % 198.11/28.29 | (28) rearsegP(all_143_1, all_139_0) = all_147_0 % 198.11/28.29 | (29) (all_143_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? % 198.11/28.29 | [v1: any] : ? [v2: any] : ? [v3: any] : (rearsegP(all_143_1, v0) % 198.11/28.29 | = v2 & rearsegP(all_139_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 % 198.11/28.29 | = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_143_1 = nil & ~ % 198.11/28.29 | (all_139_0 = nil)) % 198.11/28.29 | (30) (all_147_0 = 0 & all_145_0 = 0) | (all_143_1 = nil & all_139_0 = nil) % 198.11/28.29 | % 198.11/28.29 | REDUCE: (24), (27) imply: % 198.11/28.29 | (31) ssList(all_139_0) = 0 % 198.11/28.29 | % 198.11/28.29 | REDUCE: (23), (27) imply: % 198.11/28.29 | (32) neq(all_139_0, nil) = all_145_0 % 198.11/28.29 | % 198.11/28.29 | REDUCE: (22), (27) imply: % 198.11/28.29 | (33) $i(all_139_0) % 198.11/28.29 | % 198.11/28.29 | GROUND_INST: instantiating (2) with all_139_0, simplifying with (31), (33) % 198.11/28.29 | gives: % 198.11/28.29 | (34) all_139_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 198.11/28.29 | : (cons(v1, v0) = all_139_0 & ssItem(v1) = 0 & $i(v1))) % 198.11/28.29 | % 198.11/28.29 | GROUND_INST: instantiating (ax15) with all_139_0, simplifying with (31), (33) % 198.11/28.29 | gives: % 198.11/28.29 | (35) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_139_0, v0) = v1) | ~ $i(v0) % 198.11/28.29 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 198.11/28.29 | ~ (v0 = all_139_0)) & (v1 = 0 | v0 = all_139_0))) % 198.11/28.29 | % 198.11/28.29 | GROUND_INST: instantiating (2) with all_143_1, simplifying with (17), (19) % 198.11/28.29 | gives: % 198.11/28.30 | (36) all_143_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 198.11/28.30 | : (cons(v1, v0) = all_143_1 & ssItem(v1) = 0 & $i(v1))) % 198.11/28.30 | % 198.11/28.30 | GROUND_INST: instantiating (ax6) with all_143_1, simplifying with (17), (19) % 198.11/28.30 | gives: % 198.11/28.30 | (37) ! [v0: $i] : ! [v1: any] : ( ~ (rearsegP(all_143_1, v0) = v1) | ~ % 198.11/28.30 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 198.11/28.30 | 0) | ? [v2: $i] : (ssList(v2) = 0 & app(v2, v0) = all_143_1 & % 198.11/28.30 | $i(v2))) & (v1 = 0 | ! [v2: $i] : ( ~ (app(v2, v0) = % 198.11/28.30 | all_143_1) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 198.11/28.30 | ssList(v2) = v3))))) % 198.11/28.30 | % 198.11/28.30 | GROUND_INST: instantiating (ax15) with all_143_1, simplifying with (17), (19) % 198.11/28.30 | gives: % 198.11/28.30 | (38) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_143_1, v0) = v1) | ~ $i(v0) % 198.11/28.30 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 198.11/28.30 | ~ (v0 = all_143_1)) & (v1 = 0 | v0 = all_143_1))) % 198.11/28.30 | % 198.11/28.30 | GROUND_INST: instantiating (ax48) with all_143_1, simplifying with (17), (19) % 198.11/28.30 | gives: % 198.11/28.30 | (39) ! [v0: any] : (v0 = all_143_1 | ~ (rearsegP(all_143_1, v0) = 0) | ~ % 198.11/28.30 | $i(v0) | ? [v1: any] : ? [v2: any] : (rearsegP(v0, all_143_1) = v2 % 198.11/28.30 | & ssList(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 198.11/28.30 | % 198.11/28.30 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (3), (7) % 198.11/28.30 | gives: % 198.11/28.30 | (40) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 198.11/28.30 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 198.11/28.30 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 198.11/28.30 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 198.11/28.30 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 198.11/28.30 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 198.11/28.30 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 198.11/28.30 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 198.11/28.30 | v8)))))) % 198.11/28.30 | % 198.11/28.30 | GROUND_INST: instantiating (4) with all_129_1, all_129_0, simplifying with % 198.11/28.30 | (13) gives: % 198.11/28.30 | (41) all_129_1 = nil | ~ $i(all_129_1) | ? [v0: int] : ( ~ (v0 = 0) & % 198.11/28.30 | ssList(all_129_1) = v0) | (ssItem(all_129_0) = 0 & $i(all_129_0)) % 198.11/28.30 | % 198.11/28.30 | GROUND_INST: instantiating (6) with all_129_1, all_129_0, simplifying with % 198.11/28.30 | (13) gives: % 198.11/28.30 | (42) ~ $i(all_129_1) | ? [v0: int] : ( ~ (v0 = 0) & ssList(all_129_1) = % 198.11/28.30 | v0) | ! [v0: $i] : ! [v1: $i] : (all_129_1 = nil | ~ % 198.11/28.30 | (app(all_129_1, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 198.11/28.30 | (hd(v1) = v3 & ssList(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = % 198.11/28.30 | all_129_0))) % 198.11/28.30 | % 198.11/28.30 | GROUND_INST: instantiating (38) with nil, all_143_0, simplifying with (7), % 198.11/28.30 | (18) gives: % 198.11/28.31 | (43) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_143_0 = 0) % 198.11/28.31 | | ~ (all_143_1 = nil)) & (all_143_0 = 0 | all_143_1 = nil)) % 198.11/28.31 | % 198.11/28.31 | GROUND_INST: instantiating (37) with all_139_0, all_147_0, simplifying with % 198.11/28.31 | (28), (33) gives: % 198.11/28.31 | (44) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = v0) | (( ~ % 198.11/28.31 | (all_147_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0, % 198.11/28.31 | all_139_0) = all_143_1 & $i(v0))) & (all_147_0 = 0 | ! [v0: % 198.11/28.31 | $i] : ( ~ (app(v0, all_139_0) = all_143_1) | ~ $i(v0) | ? [v1: % 198.11/28.31 | int] : ( ~ (v1 = 0) & ssList(v0) = v1)))) % 198.11/28.31 | % 198.11/28.31 | GROUND_INST: instantiating (35) with nil, all_145_0, simplifying with (7), % 198.11/28.31 | (32) gives: % 198.11/28.31 | (45) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_145_0 = 0) % 198.11/28.31 | | ~ (all_139_0 = nil)) & (all_145_0 = 0 | all_139_0 = nil)) % 198.11/28.31 | % 198.11/28.31 | BETA: splitting (40) gives: % 198.11/28.31 | % 198.11/28.31 | Case 1: % 198.11/28.31 | | % 198.11/28.31 | | (46) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 198.11/28.31 | | % 198.11/28.31 | | REF_CLOSE: (1), (9), (46) are inconsistent by sub-proof #2. % 198.11/28.31 | | % 198.11/28.31 | Case 2: % 198.11/28.31 | | % 198.11/28.31 | | (47) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 198.11/28.31 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 198.11/28.31 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 198.11/28.31 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 198.11/28.31 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 198.11/28.31 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 198.11/28.31 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 198.11/28.31 | | 0) & ssList(v6) = v8)))))) % 198.11/28.31 | | % 198.11/28.31 | | BETA: splitting (29) gives: % 198.11/28.31 | | % 198.11/28.31 | | Case 1: % 198.11/28.31 | | | % 198.11/28.31 | | | (48) all_143_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | % 198.11/28.31 | | | ? [v1: any] : ? [v2: any] : ? [v3: any] : % 198.11/28.31 | | | (rearsegP(all_143_1, v0) = v2 & rearsegP(all_139_0, v0) = v3 & % 198.11/28.31 | | | ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)))) % 198.11/28.31 | | | % 198.11/28.31 | | | ALPHA: (48) implies: % 198.11/28.31 | | | (49) all_143_0 = 0 % 198.11/28.32 | | | (50) ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] : % 198.11/28.32 | | | ? [v2: any] : ? [v3: any] : (rearsegP(all_143_1, v0) = v2 & % 198.11/28.32 | | | rearsegP(all_139_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) % 198.11/28.32 | | | | ~ (v2 = 0) | ~ (v1 = 0)))) % 198.11/28.32 | | | % 198.11/28.32 | | | REDUCE: (18), (49) imply: % 198.11/28.32 | | | (51) neq(all_143_1, nil) = 0 % 198.11/28.32 | | | % 198.11/28.32 | | | BETA: splitting (43) gives: % 198.11/28.32 | | | % 198.11/28.32 | | | Case 1: % 198.11/28.32 | | | | % 198.11/28.32 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 198.11/28.32 | | | | % 198.11/28.32 | | | | REF_CLOSE: (1), (9), (52) are inconsistent by sub-proof #2. % 198.11/28.32 | | | | % 198.11/28.32 | | | Case 2: % 198.11/28.32 | | | | % 198.11/28.32 | | | | (53) ( ~ (all_143_0 = 0) | ~ (all_143_1 = nil)) & (all_143_0 = 0 | % 198.11/28.32 | | | | all_143_1 = nil) % 198.11/28.32 | | | | % 198.11/28.32 | | | | ALPHA: (53) implies: % 198.11/28.32 | | | | (54) ~ (all_143_0 = 0) | ~ (all_143_1 = nil) % 198.11/28.32 | | | | % 198.11/28.32 | | | | BETA: splitting (54) gives: % 198.11/28.32 | | | | % 198.11/28.32 | | | | Case 1: % 198.11/28.32 | | | | | % 198.11/28.32 | | | | | (55) ~ (all_143_1 = nil) % 198.11/28.32 | | | | | % 198.11/28.32 | | | | | BETA: splitting (30) gives: % 198.11/28.32 | | | | | % 198.11/28.32 | | | | | Case 1: % 198.11/28.32 | | | | | | % 198.11/28.32 | | | | | | (56) all_147_0 = 0 & all_145_0 = 0 % 198.11/28.32 | | | | | | % 198.11/28.32 | | | | | | ALPHA: (56) implies: % 198.11/28.32 | | | | | | (57) all_145_0 = 0 % 198.11/28.32 | | | | | | (58) all_147_0 = 0 % 198.11/28.32 | | | | | | % 198.11/28.32 | | | | | | REDUCE: (28), (58) imply: % 198.11/28.32 | | | | | | (59) rearsegP(all_143_1, all_139_0) = 0 % 198.11/28.32 | | | | | | % 198.11/28.32 | | | | | | REDUCE: (32), (57) imply: % 198.11/28.32 | | | | | | (60) neq(all_139_0, nil) = 0 % 198.11/28.32 | | | | | | % 198.11/28.32 | | | | | | BETA: splitting (45) gives: % 198.11/28.32 | | | | | | % 198.11/28.32 | | | | | | Case 1: % 198.11/28.32 | | | | | | | % 198.11/28.32 | | | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 198.11/28.32 | | | | | | | % 198.11/28.32 | | | | | | | REF_CLOSE: (1), (9), (61) are inconsistent by sub-proof #2. % 198.11/28.32 | | | | | | | % 198.11/28.32 | | | | | | Case 2: % 198.11/28.32 | | | | | | | % 198.11/28.32 | | | | | | | (62) ( ~ (all_145_0 = 0) | ~ (all_139_0 = nil)) & (all_145_0 = % 198.11/28.32 | | | | | | | 0 | all_139_0 = nil) % 198.11/28.32 | | | | | | | % 198.11/28.32 | | | | | | | ALPHA: (62) implies: % 198.11/28.32 | | | | | | | (63) ~ (all_145_0 = 0) | ~ (all_139_0 = nil) % 198.11/28.32 | | | | | | | % 198.11/28.32 | | | | | | | BETA: splitting (36) gives: % 198.11/28.32 | | | | | | | % 198.11/28.32 | | | | | | | Case 1: % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | (64) all_143_1 = nil % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | REDUCE: (55), (64) imply: % 198.11/28.32 | | | | | | | | (65) $false % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | CLOSE: (65) is inconsistent. % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | Case 2: % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | (66) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 198.11/28.32 | | | | | | | | (cons(v1, v0) = all_143_1 & ssItem(v1) = 0 & $i(v1))) % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | DELTA: instantiating (66) with fresh symbol all_365_0 gives: % 198.11/28.32 | | | | | | | | (67) ssList(all_365_0) = 0 & $i(all_365_0) & ? [v0: $i] : % 198.11/28.32 | | | | | | | | (cons(v0, all_365_0) = all_143_1 & ssItem(v0) = 0 & % 198.11/28.32 | | | | | | | | $i(v0)) % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | ALPHA: (67) implies: % 198.11/28.32 | | | | | | | | (68) ? [v0: $i] : (cons(v0, all_365_0) = all_143_1 & % 198.11/28.32 | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | DELTA: instantiating (68) with fresh symbol all_367_0 gives: % 198.11/28.32 | | | | | | | | (69) cons(all_367_0, all_365_0) = all_143_1 & % 198.11/28.32 | | | | | | | | ssItem(all_367_0) = 0 & $i(all_367_0) % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | ALPHA: (69) implies: % 198.11/28.32 | | | | | | | | (70) $i(all_367_0) % 198.11/28.32 | | | | | | | | (71) ssItem(all_367_0) = 0 % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | BETA: splitting (44) gives: % 198.11/28.32 | | | | | | | | % 198.11/28.32 | | | | | | | | Case 1: % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | | (72) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = v0) % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | | DELTA: instantiating (72) with fresh symbol all_371_0 gives: % 198.11/28.32 | | | | | | | | | (73) ~ (all_371_0 = 0) & ssList(all_139_0) = all_371_0 % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | | ALPHA: (73) implies: % 198.11/28.32 | | | | | | | | | (74) ~ (all_371_0 = 0) % 198.11/28.32 | | | | | | | | | (75) ssList(all_139_0) = all_371_0 % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_371_0, all_139_0, % 198.11/28.32 | | | | | | | | | simplifying with (31), (75) gives: % 198.11/28.32 | | | | | | | | | (76) all_371_0 = 0 % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | | REDUCE: (74), (76) imply: % 198.11/28.32 | | | | | | | | | (77) $false % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | | CLOSE: (77) is inconsistent. % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | Case 2: % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | | (78) ( ~ (all_147_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & % 198.11/28.32 | | | | | | | | | app(v0, all_139_0) = all_143_1 & $i(v0))) & % 198.11/28.32 | | | | | | | | | (all_147_0 = 0 | ! [v0: $i] : ( ~ (app(v0, all_139_0) % 198.11/28.32 | | | | | | | | | = all_143_1) | ~ $i(v0) | ? [v1: int] : ( ~ % 198.11/28.32 | | | | | | | | | (v1 = 0) & ssList(v0) = v1))) % 198.11/28.32 | | | | | | | | | % 198.11/28.32 | | | | | | | | | ALPHA: (78) implies: % 198.11/28.32 | | | | | | | | | (79) ~ (all_147_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & % 198.11/28.32 | | | | | | | | | app(v0, all_139_0) = all_143_1 & $i(v0)) % 198.11/28.32 | | | | | | | | | % 198.11/28.33 | | | | | | | | | BETA: splitting (63) gives: % 198.11/28.33 | | | | | | | | | % 198.11/28.33 | | | | | | | | | Case 1: % 198.11/28.33 | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | (80) ~ (all_139_0 = nil) % 198.11/28.33 | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | BETA: splitting (79) gives: % 198.11/28.33 | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | Case 1: % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | (81) ~ (all_147_0 = 0) % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | REDUCE: (58), (81) imply: % 198.11/28.33 | | | | | | | | | | | (82) $false % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | CLOSE: (82) is inconsistent. % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | Case 2: % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | (83) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_139_0) % 198.11/28.33 | | | | | | | | | | | = all_143_1 & $i(v0)) % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | DELTA: instantiating (83) with fresh symbol all_377_0 % 198.11/28.33 | | | | | | | | | | | gives: % 198.11/28.33 | | | | | | | | | | | (84) ssList(all_377_0) = 0 & app(all_377_0, all_139_0) % 198.11/28.33 | | | | | | | | | | | = all_143_1 & $i(all_377_0) % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | ALPHA: (84) implies: % 198.11/28.33 | | | | | | | | | | | (85) $i(all_377_0) % 198.11/28.33 | | | | | | | | | | | (86) app(all_377_0, all_139_0) = all_143_1 % 198.11/28.33 | | | | | | | | | | | (87) ssList(all_377_0) = 0 % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | BETA: splitting (34) gives: % 198.11/28.33 | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | Case 1: % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | (88) all_139_0 = nil % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | REDUCE: (80), (88) imply: % 198.11/28.33 | | | | | | | | | | | | (89) $false % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | CLOSE: (89) is inconsistent. % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | Case 2: % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | (90) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: % 198.11/28.33 | | | | | | | | | | | | $i] : (cons(v1, v0) = all_139_0 & ssItem(v1) = % 198.11/28.33 | | | | | | | | | | | | 0 & $i(v1))) % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | DELTA: instantiating (90) with fresh symbol all_383_0 % 198.11/28.33 | | | | | | | | | | | | gives: % 198.11/28.33 | | | | | | | | | | | | (91) ssList(all_383_0) = 0 & $i(all_383_0) & ? [v0: % 198.11/28.33 | | | | | | | | | | | | $i] : (cons(v0, all_383_0) = all_139_0 & % 198.11/28.33 | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | ALPHA: (91) implies: % 198.11/28.33 | | | | | | | | | | | | (92) $i(all_383_0) % 198.11/28.33 | | | | | | | | | | | | (93) ssList(all_383_0) = 0 % 198.11/28.33 | | | | | | | | | | | | (94) ? [v0: $i] : (cons(v0, all_383_0) = all_139_0 & % 198.11/28.33 | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | DELTA: instantiating (94) with fresh symbol all_385_0 % 198.11/28.33 | | | | | | | | | | | | gives: % 198.11/28.33 | | | | | | | | | | | | (95) cons(all_385_0, all_383_0) = all_139_0 & % 198.11/28.33 | | | | | | | | | | | | ssItem(all_385_0) = 0 & $i(all_385_0) % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | ALPHA: (95) implies: % 198.11/28.33 | | | | | | | | | | | | (96) $i(all_385_0) % 198.11/28.33 | | | | | | | | | | | | (97) ssItem(all_385_0) = 0 % 198.11/28.33 | | | | | | | | | | | | (98) cons(all_385_0, all_383_0) = all_139_0 % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | BETA: splitting (42) gives: % 198.11/28.33 | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | Case 1: % 198.11/28.33 | | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_385_0, simplifying % 198.11/28.33 | | | | | | | | | | | | | with (96), (97) gives: % 198.11/28.33 | | | | | | | | | | | | | (99) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | % 198.11/28.33 | | | | | | | | | | | | | ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | % 198.11/28.33 | | | | | | | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 198.11/28.33 | | | | | | | | | | | | | (cons(all_385_0, v2) = v3) | ~ (app(v1, v3) % 198.11/28.33 | | | | | | | | | | | | | = v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 % 198.11/28.33 | | | | | | | | | | | | | = 0) & ssList(v2) = v5) | ! [v5: $i] : % 198.11/28.33 | | | | | | | | | | | | | ! [v6: $i] : ( ~ (v0 = all_385_0) | ~ % 198.11/28.33 | | | | | | | | | | | | | (cons(all_385_0, v5) = v6) | ~ (app(v4, % 198.11/28.33 | | | | | | | | | | | | | v6) = nil) | ~ $i(v5) | ? [v7: int] % 198.11/28.33 | | | | | | | | | | | | | : ( ~ (v7 = 0) & ssList(v5) = v7))))) % 198.11/28.33 | | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | | GROUND_INST: instantiating (50) with all_139_0, simplifying % 198.11/28.33 | | | | | | | | | | | | | with (33), (60) gives: % 198.11/28.33 | | | | | | | | | | | | | (100) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 198.11/28.33 | | | | | | | | | | | | | (rearsegP(all_143_1, all_139_0) = v1 & % 198.11/28.33 | | | | | | | | | | | | | rearsegP(all_139_0, all_139_0) = v2 & % 198.11/28.33 | | | | | | | | | | | | | ssList(all_139_0) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 198.11/28.33 | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 198.11/28.33 | | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | | GROUND_INST: instantiating (50) with all_143_1, simplifying % 198.11/28.33 | | | | | | | | | | | | | with (17), (51) gives: % 198.11/28.33 | | | | | | | | | | | | | (101) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 198.11/28.33 | | | | | | | | | | | | | (rearsegP(all_143_1, all_143_1) = v1 & % 198.11/28.33 | | | | | | | | | | | | | rearsegP(all_139_0, all_143_1) = v2 & % 198.11/28.33 | | | | | | | | | | | | | ssList(all_143_1) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 198.11/28.33 | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 198.11/28.33 | | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_139_0, simplifying % 198.11/28.33 | | | | | | | | | | | | | with (33), (59) gives: % 198.11/28.33 | | | | | | | | | | | | | (102) all_143_1 = all_139_0 | ? [v0: any] : ? [v1: % 198.11/28.33 | | | | | | | | | | | | | any] : (rearsegP(all_139_0, all_143_1) = v1 & % 198.11/28.33 | | | | | | | | | | | | | ssList(all_139_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 198.11/28.33 | | | | | | | | | | | | | 0))) % 198.11/28.33 | | | | | | | | | | | | | % 198.11/28.33 | | | | | | | | | | | | | GROUND_INST: instantiating (99) with all_367_0, simplifying % 198.11/28.33 | | | | | | | | | | | | | with (70), (71) gives: % 198.11/28.34 | | | | | | | | | | | | | (103) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | % 198.11/28.34 | | | | | | | | | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 198.11/28.34 | | | | | | | | | | | | | (cons(all_385_0, v1) = v2) | ~ (app(v0, v2) = % 198.11/28.34 | | | | | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 198.11/28.34 | | | | | | | | | | | | | 0) & ssList(v1) = v4) | ! [v4: $i] : ! % 198.11/28.34 | | | | | | | | | | | | | [v5: $i] : ( ~ (all_385_0 = all_367_0) | ~ % 198.11/28.34 | | | | | | | | | | | | | (cons(all_367_0, v4) = v5) | ~ (app(v3, v5) % 198.11/28.34 | | | | | | | | | | | | | = nil) | ~ $i(v4) | ? [v6: int] : ( ~ % 198.11/28.34 | | | | | | | | | | | | | (v6 = 0) & ssList(v4) = v6)))) % 198.11/28.34 | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | GROUND_INST: instantiating (103) with all_377_0, simplifying % 198.11/28.34 | | | | | | | | | | | | | with (85), (87) gives: % 198.11/28.34 | | | | | | | | | | | | | (104) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 198.11/28.34 | | | | | | | | | | | | | (cons(all_385_0, v0) = v1) | ~ (app(all_377_0, % 198.11/28.34 | | | | | | | | | | | | | v1) = v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 198.11/28.34 | | | | | | | | | | | | | (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : ! % 198.11/28.34 | | | | | | | | | | | | | [v4: $i] : ( ~ (all_385_0 = all_367_0) | ~ % 198.11/28.34 | | | | | | | | | | | | | (cons(all_367_0, v3) = v4) | ~ (app(v2, v4) = % 198.11/28.34 | | | | | | | | | | | | | nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = % 198.11/28.34 | | | | | | | | | | | | | 0) & ssList(v3) = v5))) % 198.11/28.34 | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | GROUND_INST: instantiating (104) with all_383_0, all_139_0, % 198.11/28.34 | | | | | | | | | | | | | all_143_1, simplifying with (86), (92), (98) % 198.11/28.34 | | | | | | | | | | | | | gives: % 198.11/28.34 | | | | | | | | | | | | | (105) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_383_0) = % 198.11/28.34 | | | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ (all_385_0 % 198.11/28.34 | | | | | | | | | | | | | = all_367_0) | ~ (cons(all_367_0, v0) = v1) | % 198.11/28.34 | | | | | | | | | | | | | ~ (app(all_143_1, v1) = nil) | ~ $i(v0) | ? % 198.11/28.34 | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 198.11/28.34 | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | DELTA: instantiating (101) with fresh symbols all_754_0, % 198.11/28.34 | | | | | | | | | | | | | all_754_1, all_754_2 gives: % 198.11/28.34 | | | | | | | | | | | | | (106) rearsegP(all_143_1, all_143_1) = all_754_1 & % 198.11/28.34 | | | | | | | | | | | | | rearsegP(all_139_0, all_143_1) = all_754_0 & % 198.11/28.34 | | | | | | | | | | | | | ssList(all_143_1) = all_754_2 & ( ~ (all_754_0 = % 198.11/28.34 | | | | | | | | | | | | | 0) | ~ (all_754_1 = 0) | ~ (all_754_2 = 0)) % 198.11/28.34 | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | ALPHA: (106) implies: % 198.11/28.34 | | | | | | | | | | | | | (107) rearsegP(all_139_0, all_143_1) = all_754_0 % 198.11/28.34 | | | | | | | | | | | | | (108) rearsegP(all_143_1, all_143_1) = all_754_1 % 198.11/28.34 | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | DELTA: instantiating (100) with fresh symbols all_756_0, % 198.11/28.34 | | | | | | | | | | | | | all_756_1, all_756_2 gives: % 198.11/28.34 | | | | | | | | | | | | | (109) rearsegP(all_143_1, all_139_0) = all_756_1 & % 198.11/28.34 | | | | | | | | | | | | | rearsegP(all_139_0, all_139_0) = all_756_0 & % 198.11/28.34 | | | | | | | | | | | | | ssList(all_139_0) = all_756_2 & ( ~ (all_756_0 = % 198.11/28.34 | | | | | | | | | | | | | 0) | ~ (all_756_1 = 0) | ~ (all_756_2 = 0)) % 198.11/28.34 | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | ALPHA: (109) implies: % 198.11/28.34 | | | | | | | | | | | | | (110) ssList(all_139_0) = all_756_2 % 198.11/28.34 | | | | | | | | | | | | | (111) rearsegP(all_139_0, all_139_0) = all_756_0 % 198.11/28.34 | | | | | | | | | | | | | (112) rearsegP(all_143_1, all_139_0) = all_756_1 % 198.11/28.34 | | | | | | | | | | | | | (113) ~ (all_756_0 = 0) | ~ (all_756_1 = 0) | ~ % 198.11/28.34 | | | | | | | | | | | | | (all_756_2 = 0) % 198.11/28.34 | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | BETA: splitting (105) gives: % 198.11/28.34 | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | Case 1: % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | (114) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_383_0) = % 198.11/28.34 | | | | | | | | | | | | | | v0) % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | DELTA: instantiating (114) with fresh symbol all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | gives: % 198.11/28.34 | | | | | | | | | | | | | | (115) ~ (all_803_0 = 0) & ssList(all_383_0) = all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | ALPHA: (115) implies: % 198.11/28.34 | | | | | | | | | | | | | | (116) ~ (all_803_0 = 0) % 198.11/28.34 | | | | | | | | | | | | | | (117) ssList(all_383_0) = all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | DELTA: instantiating (114) with fresh symbol all_805_0 % 198.11/28.34 | | | | | | | | | | | | | | gives: % 198.11/28.34 | | | | | | | | | | | | | | (118) ~ (all_805_0 = 0) & ssList(all_383_0) = all_805_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | ALPHA: (118) implies: % 198.11/28.34 | | | | | | | | | | | | | | (119) ssList(all_383_0) = all_805_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | DELTA: instantiating (114) with fresh symbol all_807_0 % 198.11/28.34 | | | | | | | | | | | | | | gives: % 198.11/28.34 | | | | | | | | | | | | | | (120) ~ (all_807_0 = 0) & ssList(all_383_0) = all_807_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | ALPHA: (120) implies: % 198.11/28.34 | | | | | | | | | | | | | | (121) ssList(all_383_0) = all_807_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | DELTA: instantiating (114) with fresh symbol all_809_0 % 198.11/28.34 | | | | | | | | | | | | | | gives: % 198.11/28.34 | | | | | | | | | | | | | | (122) ~ (all_809_0 = 0) & ssList(all_383_0) = all_809_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | ALPHA: (122) implies: % 198.11/28.34 | | | | | | | | | | | | | | (123) ssList(all_383_0) = all_809_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | DELTA: instantiating (114) with fresh symbol all_811_0 % 198.11/28.34 | | | | | | | | | | | | | | gives: % 198.11/28.34 | | | | | | | | | | | | | | (124) ~ (all_811_0 = 0) & ssList(all_383_0) = all_811_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | ALPHA: (124) implies: % 198.11/28.34 | | | | | | | | | | | | | | (125) ssList(all_383_0) = all_811_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_805_0, all_383_0, % 198.11/28.34 | | | | | | | | | | | | | | simplifying with (93), (119) gives: % 198.11/28.34 | | | | | | | | | | | | | | (126) all_805_0 = 0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_807_0, all_809_0, % 198.11/28.34 | | | | | | | | | | | | | | all_383_0, simplifying with (121), (123) gives: % 198.11/28.34 | | | | | | | | | | | | | | (127) all_809_0 = all_807_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_805_0, all_809_0, % 198.11/28.34 | | | | | | | | | | | | | | all_383_0, simplifying with (119), (123) gives: % 198.11/28.34 | | | | | | | | | | | | | | (128) all_809_0 = all_805_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_809_0, all_811_0, % 198.11/28.34 | | | | | | | | | | | | | | all_383_0, simplifying with (123), (125) gives: % 198.11/28.34 | | | | | | | | | | | | | | (129) all_811_0 = all_809_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_803_0, all_811_0, % 198.11/28.34 | | | | | | | | | | | | | | all_383_0, simplifying with (117), (125) gives: % 198.11/28.34 | | | | | | | | | | | | | | (130) all_811_0 = all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | COMBINE_EQS: (129), (130) imply: % 198.11/28.34 | | | | | | | | | | | | | | (131) all_809_0 = all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | SIMP: (131) implies: % 198.11/28.34 | | | | | | | | | | | | | | (132) all_809_0 = all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | COMBINE_EQS: (127), (132) imply: % 198.11/28.34 | | | | | | | | | | | | | | (133) all_807_0 = all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | COMBINE_EQS: (127), (128) imply: % 198.11/28.34 | | | | | | | | | | | | | | (134) all_807_0 = all_805_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | COMBINE_EQS: (133), (134) imply: % 198.11/28.34 | | | | | | | | | | | | | | (135) all_805_0 = all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | SIMP: (135) implies: % 198.11/28.34 | | | | | | | | | | | | | | (136) all_805_0 = all_803_0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | COMBINE_EQS: (126), (136) imply: % 198.11/28.34 | | | | | | | | | | | | | | (137) all_803_0 = 0 % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | REDUCE: (116), (137) imply: % 198.11/28.34 | | | | | | | | | | | | | | (138) $false % 198.11/28.34 | | | | | | | | | | | | | | % 198.11/28.34 | | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 198.11/28.34 | | | | | | | | | | | | | | % 198.39/28.34 | | | | | | | | | | | | | Case 2: % 198.39/28.34 | | | | | | | | | | | | | | % 198.39/28.34 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_756_2, all_139_0, % 198.39/28.35 | | | | | | | | | | | | | | simplifying with (31), (110) gives: % 198.39/28.35 | | | | | | | | | | | | | | (139) all_756_2 = 0 % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_756_1, all_139_0, % 198.39/28.35 | | | | | | | | | | | | | | all_143_1, simplifying with (59), (112) gives: % 198.39/28.35 | | | | | | | | | | | | | | (140) all_756_1 = 0 % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | BETA: splitting (113) gives: % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | Case 1: % 198.39/28.35 | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | (141) ~ (all_756_0 = 0) % 198.39/28.35 | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 198.39/28.35 | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | Case 1: % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | (142) all_143_1 = all_139_0 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | REDUCE: (108), (142) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (143) rearsegP(all_139_0, all_139_0) = all_754_1 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | REDUCE: (59), (142) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (144) rearsegP(all_139_0, all_139_0) = 0 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | REDUCE: (107), (142) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (145) rearsegP(all_139_0, all_139_0) = all_754_0 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_756_0, all_754_1, % 198.39/28.35 | | | | | | | | | | | | | | | | all_139_0, all_139_0, simplifying with (111), % 198.39/28.35 | | | | | | | | | | | | | | | | (143) gives: % 198.39/28.35 | | | | | | | | | | | | | | | | (146) all_756_0 = all_754_1 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_756_0, all_754_0, % 198.39/28.35 | | | | | | | | | | | | | | | | all_139_0, all_139_0, simplifying with (111), % 198.39/28.35 | | | | | | | | | | | | | | | | (145) gives: % 198.39/28.35 | | | | | | | | | | | | | | | | (147) all_756_0 = all_754_0 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_754_0, all_139_0, % 198.39/28.35 | | | | | | | | | | | | | | | | all_139_0, simplifying with (144), (145) gives: % 198.39/28.35 | | | | | | | | | | | | | | | | (148) all_754_0 = 0 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (146), (147) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (149) all_754_0 = all_754_1 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | SIMP: (149) implies: % 198.39/28.35 | | | | | | | | | | | | | | | | (150) all_754_0 = all_754_1 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (150) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (151) all_754_1 = 0 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (146), (151) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (152) all_756_0 = 0 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | REDUCE: (141), (152) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (153) $false % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | Case 2: % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | (154) ? [v0: any] : ? [v1: any] : (rearsegP(all_139_0, % 198.39/28.35 | | | | | | | | | | | | | | | | all_143_1) = v1 & ssList(all_139_0) = v0 & ( ~ % 198.39/28.35 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | DELTA: instantiating (154) with fresh symbols all_884_0, % 198.39/28.35 | | | | | | | | | | | | | | | | all_884_1 gives: % 198.39/28.35 | | | | | | | | | | | | | | | | (155) rearsegP(all_139_0, all_143_1) = all_884_0 & % 198.39/28.35 | | | | | | | | | | | | | | | | ssList(all_139_0) = all_884_1 & ( ~ (all_884_0 = % 198.39/28.35 | | | | | | | | | | | | | | | | 0) | ~ (all_884_1 = 0)) % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | ALPHA: (155) implies: % 198.39/28.35 | | | | | | | | | | | | | | | | (156) ssList(all_139_0) = all_884_1 % 198.39/28.35 | | | | | | | | | | | | | | | | (157) ~ (all_884_0 = 0) | ~ (all_884_1 = 0) % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_884_1, all_139_0, % 198.39/28.35 | | | | | | | | | | | | | | | | simplifying with (31), (156) gives: % 198.39/28.35 | | | | | | | | | | | | | | | | (158) all_884_1 = 0 % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | Case 1: % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (ax49) with all_139_0, all_756_0, % 198.39/28.35 | | | | | | | | | | | | | | | | | simplifying with (33), (111) gives: % 198.39/28.35 | | | | | | | | | | | | | | | | | (159) all_756_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 198.39/28.35 | | | | | | | | | | | | | | | | | ssList(all_139_0) = v0) % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | Case 1: % 198.39/28.35 | | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | | (160) all_756_0 = 0 % 198.39/28.35 | | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | | REDUCE: (141), (160) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | | | (161) $false % 198.39/28.35 | | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent. % 198.39/28.35 | | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | Case 2: % 198.39/28.35 | | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | | (162) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = % 198.39/28.35 | | | | | | | | | | | | | | | | | | v0) % 198.39/28.35 | | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (31), (162) are inconsistent by sub-proof #1. % 198.39/28.35 | | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | End of split % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | Case 2: % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | (163) ~ (all_884_1 = 0) % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | REDUCE: (158), (163) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | | (164) $false % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 198.39/28.35 | | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | End of split % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | End of split % 198.39/28.35 | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | Case 2: % 198.39/28.35 | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | (165) ~ (all_756_1 = 0) | ~ (all_756_2 = 0) % 198.39/28.35 | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 198.39/28.35 | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | Case 1: % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | (166) ~ (all_756_1 = 0) % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | REDUCE: (140), (166) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (167) $false % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | Case 2: % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | (168) ~ (all_756_2 = 0) % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | REDUCE: (139), (168) imply: % 198.39/28.35 | | | | | | | | | | | | | | | | (169) $false % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent. % 198.39/28.35 | | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | | End of split % 198.39/28.35 | | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | End of split % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | End of split % 198.39/28.35 | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | Case 2: % 198.39/28.35 | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | (170) $i(all_129_1) % 198.39/28.35 | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | BETA: splitting (41) gives: % 198.39/28.35 | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | Case 1: % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | (171) ~ $i(all_129_1) % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | PRED_UNIFY: (170), (171) imply: % 198.39/28.35 | | | | | | | | | | | | | | (172) $false % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | Case 2: % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | % 198.39/28.35 | | | | | | | | | | | | | | GROUND_INST: instantiating (50) with all_139_0, simplifying % 198.39/28.35 | | | | | | | | | | | | | | with (33), (60) gives: % 198.43/28.35 | | | | | | | | | | | | | | (173) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 198.43/28.35 | | | | | | | | | | | | | | (rearsegP(all_143_1, all_139_0) = v1 & % 198.43/28.35 | | | | | | | | | | | | | | rearsegP(all_139_0, all_139_0) = v2 & % 198.43/28.35 | | | | | | | | | | | | | | ssList(all_139_0) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 198.43/28.35 | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 198.43/28.35 | | | | | | | | | | | | | | % 198.43/28.35 | | | | | | | | | | | | | | GROUND_INST: instantiating (50) with all_143_1, simplifying % 198.43/28.35 | | | | | | | | | | | | | | with (17), (51) gives: % 198.43/28.35 | | | | | | | | | | | | | | (174) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 198.43/28.35 | | | | | | | | | | | | | | (rearsegP(all_143_1, all_143_1) = v1 & % 198.43/28.35 | | | | | | | | | | | | | | rearsegP(all_139_0, all_143_1) = v2 & % 198.43/28.35 | | | | | | | | | | | | | | ssList(all_143_1) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 198.43/28.35 | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 198.43/28.35 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_139_0, simplifying % 198.43/28.36 | | | | | | | | | | | | | | with (33), (59) gives: % 198.43/28.36 | | | | | | | | | | | | | | (175) all_143_1 = all_139_0 | ? [v0: any] : ? [v1: % 198.43/28.36 | | | | | | | | | | | | | | any] : (rearsegP(all_139_0, all_143_1) = v1 & % 198.43/28.36 | | | | | | | | | | | | | | ssList(all_139_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 198.43/28.36 | | | | | | | | | | | | | | 0))) % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | DELTA: instantiating (174) with fresh symbols all_766_0, % 198.43/28.36 | | | | | | | | | | | | | | all_766_1, all_766_2 gives: % 198.43/28.36 | | | | | | | | | | | | | | (176) rearsegP(all_143_1, all_143_1) = all_766_1 & % 198.43/28.36 | | | | | | | | | | | | | | rearsegP(all_139_0, all_143_1) = all_766_0 & % 198.43/28.36 | | | | | | | | | | | | | | ssList(all_143_1) = all_766_2 & ( ~ (all_766_0 = % 198.43/28.36 | | | | | | | | | | | | | | 0) | ~ (all_766_1 = 0) | ~ (all_766_2 = 0)) % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | ALPHA: (176) implies: % 198.43/28.36 | | | | | | | | | | | | | | (177) rearsegP(all_139_0, all_143_1) = all_766_0 % 198.43/28.36 | | | | | | | | | | | | | | (178) rearsegP(all_143_1, all_143_1) = all_766_1 % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | DELTA: instantiating (173) with fresh symbols all_768_0, % 198.43/28.36 | | | | | | | | | | | | | | all_768_1, all_768_2 gives: % 198.43/28.36 | | | | | | | | | | | | | | (179) rearsegP(all_143_1, all_139_0) = all_768_1 & % 198.43/28.36 | | | | | | | | | | | | | | rearsegP(all_139_0, all_139_0) = all_768_0 & % 198.43/28.36 | | | | | | | | | | | | | | ssList(all_139_0) = all_768_2 & ( ~ (all_768_0 = % 198.43/28.36 | | | | | | | | | | | | | | 0) | ~ (all_768_1 = 0) | ~ (all_768_2 = 0)) % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | ALPHA: (179) implies: % 198.43/28.36 | | | | | | | | | | | | | | (180) ssList(all_139_0) = all_768_2 % 198.43/28.36 | | | | | | | | | | | | | | (181) rearsegP(all_139_0, all_139_0) = all_768_0 % 198.43/28.36 | | | | | | | | | | | | | | (182) rearsegP(all_143_1, all_139_0) = all_768_1 % 198.43/28.36 | | | | | | | | | | | | | | (183) ~ (all_768_0 = 0) | ~ (all_768_1 = 0) | ~ % 198.43/28.36 | | | | | | | | | | | | | | (all_768_2 = 0) % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_768_2, all_139_0, % 198.43/28.36 | | | | | | | | | | | | | | simplifying with (31), (180) gives: % 198.43/28.36 | | | | | | | | | | | | | | (184) all_768_2 = 0 % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_768_1, all_139_0, % 198.43/28.36 | | | | | | | | | | | | | | all_143_1, simplifying with (59), (182) gives: % 198.43/28.36 | | | | | | | | | | | | | | (185) all_768_1 = 0 % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | BETA: splitting (183) gives: % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | Case 1: % 198.43/28.36 | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | (186) ~ (all_768_0 = 0) % 198.43/28.36 | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 198.43/28.36 | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | Case 1: % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | (187) all_143_1 = all_139_0 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | REDUCE: (178), (187) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (188) rearsegP(all_139_0, all_139_0) = all_766_1 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | REDUCE: (59), (187) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (189) rearsegP(all_139_0, all_139_0) = 0 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | REDUCE: (177), (187) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (190) rearsegP(all_139_0, all_139_0) = all_766_0 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_768_0, 0, all_139_0, % 198.43/28.36 | | | | | | | | | | | | | | | | all_139_0, simplifying with (181), (189) gives: % 198.43/28.36 | | | | | | | | | | | | | | | | (191) all_768_0 = 0 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_768_0, all_766_1, % 198.43/28.36 | | | | | | | | | | | | | | | | all_139_0, all_139_0, simplifying with (181), % 198.43/28.36 | | | | | | | | | | | | | | | | (188) gives: % 198.43/28.36 | | | | | | | | | | | | | | | | (192) all_768_0 = all_766_1 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_768_0, all_766_0, % 198.43/28.36 | | | | | | | | | | | | | | | | all_139_0, all_139_0, simplifying with (181), % 198.43/28.36 | | | | | | | | | | | | | | | | (190) gives: % 198.43/28.36 | | | | | | | | | | | | | | | | (193) all_768_0 = all_766_0 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (193) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (194) all_766_0 = all_766_1 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (193) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (195) all_766_0 = 0 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (195) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (196) all_766_1 = 0 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | REDUCE: (186), (191) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (197) $false % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | Case 2: % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | (198) ? [v0: any] : ? [v1: any] : (rearsegP(all_139_0, % 198.43/28.36 | | | | | | | | | | | | | | | | all_143_1) = v1 & ssList(all_139_0) = v0 & ( ~ % 198.43/28.36 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | DELTA: instantiating (198) with fresh symbols all_913_0, % 198.43/28.36 | | | | | | | | | | | | | | | | all_913_1 gives: % 198.43/28.36 | | | | | | | | | | | | | | | | (199) rearsegP(all_139_0, all_143_1) = all_913_0 & % 198.43/28.36 | | | | | | | | | | | | | | | | ssList(all_139_0) = all_913_1 & ( ~ (all_913_0 = % 198.43/28.36 | | | | | | | | | | | | | | | | 0) | ~ (all_913_1 = 0)) % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 198.43/28.36 | | | | | | | | | | | | | | | | (200) ssList(all_139_0) = all_913_1 % 198.43/28.36 | | | | | | | | | | | | | | | | (201) ~ (all_913_0 = 0) | ~ (all_913_1 = 0) % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_913_1, all_139_0, % 198.43/28.36 | | | | | | | | | | | | | | | | simplifying with (31), (200) gives: % 198.43/28.36 | | | | | | | | | | | | | | | | (202) all_913_1 = 0 % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | Case 1: % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (ax49) with all_139_0, all_768_0, % 198.43/28.36 | | | | | | | | | | | | | | | | | simplifying with (33), (181) gives: % 198.43/28.36 | | | | | | | | | | | | | | | | | (203) all_768_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 198.43/28.36 | | | | | | | | | | | | | | | | | ssList(all_139_0) = v0) % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | Case 1: % 198.43/28.36 | | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | | (204) all_768_0 = 0 % 198.43/28.36 | | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | | REDUCE: (186), (204) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | | | (205) $false % 198.43/28.36 | | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 198.43/28.36 | | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | Case 2: % 198.43/28.36 | | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | | (206) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = % 198.43/28.36 | | | | | | | | | | | | | | | | | | v0) % 198.43/28.36 | | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (31), (206) are inconsistent by sub-proof #1. % 198.43/28.36 | | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | Case 2: % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | (207) ~ (all_913_1 = 0) % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | REDUCE: (202), (207) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | | (208) $false % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | | CLOSE: (208) is inconsistent. % 198.43/28.36 | | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | Case 2: % 198.43/28.36 | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | (209) ~ (all_768_1 = 0) | ~ (all_768_2 = 0) % 198.43/28.36 | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 198.43/28.36 | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | Case 1: % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | (210) ~ (all_768_1 = 0) % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | REDUCE: (185), (210) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (211) $false % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent. % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | Case 2: % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | (212) ~ (all_768_2 = 0) % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | REDUCE: (184), (212) imply: % 198.43/28.36 | | | | | | | | | | | | | | | | (213) $false % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent. % 198.43/28.36 | | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | End of split % 198.43/28.36 | | | | | | | | | | % 198.43/28.36 | | | | | | | | | Case 2: % 198.43/28.36 | | | | | | | | | | % 198.43/28.36 | | | | | | | | | | (214) ~ (all_145_0 = 0) % 198.43/28.36 | | | | | | | | | | % 198.43/28.37 | | | | | | | | | | REDUCE: (57), (214) imply: % 198.43/28.37 | | | | | | | | | | (215) $false % 198.43/28.37 | | | | | | | | | | % 198.43/28.37 | | | | | | | | | | CLOSE: (215) is inconsistent. % 198.43/28.37 | | | | | | | | | | % 198.43/28.37 | | | | | | | | | End of split % 198.43/28.37 | | | | | | | | | % 198.43/28.37 | | | | | | | | End of split % 198.43/28.37 | | | | | | | | % 198.43/28.37 | | | | | | | End of split % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | End of split % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | Case 2: % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | (216) all_143_1 = nil & all_139_0 = nil % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | ALPHA: (216) implies: % 198.43/28.37 | | | | | | (217) all_143_1 = nil % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | REDUCE: (55), (217) imply: % 198.43/28.37 | | | | | | (218) $false % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | CLOSE: (218) is inconsistent. % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | End of split % 198.43/28.37 | | | | | % 198.43/28.37 | | | | Case 2: % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | (219) ~ (all_143_0 = 0) % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | REDUCE: (49), (219) imply: % 198.43/28.37 | | | | | (220) $false % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | CLOSE: (220) is inconsistent. % 198.43/28.37 | | | | | % 198.43/28.37 | | | | End of split % 198.43/28.37 | | | | % 198.43/28.37 | | | End of split % 198.43/28.37 | | | % 198.43/28.37 | | Case 2: % 198.43/28.37 | | | % 198.43/28.37 | | | (221) all_143_1 = nil & ~ (all_139_0 = nil) % 198.43/28.37 | | | % 198.43/28.37 | | | ALPHA: (221) implies: % 198.43/28.37 | | | (222) all_143_1 = nil % 198.43/28.37 | | | (223) ~ (all_139_0 = nil) % 198.43/28.37 | | | % 198.43/28.37 | | | BETA: splitting (30) gives: % 198.43/28.37 | | | % 198.43/28.37 | | | Case 1: % 198.43/28.37 | | | | % 198.43/28.37 | | | | (224) all_147_0 = 0 & all_145_0 = 0 % 198.43/28.37 | | | | % 198.43/28.37 | | | | ALPHA: (224) implies: % 198.43/28.37 | | | | (225) all_147_0 = 0 % 198.43/28.37 | | | | % 198.43/28.37 | | | | BETA: splitting (44) gives: % 198.43/28.37 | | | | % 198.43/28.37 | | | | Case 1: % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | (226) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = v0) % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | REF_CLOSE: (9), (31), (226) are inconsistent by sub-proof #1. % 198.43/28.37 | | | | | % 198.43/28.37 | | | | Case 2: % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | (227) ( ~ (all_147_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0, % 198.43/28.37 | | | | | all_139_0) = all_143_1 & $i(v0))) & (all_147_0 = 0 | ! % 198.43/28.37 | | | | | [v0: $i] : ( ~ (app(v0, all_139_0) = all_143_1) | ~ $i(v0) % 198.43/28.37 | | | | | | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1))) % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | ALPHA: (227) implies: % 198.43/28.37 | | | | | (228) ~ (all_147_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0, % 198.43/28.37 | | | | | all_139_0) = all_143_1 & $i(v0)) % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | BETA: splitting (228) gives: % 198.43/28.37 | | | | | % 198.43/28.37 | | | | | Case 1: % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | (229) ~ (all_147_0 = 0) % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | REDUCE: (225), (229) imply: % 198.43/28.37 | | | | | | (230) $false % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | CLOSE: (230) is inconsistent. % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | Case 2: % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | (231) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_139_0) = % 198.43/28.37 | | | | | | all_143_1 & $i(v0)) % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | DELTA: instantiating (231) with fresh symbol all_370_0 gives: % 198.43/28.37 | | | | | | (232) ssList(all_370_0) = 0 & app(all_370_0, all_139_0) = % 198.43/28.37 | | | | | | all_143_1 & $i(all_370_0) % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | ALPHA: (232) implies: % 198.43/28.37 | | | | | | (233) $i(all_370_0) % 198.43/28.37 | | | | | | (234) app(all_370_0, all_139_0) = all_143_1 % 198.43/28.37 | | | | | | (235) ssList(all_370_0) = 0 % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | REDUCE: (222), (234) imply: % 198.43/28.37 | | | | | | (236) app(all_370_0, all_139_0) = nil % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | GROUND_INST: instantiating (5) with all_370_0, simplifying with % 198.43/28.37 | | | | | | (233), (235) gives: % 198.43/28.37 | | | | | | (237) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_370_0, v0) = v1) | % 198.43/28.37 | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = % 198.43/28.37 | | | | | | v2) | (( ~ (v1 = nil) | (v0 = nil & all_370_0 = nil)) & % 198.43/28.37 | | | | | | ( ~ (v0 = nil) | ~ (all_370_0 = nil) | v1 = nil))) % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | GROUND_INST: instantiating (237) with all_139_0, nil, simplifying % 198.43/28.37 | | | | | | with (33), (236) gives: % 198.43/28.37 | | | | | | (238) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = v0) | % 198.43/28.37 | | | | | | (all_370_0 = nil & all_139_0 = nil) % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | BETA: splitting (238) gives: % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | | Case 1: % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | | (239) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = v0) % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | | REF_CLOSE: (9), (31), (239) are inconsistent by sub-proof #1. % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | Case 2: % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | | (240) all_370_0 = nil & all_139_0 = nil % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | | ALPHA: (240) implies: % 198.43/28.37 | | | | | | | (241) all_139_0 = nil % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | | REDUCE: (223), (241) imply: % 198.43/28.37 | | | | | | | (242) $false % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | | CLOSE: (242) is inconsistent. % 198.43/28.37 | | | | | | | % 198.43/28.37 | | | | | | End of split % 198.43/28.37 | | | | | | % 198.43/28.37 | | | | | End of split % 198.43/28.37 | | | | | % 198.43/28.37 | | | | End of split % 198.43/28.37 | | | | % 198.43/28.37 | | | Case 2: % 198.43/28.37 | | | | % 198.43/28.37 | | | | (243) all_143_1 = nil & all_139_0 = nil % 198.43/28.37 | | | | % 198.43/28.37 | | | | ALPHA: (243) implies: % 198.43/28.37 | | | | (244) all_139_0 = nil % 198.43/28.37 | | | | % 198.43/28.37 | | | | REDUCE: (223), (244) imply: % 198.43/28.37 | | | | (245) $false % 198.43/28.37 | | | | % 198.43/28.37 | | | | CLOSE: (245) is inconsistent. % 198.43/28.37 | | | | % 198.43/28.37 | | | End of split % 198.43/28.37 | | | % 198.43/28.37 | | End of split % 198.43/28.37 | | % 198.43/28.37 | End of split % 198.43/28.37 | % 198.43/28.37 End of proof % 198.43/28.37 % 198.43/28.37 Sub-proof #1 shows that the following formulas are inconsistent: % 198.43/28.37 ---------------------------------------------------------------- % 198.43/28.37 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_0) = v0) % 198.43/28.37 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 198.43/28.37 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 198.43/28.37 (3) ssList(all_139_0) = 0 % 198.43/28.37 % 198.43/28.37 Begin of proof % 198.43/28.37 | % 198.43/28.37 | DELTA: instantiating (1) with fresh symbol all_867_0 gives: % 198.43/28.37 | (4) ~ (all_867_0 = 0) & ssList(all_139_0) = all_867_0 % 198.43/28.37 | % 198.43/28.37 | ALPHA: (4) implies: % 198.43/28.37 | (5) ~ (all_867_0 = 0) % 198.43/28.37 | (6) ssList(all_139_0) = all_867_0 % 198.43/28.37 | % 198.43/28.37 | GROUND_INST: instantiating (2) with 0, all_867_0, all_139_0, simplifying with % 198.43/28.37 | (3), (6) gives: % 198.43/28.37 | (7) all_867_0 = 0 % 198.43/28.37 | % 198.43/28.37 | REDUCE: (5), (7) imply: % 198.43/28.37 | (8) $false % 198.43/28.37 | % 198.43/28.37 | CLOSE: (8) is inconsistent. % 198.43/28.37 | % 198.43/28.37 End of proof % 198.43/28.37 % 198.43/28.37 Sub-proof #2 shows that the following formulas are inconsistent: % 198.43/28.37 ---------------------------------------------------------------- % 198.43/28.37 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 198.43/28.38 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 198.43/28.38 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 198.43/28.38 (3) ssList(nil) = 0 % 198.43/28.38 % 198.43/28.38 Begin of proof % 198.43/28.38 | % 198.43/28.38 | DELTA: instantiating (1) with fresh symbol all_304_0 gives: % 198.43/28.38 | (4) ~ (all_304_0 = 0) & ssList(nil) = all_304_0 % 198.43/28.38 | % 198.43/28.38 | ALPHA: (4) implies: % 198.43/28.38 | (5) ~ (all_304_0 = 0) % 198.43/28.38 | (6) ssList(nil) = all_304_0 % 198.43/28.38 | % 198.43/28.38 | DELTA: instantiating (1) with fresh symbol all_306_0 gives: % 198.43/28.38 | (7) ~ (all_306_0 = 0) & ssList(nil) = all_306_0 % 198.43/28.38 | % 198.43/28.38 | ALPHA: (7) implies: % 198.43/28.38 | (8) ssList(nil) = all_306_0 % 198.43/28.38 | % 198.43/28.38 | DELTA: instantiating (1) with fresh symbol all_308_0 gives: % 198.43/28.38 | (9) ~ (all_308_0 = 0) & ssList(nil) = all_308_0 % 198.43/28.38 | % 198.43/28.38 | ALPHA: (9) implies: % 198.43/28.38 | (10) ssList(nil) = all_308_0 % 198.43/28.38 | % 198.43/28.38 | DELTA: instantiating (1) with fresh symbol all_310_0 gives: % 198.43/28.38 | (11) ~ (all_310_0 = 0) & ssList(nil) = all_310_0 % 198.43/28.38 | % 198.43/28.38 | ALPHA: (11) implies: % 198.43/28.38 | (12) ssList(nil) = all_310_0 % 198.43/28.38 | % 198.43/28.38 | DELTA: instantiating (1) with fresh symbol all_312_0 gives: % 198.43/28.38 | (13) ~ (all_312_0 = 0) & ssList(nil) = all_312_0 % 198.43/28.38 | % 198.43/28.38 | ALPHA: (13) implies: % 198.43/28.38 | (14) ssList(nil) = all_312_0 % 198.43/28.38 | % 198.43/28.38 | DELTA: instantiating (1) with fresh symbol all_314_0 gives: % 198.43/28.38 | (15) ~ (all_314_0 = 0) & ssList(nil) = all_314_0 % 198.43/28.38 | % 198.43/28.38 | ALPHA: (15) implies: % 198.43/28.38 | (16) ssList(nil) = all_314_0 % 198.43/28.38 | % 198.43/28.38 | DELTA: instantiating (1) with fresh symbol all_316_0 gives: % 198.43/28.38 | (17) ~ (all_316_0 = 0) & ssList(nil) = all_316_0 % 198.43/28.38 | % 198.43/28.38 | ALPHA: (17) implies: % 198.43/28.38 | (18) ssList(nil) = all_316_0 % 198.43/28.38 | % 198.43/28.38 | GROUND_INST: instantiating (2) with 0, all_312_0, nil, simplifying with (3), % 198.43/28.38 | (14) gives: % 198.43/28.38 | (19) all_312_0 = 0 % 198.43/28.38 | % 198.43/28.38 | GROUND_INST: instantiating (2) with all_308_0, all_312_0, nil, simplifying % 198.43/28.38 | with (10), (14) gives: % 198.43/28.38 | (20) all_312_0 = all_308_0 % 198.43/28.38 | % 198.43/28.38 | GROUND_INST: instantiating (2) with all_310_0, all_314_0, nil, simplifying % 198.43/28.38 | with (12), (16) gives: % 198.43/28.38 | (21) all_314_0 = all_310_0 % 198.43/28.38 | % 198.43/28.38 | GROUND_INST: instantiating (2) with all_308_0, all_314_0, nil, simplifying % 198.43/28.38 | with (10), (16) gives: % 198.43/28.38 | (22) all_314_0 = all_308_0 % 198.43/28.38 | % 198.43/28.38 | GROUND_INST: instantiating (2) with all_306_0, all_314_0, nil, simplifying % 198.43/28.38 | with (8), (16) gives: % 198.43/28.38 | (23) all_314_0 = all_306_0 % 198.43/28.38 | % 198.43/28.38 | GROUND_INST: instantiating (2) with all_310_0, all_316_0, nil, simplifying % 198.43/28.38 | with (12), (18) gives: % 198.43/28.38 | (24) all_316_0 = all_310_0 % 198.43/28.38 | % 198.43/28.38 | GROUND_INST: instantiating (2) with all_304_0, all_316_0, nil, simplifying % 198.43/28.38 | with (6), (18) gives: % 198.43/28.38 | (25) all_316_0 = all_304_0 % 198.43/28.38 | % 198.43/28.38 | COMBINE_EQS: (24), (25) imply: % 198.43/28.38 | (26) all_310_0 = all_304_0 % 198.43/28.38 | % 198.43/28.38 | SIMP: (26) implies: % 198.43/28.38 | (27) all_310_0 = all_304_0 % 198.43/28.38 | % 198.43/28.38 | COMBINE_EQS: (22), (23) imply: % 198.43/28.38 | (28) all_308_0 = all_306_0 % 198.43/28.38 | % 198.43/28.38 | SIMP: (28) implies: % 198.43/28.38 | (29) all_308_0 = all_306_0 % 198.43/28.38 | % 198.43/28.38 | COMBINE_EQS: (21), (23) imply: % 198.43/28.38 | (30) all_310_0 = all_306_0 % 198.43/28.38 | % 198.43/28.38 | SIMP: (30) implies: % 198.43/28.38 | (31) all_310_0 = all_306_0 % 198.43/28.38 | % 198.43/28.38 | COMBINE_EQS: (19), (20) imply: % 198.43/28.38 | (32) all_308_0 = 0 % 198.43/28.38 | % 198.43/28.38 | SIMP: (32) implies: % 198.43/28.38 | (33) all_308_0 = 0 % 198.43/28.38 | % 198.43/28.38 | COMBINE_EQS: (27), (31) imply: % 198.43/28.38 | (34) all_306_0 = all_304_0 % 198.43/28.38 | % 198.43/28.38 | SIMP: (34) implies: % 198.43/28.38 | (35) all_306_0 = all_304_0 % 198.43/28.38 | % 198.43/28.38 | COMBINE_EQS: (29), (33) imply: % 198.43/28.38 | (36) all_306_0 = 0 % 198.43/28.38 | % 198.43/28.38 | SIMP: (36) implies: % 198.43/28.38 | (37) all_306_0 = 0 % 198.43/28.38 | % 198.43/28.38 | COMBINE_EQS: (35), (37) imply: % 198.43/28.38 | (38) all_304_0 = 0 % 198.43/28.38 | % 198.43/28.38 | SIMP: (38) implies: % 198.43/28.38 | (39) all_304_0 = 0 % 198.43/28.38 | % 198.43/28.38 | REDUCE: (5), (39) imply: % 198.43/28.38 | (40) $false % 198.43/28.38 | % 198.43/28.38 | CLOSE: (40) is inconsistent. % 198.43/28.38 | % 198.43/28.38 End of proof % 198.43/28.38 % SZS output end Proof for theBenchmark % 198.43/28.38 % 198.43/28.38 27773ms %------------------------------------------------------------------------------