%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC049+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 : n011.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 31.35s 4.92s % Output : Proof 110.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SWC049+1 : TPTP v8.1.2. Released v2.4.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Mon Aug 28 18:26:26 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.96/1.53 Prover 1: Preprocessing ... % 5.96/1.55 Prover 4: Preprocessing ... % 5.96/1.57 Prover 5: Preprocessing ... % 5.96/1.57 Prover 2: Preprocessing ... % 5.96/1.57 Prover 3: Preprocessing ... % 5.96/1.57 Prover 6: Preprocessing ... % 5.96/1.57 Prover 0: Preprocessing ... % 15.34/2.84 Prover 2: Proving ... % 16.31/2.93 Prover 3: Constructing countermodel ... % 16.46/2.95 Prover 5: Constructing countermodel ... % 16.46/2.95 Prover 6: Proving ... % 16.46/2.95 Prover 1: Constructing countermodel ... % 21.57/3.63 Prover 4: Constructing countermodel ... % 21.57/3.76 Prover 0: Proving ... % 31.35/4.92 Prover 3: proved (4279ms) % 31.35/4.92 % 31.35/4.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 31.35/4.92 % 31.35/4.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 31.35/4.92 Prover 6: stopped % 31.35/4.93 Prover 5: stopped % 31.35/4.95 Prover 0: stopped % 31.35/4.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 31.35/4.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 31.35/4.95 Prover 2: stopped % 31.35/4.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 31.35/4.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 32.85/5.16 Prover 7: Preprocessing ... % 33.53/5.20 Prover 8: Preprocessing ... % 33.53/5.25 Prover 10: Preprocessing ... % 33.53/5.28 Prover 11: Preprocessing ... % 34.30/5.30 Prover 13: Preprocessing ... % 34.30/5.46 Prover 7: Constructing countermodel ... % 34.30/5.48 Prover 10: Constructing countermodel ... % 36.59/5.65 Prover 8: Warning: ignoring some quantifiers % 36.59/5.68 Prover 8: Constructing countermodel ... % 37.30/5.72 Prover 13: Constructing countermodel ... % 42.71/6.46 Prover 11: Constructing countermodel ... % 70.50/10.05 Prover 13: stopped % 70.50/10.05 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 71.20/10.17 Prover 16: Preprocessing ... % 73.23/10.39 Prover 16: Constructing countermodel ... % 109.34/15.16 Prover 1: Found proof (size 172) % 109.34/15.16 Prover 1: proved (14527ms) % 109.34/15.16 Prover 8: stopped % 109.34/15.16 Prover 7: stopped % 109.34/15.16 Prover 11: stopped % 109.34/15.16 Prover 10: stopped % 109.34/15.16 Prover 4: stopped % 109.77/15.17 Prover 16: stopped % 109.77/15.17 % 109.77/15.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 109.77/15.17 % 109.77/15.18 % SZS output start Proof for theBenchmark % 109.77/15.19 Assumptions after simplification: % 109.77/15.19 --------------------------------- % 109.77/15.19 % 109.77/15.19 (ax13) % 109.77/15.22 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ? % 109.77/15.22 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] : % 109.77/15.22 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) | % 109.77/15.22 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5: % 109.77/15.22 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~ % 109.77/15.22 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & % 109.77/15.22 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) | % 109.77/15.22 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) | % 109.77/15.22 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 = % 109.77/15.22 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) = % 109.77/15.22 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] : % 109.77/15.22 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 & % 109.77/15.22 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ? % 109.77/15.22 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 & % 109.77/15.22 app(v7, v9) = v0 & $i(v9) & $i(v8))))))))) % 109.77/15.22 % 109.77/15.22 (ax15) % 109.77/15.22 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 109.77/15.23 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 109.77/15.23 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 109.77/15.23 % 109.77/15.23 (ax17) % 109.77/15.23 ssList(nil) = 0 & $i(nil) % 109.77/15.23 % 109.77/15.23 (ax20) % 109.77/15.23 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 109.77/15.23 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 109.77/15.23 ssItem(v2) = 0 & $i(v2)))) % 109.77/15.23 % 109.77/15.23 (ax48) % 109.77/15.23 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~ % 109.77/15.23 (rearsegP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : % 109.77/15.23 (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 109.77/15.23 % 109.77/15.23 (ax49) % 109.77/15.23 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ~ $i(v0) % 109.77/15.23 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 109.77/15.23 % 109.77/15.23 (ax6) % 109.77/15.23 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 109.77/15.23 ( ~ (rearsegP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 109.77/15.23 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : (ssList(v3) = 0 & % 109.77/15.23 app(v3, v1) = v0 & $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (app(v3, % 109.77/15.23 v1) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) % 109.77/15.23 = v4)))))) % 109.77/15.23 % 109.77/15.23 (ax72) % 109.77/15.23 duplicatefreeP(nil) = 0 & $i(nil) % 109.77/15.23 % 109.77/15.23 (co1) % 109.77/15.24 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 109.77/15.24 0 & $i(v1) & ? [v2: $i] : ? [v3: any] : (ssList(v2) = 0 & neq(v2, nil) = % 109.77/15.24 v3 & $i(v2) & ? [v4: any] : ? [v5: any] : (v2 = v0 & rearsegP(v1, v0) % 109.77/15.24 = v5 & neq(v1, nil) = v4 & ! [v6: $i] : ( ~ (neq(v6, nil) = 0) | ~ % 109.77/15.24 $i(v6) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (rearsegP(v1, % 109.77/15.24 v6) = v8 & rearsegP(v0, v6) = v9 & ssList(v6) = v7 & ( ~ (v9 = % 109.77/15.24 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ( ~ (v4 = 0) | (v5 = 0 & % 109.77/15.24 v3 = 0)) & ( ~ (v1 = nil) | ~ (v0 = nil)) & ( ~ (v1 = nil) | v0 = % 109.77/15.24 nil))))) % 109.77/15.24 % 109.77/15.24 (function-axioms) % 109.77/15.25 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 109.77/15.25 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 109.77/15.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 109.77/15.25 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 109.77/15.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 109.77/15.25 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 109.77/15.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 109.77/15.25 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 109.77/15.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 109.77/15.25 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 109.77/15.25 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 109.77/15.25 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 109.77/15.25 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 109.77/15.25 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 109.77/15.25 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 109.77/15.25 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 109.77/15.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 109.77/15.25 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 109.77/15.25 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 109.77/15.25 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 109.77/15.25 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 109.77/15.25 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 109.77/15.25 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 109.77/15.25 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 109.77/15.25 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 109.77/15.25 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.77/15.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 109.77/15.25 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.77/15.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 109.77/15.25 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.77/15.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 109.77/15.25 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.77/15.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 109.77/15.25 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.77/15.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 109.77/15.25 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.77/15.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 109.77/15.25 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.77/15.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 109.77/15.25 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 109.77/15.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 109.77/15.25 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 109.77/15.25 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 109.77/15.25 % 109.77/15.25 Further assumptions not needed in the proof: % 109.77/15.25 -------------------------------------------- % 109.77/15.25 ax1, ax10, ax11, ax12, ax14, ax16, ax18, ax19, ax2, ax21, ax22, ax23, ax24, % 109.77/15.25 ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 109.77/15.25 ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax5, % 109.77/15.25 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax60, ax61, ax62, % 109.77/15.25 ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax73, ax74, ax75, % 109.77/15.25 ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87, % 109.77/15.25 ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 109.77/15.25 % 109.77/15.25 Those formulas are unsatisfiable: % 109.77/15.25 --------------------------------- % 109.77/15.25 % 109.77/15.25 Begin of proof % 109.77/15.25 | % 109.77/15.25 | ALPHA: (ax17) implies: % 110.16/15.25 | (1) ssList(nil) = 0 % 110.16/15.25 | % 110.16/15.25 | ALPHA: (ax20) implies: % 110.16/15.25 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 110.16/15.25 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 110.16/15.25 | ssItem(v2) = 0 & $i(v2)))) % 110.16/15.25 | % 110.16/15.25 | ALPHA: (ax72) implies: % 110.16/15.25 | (3) duplicatefreeP(nil) = 0 % 110.16/15.25 | % 110.16/15.25 | ALPHA: (co1) implies: % 110.16/15.25 | (4) $i(nil) % 110.16/15.26 | (5) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 110.16/15.26 | & $i(v1) & ? [v2: $i] : ? [v3: any] : (ssList(v2) = 0 & neq(v2, % 110.16/15.26 | nil) = v3 & $i(v2) & ? [v4: any] : ? [v5: any] : (v2 = v0 & % 110.16/15.26 | rearsegP(v1, v0) = v5 & neq(v1, nil) = v4 & ! [v6: $i] : ( ~ % 110.16/15.26 | (neq(v6, nil) = 0) | ~ $i(v6) | ? [v7: any] : ? [v8: any] % 110.16/15.26 | : ? [v9: any] : (rearsegP(v1, v6) = v8 & rearsegP(v0, v6) = % 110.16/15.26 | v9 & ssList(v6) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 % 110.16/15.26 | = 0)))) & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)) & ( ~ (v1 = % 110.16/15.26 | nil) | ~ (v0 = nil)) & ( ~ (v1 = nil) | v0 = nil))))) % 110.16/15.26 | % 110.16/15.26 | ALPHA: (function-axioms) implies: % 110.16/15.26 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 110.16/15.26 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 110.16/15.26 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 110.16/15.26 | ! [v3: $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, % 110.16/15.26 | v2) = v0)) % 110.16/15.26 | % 110.16/15.26 | DELTA: instantiating (5) with fresh symbol all_93_0 gives: % 110.16/15.26 | (8) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 110.16/15.26 | $i(v0) & ? [v1: $i] : ? [v2: any] : (ssList(v1) = 0 & neq(v1, nil) % 110.16/15.26 | = v2 & $i(v1) & ? [v3: any] : ? [v4: any] : (v1 = all_93_0 & % 110.16/15.26 | rearsegP(v0, all_93_0) = v4 & neq(v0, nil) = v3 & ! [v5: $i] : ( % 110.16/15.26 | ~ (neq(v5, nil) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] % 110.16/15.26 | : ? [v8: any] : (rearsegP(v0, v5) = v7 & rearsegP(all_93_0, % 110.16/15.26 | v5) = v8 & ssList(v5) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | % 110.16/15.26 | ~ (v6 = 0)))) & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)) & ( ~ (v0 % 110.16/15.26 | = nil) | ~ (all_93_0 = nil)) & ( ~ (v0 = nil) | all_93_0 = % 110.16/15.26 | nil)))) % 110.16/15.26 | % 110.16/15.26 | ALPHA: (8) implies: % 110.16/15.26 | (9) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 110.16/15.26 | (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ? [v3: any] : ? [v4: % 110.16/15.26 | any] : (v1 = all_93_0 & rearsegP(v0, all_93_0) = v4 & neq(v0, % 110.16/15.26 | nil) = v3 & ! [v5: $i] : ( ~ (neq(v5, nil) = 0) | ~ $i(v5) | % 110.16/15.26 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (rearsegP(v0, v5) = % 110.16/15.26 | v7 & rearsegP(all_93_0, v5) = v8 & ssList(v5) = v6 & ( ~ (v8 % 110.16/15.26 | = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ( ~ (v3 = 0) | (v4 % 110.16/15.26 | = 0 & v2 = 0)) & ( ~ (v0 = nil) | ~ (all_93_0 = nil)) & ( ~ % 110.16/15.26 | (v0 = nil) | all_93_0 = nil)))) % 110.16/15.26 | % 110.16/15.26 | DELTA: instantiating (9) with fresh symbol all_97_0 gives: % 110.16/15.27 | (10) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: $i] : ? [v1: any] : % 110.16/15.27 | (ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v2: any] : ? [v3: % 110.16/15.27 | any] : (v0 = all_93_0 & rearsegP(all_97_0, all_93_0) = v3 & % 110.16/15.27 | neq(all_97_0, nil) = v2 & ! [v4: $i] : ( ~ (neq(v4, nil) = 0) | % 110.16/15.27 | ~ $i(v4) | ? [v5: any] : ? [v6: any] : ? [v7: any] : % 110.16/15.27 | (rearsegP(all_97_0, v4) = v6 & rearsegP(all_93_0, v4) = v7 & % 110.16/15.27 | ssList(v4) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) % 110.16/15.27 | & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)) & ( ~ (all_97_0 = nil) | ~ % 110.16/15.27 | (all_93_0 = nil)) & ( ~ (all_97_0 = nil) | all_93_0 = nil))) % 110.16/15.27 | % 110.16/15.27 | ALPHA: (10) implies: % 110.16/15.27 | (11) $i(all_97_0) % 110.16/15.27 | (12) ssList(all_97_0) = 0 % 110.16/15.27 | (13) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 110.16/15.27 | $i(v0) & ? [v2: any] : ? [v3: any] : (v0 = all_93_0 & % 110.16/15.27 | rearsegP(all_97_0, all_93_0) = v3 & neq(all_97_0, nil) = v2 & ! % 110.16/15.27 | [v4: $i] : ( ~ (neq(v4, nil) = 0) | ~ $i(v4) | ? [v5: any] : ? % 110.16/15.27 | [v6: any] : ? [v7: any] : (rearsegP(all_97_0, v4) = v6 & % 110.16/15.27 | rearsegP(all_93_0, v4) = v7 & ssList(v4) = v5 & ( ~ (v7 = 0) | % 110.16/15.27 | ~ (v6 = 0) | ~ (v5 = 0)))) & ( ~ (v2 = 0) | (v3 = 0 & v1 = % 110.16/15.27 | 0)) & ( ~ (all_97_0 = nil) | ~ (all_93_0 = nil)) & ( ~ % 110.16/15.27 | (all_97_0 = nil) | all_93_0 = nil))) % 110.16/15.27 | % 110.16/15.27 | DELTA: instantiating (13) with fresh symbols all_99_0, all_99_1 gives: % 110.16/15.27 | (14) ssList(all_99_1) = 0 & neq(all_99_1, nil) = all_99_0 & $i(all_99_1) & % 110.16/15.27 | ? [v0: any] : ? [v1: any] : (all_99_1 = all_93_0 & rearsegP(all_97_0, % 110.16/15.27 | all_93_0) = v1 & neq(all_97_0, nil) = v0 & ! [v2: $i] : ( ~ % 110.16/15.27 | (neq(v2, nil) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4: any] : ? % 110.16/15.27 | [v5: any] : (rearsegP(all_97_0, v2) = v4 & rearsegP(all_93_0, v2) % 110.16/15.27 | = v5 & ssList(v2) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 110.16/15.27 | 0)))) & ( ~ (v0 = 0) | (v1 = 0 & all_99_0 = 0)) & ( ~ % 110.16/15.27 | (all_97_0 = nil) | ~ (all_93_0 = nil)) & ( ~ (all_97_0 = nil) | % 110.16/15.27 | all_93_0 = nil)) % 110.16/15.27 | % 110.16/15.27 | ALPHA: (14) implies: % 110.16/15.27 | (15) $i(all_99_1) % 110.16/15.27 | (16) neq(all_99_1, nil) = all_99_0 % 110.16/15.27 | (17) ssList(all_99_1) = 0 % 110.16/15.27 | (18) ? [v0: any] : ? [v1: any] : (all_99_1 = all_93_0 & % 110.16/15.27 | rearsegP(all_97_0, all_93_0) = v1 & neq(all_97_0, nil) = v0 & ! % 110.16/15.27 | [v2: $i] : ( ~ (neq(v2, nil) = 0) | ~ $i(v2) | ? [v3: any] : ? % 110.16/15.27 | [v4: any] : ? [v5: any] : (rearsegP(all_97_0, v2) = v4 & % 110.16/15.27 | rearsegP(all_93_0, v2) = v5 & ssList(v2) = v3 & ( ~ (v5 = 0) | % 110.16/15.27 | ~ (v4 = 0) | ~ (v3 = 0)))) & ( ~ (v0 = 0) | (v1 = 0 & % 110.16/15.27 | all_99_0 = 0)) & ( ~ (all_97_0 = nil) | ~ (all_93_0 = nil)) & ( % 110.16/15.27 | ~ (all_97_0 = nil) | all_93_0 = nil)) % 110.16/15.27 | % 110.16/15.27 | DELTA: instantiating (18) with fresh symbols all_101_0, all_101_1 gives: % 110.16/15.27 | (19) all_99_1 = all_93_0 & rearsegP(all_97_0, all_93_0) = all_101_0 & % 110.16/15.27 | neq(all_97_0, nil) = all_101_1 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) % 110.16/15.27 | | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] : % 110.16/15.28 | (rearsegP(all_97_0, v0) = v2 & rearsegP(all_93_0, v0) = v3 & % 110.16/15.28 | ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)))) & ( % 110.16/15.28 | ~ (all_101_1 = 0) | (all_101_0 = 0 & all_99_0 = 0)) & ( ~ (all_97_0 % 110.16/15.28 | = nil) | ~ (all_93_0 = nil)) & ( ~ (all_97_0 = nil) | all_93_0 = % 110.16/15.28 | nil) % 110.16/15.28 | % 110.16/15.28 | ALPHA: (19) implies: % 110.16/15.28 | (20) all_99_1 = all_93_0 % 110.16/15.28 | (21) neq(all_97_0, nil) = all_101_1 % 110.16/15.28 | (22) rearsegP(all_97_0, all_93_0) = all_101_0 % 110.16/15.28 | (23) ~ (all_97_0 = nil) | all_93_0 = nil % 110.16/15.28 | (24) ~ (all_97_0 = nil) | ~ (all_93_0 = nil) % 110.16/15.28 | (25) ~ (all_101_1 = 0) | (all_101_0 = 0 & all_99_0 = 0) % 110.16/15.28 | (26) ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] : ? % 110.16/15.28 | [v2: any] : ? [v3: any] : (rearsegP(all_97_0, v0) = v2 & % 110.16/15.28 | rearsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ % 110.16/15.28 | (v2 = 0) | ~ (v1 = 0)))) % 110.16/15.28 | % 110.16/15.28 | REDUCE: (17), (20) imply: % 110.16/15.28 | (27) ssList(all_93_0) = 0 % 110.16/15.28 | % 110.16/15.28 | REDUCE: (16), (20) imply: % 110.16/15.28 | (28) neq(all_93_0, nil) = all_99_0 % 110.16/15.28 | % 110.16/15.28 | REDUCE: (15), (20) imply: % 110.16/15.28 | (29) $i(all_93_0) % 110.16/15.28 | % 110.16/15.28 | GROUND_INST: instantiating (2) with all_93_0, simplifying with (27), (29) % 110.16/15.28 | gives: % 110.16/15.28 | (30) all_93_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 110.16/15.28 | : (cons(v1, v0) = all_93_0 & ssItem(v1) = 0 & $i(v1))) % 110.16/15.28 | % 110.16/15.28 | GROUND_INST: instantiating (ax15) with all_93_0, simplifying with (27), (29) % 110.16/15.28 | gives: % 110.16/15.28 | (31) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_0, v0) = v1) | ~ $i(v0) % 110.16/15.28 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 110.16/15.28 | ~ (v0 = all_93_0)) & (v1 = 0 | v0 = all_93_0))) % 110.16/15.28 | % 110.16/15.28 | GROUND_INST: instantiating (2) with all_97_0, simplifying with (11), (12) % 110.16/15.28 | gives: % 110.31/15.28 | (32) all_97_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 110.31/15.28 | : (cons(v1, v0) = all_97_0 & ssItem(v1) = 0 & $i(v1))) % 110.31/15.28 | % 110.31/15.28 | GROUND_INST: instantiating (ax6) with all_97_0, simplifying with (11), (12) % 110.31/15.28 | gives: % 110.31/15.28 | (33) ! [v0: $i] : ! [v1: any] : ( ~ (rearsegP(all_97_0, v0) = v1) | ~ % 110.31/15.28 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 110.31/15.28 | 0) | ? [v2: $i] : (ssList(v2) = 0 & app(v2, v0) = all_97_0 & % 110.31/15.28 | $i(v2))) & (v1 = 0 | ! [v2: $i] : ( ~ (app(v2, v0) = % 110.31/15.28 | all_97_0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 110.31/15.28 | ssList(v2) = v3))))) % 110.31/15.28 | % 110.31/15.28 | GROUND_INST: instantiating (ax15) with all_97_0, simplifying with (11), (12) % 110.31/15.28 | gives: % 110.31/15.29 | (34) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_0, v0) = v1) | ~ $i(v0) % 110.31/15.29 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 110.31/15.29 | ~ (v0 = all_97_0)) & (v1 = 0 | v0 = all_97_0))) % 110.31/15.29 | % 110.31/15.29 | GROUND_INST: instantiating (ax48) with all_97_0, simplifying with (11), (12) % 110.31/15.29 | gives: % 110.31/15.29 | (35) ! [v0: any] : (v0 = all_97_0 | ~ (rearsegP(all_97_0, v0) = 0) | ~ % 110.31/15.29 | $i(v0) | ? [v1: any] : ? [v2: any] : (rearsegP(v0, all_97_0) = v2 % 110.31/15.29 | & ssList(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 110.31/15.29 | % 110.31/15.29 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (3), (4) % 110.31/15.29 | gives: % 110.31/15.29 | (36) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~ % 110.31/15.29 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) | % 110.31/15.29 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | ! % 110.31/15.29 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) | % 110.31/15.29 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = % 110.31/15.29 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 110.31/15.29 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil) % 110.31/15.29 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) = % 110.31/15.29 | v8)))))) % 110.31/15.29 | % 110.31/15.29 | GROUND_INST: instantiating (34) with nil, all_101_1, simplifying with (4), % 110.31/15.29 | (21) gives: % 110.31/15.29 | (37) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_101_1 = 0) % 110.31/15.29 | | ~ (all_97_0 = nil)) & (all_101_1 = 0 | all_97_0 = nil)) % 110.31/15.29 | % 110.31/15.29 | GROUND_INST: instantiating (33) with all_93_0, all_101_0, simplifying with % 110.31/15.29 | (22), (29) gives: % 110.31/15.29 | (38) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_0) = v0) | (( ~ (all_101_0 % 110.31/15.29 | = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_93_0) = % 110.31/15.29 | all_97_0 & $i(v0))) & (all_101_0 = 0 | ! [v0: $i] : ( ~ % 110.31/15.29 | (app(v0, all_93_0) = all_97_0) | ~ $i(v0) | ? [v1: int] : ( ~ % 110.31/15.29 | (v1 = 0) & ssList(v0) = v1)))) % 110.31/15.29 | % 110.31/15.29 | GROUND_INST: instantiating (31) with nil, all_99_0, simplifying with (4), (28) % 110.31/15.29 | gives: % 110.31/15.29 | (39) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_99_0 = 0) % 110.31/15.29 | | ~ (all_93_0 = nil)) & (all_99_0 = 0 | all_93_0 = nil)) % 110.31/15.29 | % 110.31/15.29 | BETA: splitting (36) gives: % 110.31/15.29 | % 110.31/15.29 | Case 1: % 110.31/15.29 | | % 110.31/15.29 | | (40) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 110.31/15.29 | | % 110.31/15.29 | | DELTA: instantiating (40) with fresh symbol all_280_0 gives: % 110.31/15.29 | | (41) ~ (all_280_0 = 0) & ssList(nil) = all_280_0 % 110.31/15.29 | | % 110.31/15.29 | | ALPHA: (41) implies: % 110.31/15.29 | | (42) ~ (all_280_0 = 0) % 110.31/15.29 | | (43) ssList(nil) = all_280_0 % 110.31/15.29 | | % 110.31/15.29 | | DELTA: instantiating (40) with fresh symbol all_282_0 gives: % 110.31/15.29 | | (44) ~ (all_282_0 = 0) & ssList(nil) = all_282_0 % 110.31/15.29 | | % 110.31/15.29 | | ALPHA: (44) implies: % 110.31/15.30 | | (45) ssList(nil) = all_282_0 % 110.31/15.30 | | % 110.31/15.30 | | DELTA: instantiating (40) with fresh symbol all_284_0 gives: % 110.31/15.30 | | (46) ~ (all_284_0 = 0) & ssList(nil) = all_284_0 % 110.31/15.30 | | % 110.31/15.30 | | ALPHA: (46) implies: % 110.31/15.30 | | (47) ssList(nil) = all_284_0 % 110.31/15.30 | | % 110.31/15.30 | | GROUND_INST: instantiating (6) with 0, all_282_0, nil, simplifying with (1), % 110.31/15.30 | | (45) gives: % 110.31/15.30 | | (48) all_282_0 = 0 % 110.31/15.30 | | % 110.31/15.30 | | GROUND_INST: instantiating (6) with all_282_0, all_284_0, nil, simplifying % 110.31/15.30 | | with (45), (47) gives: % 110.31/15.30 | | (49) all_284_0 = all_282_0 % 110.31/15.30 | | % 110.31/15.30 | | GROUND_INST: instantiating (6) with all_280_0, all_284_0, nil, simplifying % 110.31/15.30 | | with (43), (47) gives: % 110.31/15.30 | | (50) all_284_0 = all_280_0 % 110.31/15.30 | | % 110.31/15.30 | | COMBINE_EQS: (49), (50) imply: % 110.31/15.30 | | (51) all_282_0 = all_280_0 % 110.31/15.30 | | % 110.31/15.30 | | SIMP: (51) implies: % 110.31/15.30 | | (52) all_282_0 = all_280_0 % 110.31/15.30 | | % 110.31/15.30 | | COMBINE_EQS: (48), (52) imply: % 110.31/15.30 | | (53) all_280_0 = 0 % 110.31/15.30 | | % 110.31/15.30 | | SIMP: (53) implies: % 110.31/15.30 | | (54) all_280_0 = 0 % 110.31/15.30 | | % 110.31/15.30 | | REDUCE: (42), (54) imply: % 110.31/15.30 | | (55) $false % 110.31/15.30 | | % 110.31/15.30 | | CLOSE: (55) is inconsistent. % 110.31/15.30 | | % 110.31/15.30 | Case 2: % 110.31/15.30 | | % 110.31/15.30 | | (56) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 110.31/15.30 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = % 110.31/15.30 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( % 110.31/15.30 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) | % 110.31/15.30 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i] % 110.31/15.30 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ % 110.31/15.30 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = % 110.31/15.30 | | 0) & ssList(v6) = v8)))))) % 110.31/15.30 | | % 110.31/15.30 | | BETA: splitting (24) gives: % 110.31/15.30 | | % 110.31/15.30 | | Case 1: % 110.31/15.30 | | | % 110.31/15.30 | | | (57) ~ (all_97_0 = nil) % 110.31/15.30 | | | % 110.31/15.30 | | | BETA: splitting (37) gives: % 110.31/15.30 | | | % 110.31/15.30 | | | Case 1: % 110.31/15.30 | | | | % 110.31/15.30 | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 110.31/15.30 | | | | % 110.31/15.30 | | | | DELTA: instantiating (58) with fresh symbol all_307_0 gives: % 110.31/15.30 | | | | (59) ~ (all_307_0 = 0) & ssList(nil) = all_307_0 % 110.31/15.30 | | | | % 110.31/15.30 | | | | ALPHA: (59) implies: % 110.31/15.30 | | | | (60) ~ (all_307_0 = 0) % 110.31/15.30 | | | | (61) ssList(nil) = all_307_0 % 110.31/15.30 | | | | % 110.31/15.30 | | | | GROUND_INST: instantiating (6) with 0, all_307_0, nil, simplifying with % 110.31/15.30 | | | | (1), (61) gives: % 110.31/15.30 | | | | (62) all_307_0 = 0 % 110.31/15.30 | | | | % 110.31/15.30 | | | | REDUCE: (60), (62) imply: % 110.31/15.30 | | | | (63) $false % 110.31/15.30 | | | | % 110.31/15.30 | | | | CLOSE: (63) is inconsistent. % 110.31/15.30 | | | | % 110.31/15.30 | | | Case 2: % 110.31/15.30 | | | | % 110.31/15.30 | | | | (64) ( ~ (all_101_1 = 0) | ~ (all_97_0 = nil)) & (all_101_1 = 0 | % 110.31/15.30 | | | | all_97_0 = nil) % 110.31/15.30 | | | | % 110.31/15.30 | | | | ALPHA: (64) implies: % 110.31/15.30 | | | | (65) all_101_1 = 0 | all_97_0 = nil % 110.31/15.30 | | | | % 110.31/15.30 | | | | BETA: splitting (65) gives: % 110.31/15.30 | | | | % 110.31/15.30 | | | | Case 1: % 110.31/15.30 | | | | | % 110.31/15.30 | | | | | (66) all_97_0 = nil % 110.31/15.30 | | | | | % 110.31/15.30 | | | | | REDUCE: (57), (66) imply: % 110.31/15.30 | | | | | (67) $false % 110.31/15.30 | | | | | % 110.31/15.30 | | | | | CLOSE: (67) is inconsistent. % 110.31/15.30 | | | | | % 110.31/15.30 | | | | Case 2: % 110.31/15.30 | | | | | % 110.31/15.31 | | | | | (68) all_101_1 = 0 % 110.31/15.31 | | | | | % 110.31/15.31 | | | | | REDUCE: (21), (68) imply: % 110.31/15.31 | | | | | (69) neq(all_97_0, nil) = 0 % 110.31/15.31 | | | | | % 110.31/15.31 | | | | | BETA: splitting (32) gives: % 110.31/15.31 | | | | | % 110.31/15.31 | | | | | Case 1: % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | (70) all_97_0 = nil % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | REDUCE: (57), (70) imply: % 110.31/15.31 | | | | | | (71) $false % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | CLOSE: (71) is inconsistent. % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | Case 2: % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | (72) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 110.31/15.31 | | | | | | (cons(v1, v0) = all_97_0 & ssItem(v1) = 0 & $i(v1))) % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | DELTA: instantiating (72) with fresh symbol all_313_0 gives: % 110.31/15.31 | | | | | | (73) ssList(all_313_0) = 0 & $i(all_313_0) & ? [v0: $i] : % 110.31/15.31 | | | | | | (cons(v0, all_313_0) = all_97_0 & ssItem(v0) = 0 & $i(v0)) % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | ALPHA: (73) implies: % 110.31/15.31 | | | | | | (74) ? [v0: $i] : (cons(v0, all_313_0) = all_97_0 & ssItem(v0) = % 110.31/15.31 | | | | | | 0 & $i(v0)) % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | DELTA: instantiating (74) with fresh symbol all_315_0 gives: % 110.31/15.31 | | | | | | (75) cons(all_315_0, all_313_0) = all_97_0 & ssItem(all_315_0) = % 110.31/15.31 | | | | | | 0 & $i(all_315_0) % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | ALPHA: (75) implies: % 110.31/15.31 | | | | | | (76) $i(all_315_0) % 110.31/15.31 | | | | | | (77) ssItem(all_315_0) = 0 % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | BETA: splitting (25) gives: % 110.31/15.31 | | | | | | % 110.31/15.31 | | | | | | Case 1: % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | (78) ~ (all_101_1 = 0) % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | REDUCE: (68), (78) imply: % 110.31/15.31 | | | | | | | (79) $false % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | CLOSE: (79) is inconsistent. % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | Case 2: % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | (80) all_101_0 = 0 & all_99_0 = 0 % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | ALPHA: (80) implies: % 110.31/15.31 | | | | | | | (81) all_99_0 = 0 % 110.31/15.31 | | | | | | | (82) all_101_0 = 0 % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | REDUCE: (22), (82) imply: % 110.31/15.31 | | | | | | | (83) rearsegP(all_97_0, all_93_0) = 0 % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | REDUCE: (28), (81) imply: % 110.31/15.31 | | | | | | | (84) neq(all_93_0, nil) = 0 % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | BETA: splitting (39) gives: % 110.31/15.31 | | | | | | | % 110.31/15.31 | | | | | | | Case 1: % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | (85) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | DELTA: instantiating (85) with fresh symbol all_324_0 gives: % 110.31/15.31 | | | | | | | | (86) ~ (all_324_0 = 0) & ssList(nil) = all_324_0 % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | ALPHA: (86) implies: % 110.31/15.31 | | | | | | | | (87) ~ (all_324_0 = 0) % 110.31/15.31 | | | | | | | | (88) ssList(nil) = all_324_0 % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | GROUND_INST: instantiating (6) with 0, all_324_0, nil, % 110.31/15.31 | | | | | | | | simplifying with (1), (88) gives: % 110.31/15.31 | | | | | | | | (89) all_324_0 = 0 % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | REDUCE: (87), (89) imply: % 110.31/15.31 | | | | | | | | (90) $false % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | CLOSE: (90) is inconsistent. % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | Case 2: % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | (91) ( ~ (all_99_0 = 0) | ~ (all_93_0 = nil)) & (all_99_0 = % 110.31/15.31 | | | | | | | | 0 | all_93_0 = nil) % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | ALPHA: (91) implies: % 110.31/15.31 | | | | | | | | (92) ~ (all_99_0 = 0) | ~ (all_93_0 = nil) % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | BETA: splitting (92) gives: % 110.31/15.31 | | | | | | | | % 110.31/15.31 | | | | | | | | Case 1: % 110.31/15.31 | | | | | | | | | % 110.31/15.31 | | | | | | | | | (93) ~ (all_93_0 = nil) % 110.31/15.31 | | | | | | | | | % 110.31/15.31 | | | | | | | | | BETA: splitting (30) gives: % 110.31/15.31 | | | | | | | | | % 110.31/15.31 | | | | | | | | | Case 1: % 110.31/15.31 | | | | | | | | | | % 110.31/15.31 | | | | | | | | | | (94) all_93_0 = nil % 110.31/15.31 | | | | | | | | | | % 110.31/15.31 | | | | | | | | | | REDUCE: (93), (94) imply: % 110.31/15.31 | | | | | | | | | | (95) $false % 110.31/15.31 | | | | | | | | | | % 110.31/15.31 | | | | | | | | | | CLOSE: (95) is inconsistent. % 110.31/15.31 | | | | | | | | | | % 110.31/15.31 | | | | | | | | | Case 2: % 110.31/15.31 | | | | | | | | | | % 110.31/15.31 | | | | | | | | | | (96) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 110.31/15.31 | | | | | | | | | | : (cons(v1, v0) = all_93_0 & ssItem(v1) = 0 & % 110.31/15.31 | | | | | | | | | | $i(v1))) % 110.31/15.31 | | | | | | | | | | % 110.31/15.31 | | | | | | | | | | DELTA: instantiating (96) with fresh symbol all_331_0 gives: % 110.31/15.31 | | | | | | | | | | (97) ssList(all_331_0) = 0 & $i(all_331_0) & ? [v0: $i] % 110.31/15.31 | | | | | | | | | | : (cons(v0, all_331_0) = all_93_0 & ssItem(v0) = 0 & % 110.31/15.31 | | | | | | | | | | $i(v0)) % 110.31/15.31 | | | | | | | | | | % 110.31/15.31 | | | | | | | | | | ALPHA: (97) implies: % 110.31/15.32 | | | | | | | | | | (98) $i(all_331_0) % 110.31/15.32 | | | | | | | | | | (99) ssList(all_331_0) = 0 % 110.31/15.32 | | | | | | | | | | (100) ? [v0: $i] : (cons(v0, all_331_0) = all_93_0 & % 110.31/15.32 | | | | | | | | | | ssItem(v0) = 0 & $i(v0)) % 110.31/15.32 | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | DELTA: instantiating (100) with fresh symbol all_333_0 % 110.31/15.32 | | | | | | | | | | gives: % 110.31/15.32 | | | | | | | | | | (101) cons(all_333_0, all_331_0) = all_93_0 & % 110.31/15.32 | | | | | | | | | | ssItem(all_333_0) = 0 & $i(all_333_0) % 110.31/15.32 | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | ALPHA: (101) implies: % 110.31/15.32 | | | | | | | | | | (102) $i(all_333_0) % 110.31/15.32 | | | | | | | | | | (103) ssItem(all_333_0) = 0 % 110.31/15.32 | | | | | | | | | | (104) cons(all_333_0, all_331_0) = all_93_0 % 110.31/15.32 | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | BETA: splitting (38) gives: % 110.31/15.32 | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | Case 1: % 110.31/15.32 | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | (105) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_0) = % 110.31/15.32 | | | | | | | | | | | v0) % 110.31/15.32 | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | DELTA: instantiating (105) with fresh symbol all_337_0 % 110.31/15.32 | | | | | | | | | | | gives: % 110.31/15.32 | | | | | | | | | | | (106) ~ (all_337_0 = 0) & ssList(all_93_0) = all_337_0 % 110.31/15.32 | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | REF_CLOSE: (6), (27), (106) are inconsistent by sub-proof #1. % 110.31/15.32 | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | Case 2: % 110.31/15.32 | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | (107) ( ~ (all_101_0 = 0) | ? [v0: $i] : (ssList(v0) = % 110.31/15.32 | | | | | | | | | | | 0 & app(v0, all_93_0) = all_97_0 & $i(v0))) & % 110.31/15.32 | | | | | | | | | | | (all_101_0 = 0 | ! [v0: $i] : ( ~ (app(v0, % 110.31/15.32 | | | | | | | | | | | all_93_0) = all_97_0) | ~ $i(v0) | ? % 110.31/15.32 | | | | | | | | | | | [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1))) % 110.31/15.32 | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | ALPHA: (107) implies: % 110.31/15.32 | | | | | | | | | | | (108) ~ (all_101_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 % 110.31/15.32 | | | | | | | | | | | & app(v0, all_93_0) = all_97_0 & $i(v0)) % 110.31/15.32 | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | BETA: splitting (108) gives: % 110.31/15.32 | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | Case 1: % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | (109) ~ (all_101_0 = 0) % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | REDUCE: (82), (109) imply: % 110.31/15.32 | | | | | | | | | | | | (110) $false % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | CLOSE: (110) is inconsistent. % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | Case 2: % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | (111) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_93_0) % 110.31/15.32 | | | | | | | | | | | | = all_97_0 & $i(v0)) % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | DELTA: instantiating (111) with fresh symbol all_340_0 % 110.31/15.32 | | | | | | | | | | | | gives: % 110.31/15.32 | | | | | | | | | | | | (112) ssList(all_340_0) = 0 & app(all_340_0, all_93_0) = % 110.31/15.32 | | | | | | | | | | | | all_97_0 & $i(all_340_0) % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | ALPHA: (112) implies: % 110.31/15.32 | | | | | | | | | | | | (113) $i(all_340_0) % 110.31/15.32 | | | | | | | | | | | | (114) app(all_340_0, all_93_0) = all_97_0 % 110.31/15.32 | | | | | | | | | | | | (115) ssList(all_340_0) = 0 % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | GROUND_INST: instantiating (56) with all_333_0, simplifying % 110.31/15.32 | | | | | | | | | | | | with (102), (103) gives: % 110.31/15.32 | | | | | | | | | | | | (116) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | % 110.31/15.32 | | | | | | | | | | | | ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | % 110.31/15.32 | | | | | | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 110.31/15.32 | | | | | | | | | | | | (cons(all_333_0, v2) = v3) | ~ (app(v1, v3) % 110.31/15.32 | | | | | | | | | | | | = v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 % 110.31/15.32 | | | | | | | | | | | | = 0) & ssList(v2) = v5) | ! [v5: $i] : % 110.31/15.32 | | | | | | | | | | | | ! [v6: $i] : ( ~ (v0 = all_333_0) | ~ % 110.31/15.32 | | | | | | | | | | | | (cons(all_333_0, v5) = v6) | ~ (app(v4, % 110.31/15.32 | | | | | | | | | | | | v6) = nil) | ~ $i(v5) | ? [v7: int] % 110.31/15.32 | | | | | | | | | | | | : ( ~ (v7 = 0) & ssList(v5) = v7))))) % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_93_0, simplifying with % 110.31/15.32 | | | | | | | | | | | | (29), (84) gives: % 110.31/15.32 | | | | | | | | | | | | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 110.31/15.32 | | | | | | | | | | | | (rearsegP(all_97_0, all_93_0) = v1 & % 110.31/15.32 | | | | | | | | | | | | rearsegP(all_93_0, all_93_0) = v2 & % 110.31/15.32 | | | | | | | | | | | | ssList(all_93_0) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 110.31/15.32 | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_97_0, simplifying with % 110.31/15.32 | | | | | | | | | | | | (11), (69) gives: % 110.31/15.32 | | | | | | | | | | | | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 110.31/15.32 | | | | | | | | | | | | (rearsegP(all_97_0, all_97_0) = v1 & % 110.31/15.32 | | | | | | | | | | | | rearsegP(all_93_0, all_97_0) = v2 & % 110.31/15.32 | | | | | | | | | | | | ssList(all_97_0) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 110.31/15.32 | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 110.31/15.32 | | | | | | | | | | | | % 110.31/15.32 | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_93_0, simplifying with % 110.31/15.32 | | | | | | | | | | | | (29), (83) gives: % 110.31/15.33 | | | | | | | | | | | | (119) all_97_0 = all_93_0 | ? [v0: any] : ? [v1: any] % 110.31/15.33 | | | | | | | | | | | | : (rearsegP(all_93_0, all_97_0) = v1 & % 110.31/15.33 | | | | | | | | | | | | ssList(all_93_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 110.31/15.33 | | | | | | | | | | | | 0))) % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | GROUND_INST: instantiating (116) with all_315_0, simplifying % 110.31/15.33 | | | | | | | | | | | | with (76), (77) gives: % 110.31/15.33 | | | | | | | | | | | | (120) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | % 110.31/15.33 | | | | | | | | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 110.31/15.33 | | | | | | | | | | | | (cons(all_333_0, v1) = v2) | ~ (app(v0, v2) = % 110.31/15.33 | | | | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 110.31/15.33 | | | | | | | | | | | | 0) & ssList(v1) = v4) | ! [v4: $i] : ! % 110.31/15.33 | | | | | | | | | | | | [v5: $i] : ( ~ (all_333_0 = all_315_0) | ~ % 110.31/15.33 | | | | | | | | | | | | (cons(all_315_0, v4) = v5) | ~ (app(v3, v5) % 110.31/15.33 | | | | | | | | | | | | = nil) | ~ $i(v4) | ? [v6: int] : ( ~ % 110.31/15.33 | | | | | | | | | | | | (v6 = 0) & ssList(v4) = v6)))) % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | GROUND_INST: instantiating (120) with all_340_0, simplifying % 110.31/15.33 | | | | | | | | | | | | with (113), (115) gives: % 110.31/15.33 | | | | | | | | | | | | (121) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 110.31/15.33 | | | | | | | | | | | | (cons(all_333_0, v0) = v1) | ~ (app(all_340_0, % 110.31/15.33 | | | | | | | | | | | | v1) = v2) | ~ $i(v0) | ? [v3: int] : ( ~ % 110.31/15.33 | | | | | | | | | | | | (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : ! % 110.31/15.33 | | | | | | | | | | | | [v4: $i] : ( ~ (all_333_0 = all_315_0) | ~ % 110.31/15.33 | | | | | | | | | | | | (cons(all_315_0, v3) = v4) | ~ (app(v2, v4) = % 110.31/15.33 | | | | | | | | | | | | nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = % 110.31/15.33 | | | | | | | | | | | | 0) & ssList(v3) = v5))) % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | GROUND_INST: instantiating (121) with all_331_0, all_93_0, % 110.31/15.33 | | | | | | | | | | | | all_97_0, simplifying with (98), (104), (114) % 110.31/15.33 | | | | | | | | | | | | gives: % 110.31/15.33 | | | | | | | | | | | | (122) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_331_0) = % 110.31/15.33 | | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ (all_333_0 % 110.31/15.33 | | | | | | | | | | | | = all_315_0) | ~ (cons(all_315_0, v0) = v1) | % 110.31/15.33 | | | | | | | | | | | | ~ (app(all_97_0, v1) = nil) | ~ $i(v0) | ? % 110.31/15.33 | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)) % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | DELTA: instantiating (118) with fresh symbols all_697_0, % 110.31/15.33 | | | | | | | | | | | | all_697_1, all_697_2 gives: % 110.31/15.33 | | | | | | | | | | | | (123) rearsegP(all_97_0, all_97_0) = all_697_1 & % 110.31/15.33 | | | | | | | | | | | | rearsegP(all_93_0, all_97_0) = all_697_0 & % 110.31/15.33 | | | | | | | | | | | | ssList(all_97_0) = all_697_2 & ( ~ (all_697_0 = 0) % 110.31/15.33 | | | | | | | | | | | | | ~ (all_697_1 = 0) | ~ (all_697_2 = 0)) % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | ALPHA: (123) implies: % 110.31/15.33 | | | | | | | | | | | | (124) rearsegP(all_93_0, all_97_0) = all_697_0 % 110.31/15.33 | | | | | | | | | | | | (125) rearsegP(all_97_0, all_97_0) = all_697_1 % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | DELTA: instantiating (117) with fresh symbols all_699_0, % 110.31/15.33 | | | | | | | | | | | | all_699_1, all_699_2 gives: % 110.31/15.33 | | | | | | | | | | | | (126) rearsegP(all_97_0, all_93_0) = all_699_1 & % 110.31/15.33 | | | | | | | | | | | | rearsegP(all_93_0, all_93_0) = all_699_0 & % 110.31/15.33 | | | | | | | | | | | | ssList(all_93_0) = all_699_2 & ( ~ (all_699_0 = 0) % 110.31/15.33 | | | | | | | | | | | | | ~ (all_699_1 = 0) | ~ (all_699_2 = 0)) % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | ALPHA: (126) implies: % 110.31/15.33 | | | | | | | | | | | | (127) ssList(all_93_0) = all_699_2 % 110.31/15.33 | | | | | | | | | | | | (128) rearsegP(all_93_0, all_93_0) = all_699_0 % 110.31/15.33 | | | | | | | | | | | | (129) rearsegP(all_97_0, all_93_0) = all_699_1 % 110.31/15.33 | | | | | | | | | | | | (130) ~ (all_699_0 = 0) | ~ (all_699_1 = 0) | ~ % 110.31/15.33 | | | | | | | | | | | | (all_699_2 = 0) % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | BETA: splitting (122) gives: % 110.31/15.33 | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | Case 1: % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | (131) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_331_0) = % 110.31/15.33 | | | | | | | | | | | | | v0) % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | DELTA: instantiating (131) with fresh symbol all_737_0 % 110.31/15.33 | | | | | | | | | | | | | gives: % 110.31/15.33 | | | | | | | | | | | | | (132) ~ (all_737_0 = 0) & ssList(all_331_0) = all_737_0 % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | ALPHA: (132) implies: % 110.31/15.33 | | | | | | | | | | | | | (133) ~ (all_737_0 = 0) % 110.31/15.33 | | | | | | | | | | | | | (134) ssList(all_331_0) = all_737_0 % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | DELTA: instantiating (131) with fresh symbol all_739_0 % 110.31/15.33 | | | | | | | | | | | | | gives: % 110.31/15.33 | | | | | | | | | | | | | (135) ~ (all_739_0 = 0) & ssList(all_331_0) = all_739_0 % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | ALPHA: (135) implies: % 110.31/15.33 | | | | | | | | | | | | | (136) ssList(all_331_0) = all_739_0 % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_739_0, all_331_0, % 110.31/15.33 | | | | | | | | | | | | | simplifying with (99), (136) gives: % 110.31/15.33 | | | | | | | | | | | | | (137) all_739_0 = 0 % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_737_0, all_739_0, % 110.31/15.33 | | | | | | | | | | | | | all_331_0, simplifying with (134), (136) gives: % 110.31/15.33 | | | | | | | | | | | | | (138) all_739_0 = all_737_0 % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | COMBINE_EQS: (137), (138) imply: % 110.31/15.33 | | | | | | | | | | | | | (139) all_737_0 = 0 % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | SIMP: (139) implies: % 110.31/15.33 | | | | | | | | | | | | | (140) all_737_0 = 0 % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | REDUCE: (133), (140) imply: % 110.31/15.33 | | | | | | | | | | | | | (141) $false % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.33 | | | | | | | | | | | | | CLOSE: (141) is inconsistent. % 110.31/15.33 | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | Case 2: % 110.31/15.34 | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_699_2, all_93_0, % 110.31/15.34 | | | | | | | | | | | | | simplifying with (27), (127) gives: % 110.31/15.34 | | | | | | | | | | | | | (142) all_699_2 = 0 % 110.31/15.34 | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_699_1, all_93_0, % 110.31/15.34 | | | | | | | | | | | | | all_97_0, simplifying with (83), (129) gives: % 110.31/15.34 | | | | | | | | | | | | | (143) all_699_1 = 0 % 110.31/15.34 | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | BETA: splitting (130) gives: % 110.31/15.34 | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | Case 1: % 110.31/15.34 | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | (144) ~ (all_699_0 = 0) % 110.31/15.34 | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | BETA: splitting (119) gives: % 110.31/15.34 | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | Case 1: % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | (145) all_97_0 = all_93_0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | REDUCE: (125), (145) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (146) rearsegP(all_93_0, all_93_0) = all_697_1 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | REDUCE: (83), (145) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (147) rearsegP(all_93_0, all_93_0) = 0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | REDUCE: (124), (145) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (148) rearsegP(all_93_0, all_93_0) = all_697_0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_699_0, all_697_1, % 110.31/15.34 | | | | | | | | | | | | | | | all_93_0, all_93_0, simplifying with (128), (146) % 110.31/15.34 | | | | | | | | | | | | | | | gives: % 110.31/15.34 | | | | | | | | | | | | | | | (149) all_699_0 = all_697_1 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_699_0, all_697_0, % 110.31/15.34 | | | | | | | | | | | | | | | all_93_0, all_93_0, simplifying with (128), (148) % 110.31/15.34 | | | | | | | | | | | | | | | gives: % 110.31/15.34 | | | | | | | | | | | | | | | (150) all_699_0 = all_697_0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_697_0, all_93_0, % 110.31/15.34 | | | | | | | | | | | | | | | all_93_0, simplifying with (147), (148) gives: % 110.31/15.34 | | | | | | | | | | | | | | | (151) all_697_0 = 0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | COMBINE_EQS: (149), (150) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (152) all_697_0 = all_697_1 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | SIMP: (152) implies: % 110.31/15.34 | | | | | | | | | | | | | | | (153) all_697_0 = all_697_1 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | COMBINE_EQS: (151), (153) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (154) all_697_1 = 0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | SIMP: (154) implies: % 110.31/15.34 | | | | | | | | | | | | | | | (155) all_697_1 = 0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | COMBINE_EQS: (149), (155) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (156) all_699_0 = 0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | REDUCE: (144), (156) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (157) $false % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | Case 2: % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | (158) ? [v0: any] : ? [v1: any] : (rearsegP(all_93_0, % 110.31/15.34 | | | | | | | | | | | | | | | all_97_0) = v1 & ssList(all_93_0) = v0 & ( ~ % 110.31/15.34 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | DELTA: instantiating (158) with fresh symbols all_822_0, % 110.31/15.34 | | | | | | | | | | | | | | | all_822_1 gives: % 110.31/15.34 | | | | | | | | | | | | | | | (159) rearsegP(all_93_0, all_97_0) = all_822_0 & % 110.31/15.34 | | | | | | | | | | | | | | | ssList(all_93_0) = all_822_1 & ( ~ (all_822_0 = 0) % 110.31/15.34 | | | | | | | | | | | | | | | | ~ (all_822_1 = 0)) % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | ALPHA: (159) implies: % 110.31/15.34 | | | | | | | | | | | | | | | (160) ssList(all_93_0) = all_822_1 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_822_1, all_93_0, % 110.31/15.34 | | | | | | | | | | | | | | | simplifying with (27), (160) gives: % 110.31/15.34 | | | | | | | | | | | | | | | (161) all_822_1 = 0 % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (ax49) with all_93_0, all_699_0, % 110.31/15.34 | | | | | | | | | | | | | | | simplifying with (29), (128) gives: % 110.31/15.34 | | | | | | | | | | | | | | | (162) all_699_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 110.31/15.34 | | | | | | | | | | | | | | | ssList(all_93_0) = v0) % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | BETA: splitting (162) gives: % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | Case 1: % 110.31/15.34 | | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | | (163) all_699_0 = 0 % 110.31/15.34 | | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | | REDUCE: (144), (163) imply: % 110.31/15.34 | | | | | | | | | | | | | | | | (164) $false % 110.31/15.34 | | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 110.31/15.34 | | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | Case 2: % 110.31/15.34 | | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | | (165) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_0) = % 110.31/15.34 | | | | | | | | | | | | | | | | v0) % 110.31/15.34 | | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | | DELTA: instantiating (165) with fresh symbol all_337_0 % 110.31/15.34 | | | | | | | | | | | | | | | | gives: % 110.31/15.34 | | | | | | | | | | | | | | | | (166) ~ (all_337_0 = 0) & ssList(all_93_0) = all_337_0 % 110.31/15.34 | | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (27), (166) are inconsistent by sub-proof #1. % 110.31/15.34 | | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | End of split % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | End of split % 110.31/15.34 | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | Case 2: % 110.31/15.34 | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | (167) ~ (all_699_1 = 0) | ~ (all_699_2 = 0) % 110.31/15.34 | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | BETA: splitting (167) gives: % 110.31/15.34 | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | Case 1: % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | (168) ~ (all_699_1 = 0) % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | REDUCE: (143), (168) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (169) $false % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent. % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | Case 2: % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | (170) ~ (all_699_2 = 0) % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | REDUCE: (142), (170) imply: % 110.31/15.34 | | | | | | | | | | | | | | | (171) $false % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 110.31/15.34 | | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | | End of split % 110.31/15.34 | | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | | End of split % 110.31/15.34 | | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | | End of split % 110.31/15.34 | | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | | End of split % 110.31/15.34 | | | | | | | | | | | % 110.31/15.34 | | | | | | | | | | End of split % 110.31/15.34 | | | | | | | | | | % 110.31/15.34 | | | | | | | | | End of split % 110.31/15.34 | | | | | | | | | % 110.31/15.34 | | | | | | | | Case 2: % 110.31/15.34 | | | | | | | | | % 110.31/15.34 | | | | | | | | | (172) ~ (all_99_0 = 0) % 110.31/15.34 | | | | | | | | | % 110.31/15.34 | | | | | | | | | REDUCE: (81), (172) imply: % 110.31/15.34 | | | | | | | | | (173) $false % 110.31/15.34 | | | | | | | | | % 110.31/15.34 | | | | | | | | | CLOSE: (173) is inconsistent. % 110.31/15.34 | | | | | | | | | % 110.31/15.34 | | | | | | | | End of split % 110.31/15.34 | | | | | | | | % 110.31/15.34 | | | | | | | End of split % 110.31/15.34 | | | | | | | % 110.31/15.34 | | | | | | End of split % 110.31/15.34 | | | | | | % 110.31/15.34 | | | | | End of split % 110.31/15.34 | | | | | % 110.31/15.34 | | | | End of split % 110.31/15.34 | | | | % 110.31/15.34 | | | End of split % 110.31/15.34 | | | % 110.31/15.34 | | Case 2: % 110.31/15.34 | | | % 110.31/15.34 | | | (174) all_97_0 = nil % 110.31/15.34 | | | (175) ~ (all_93_0 = nil) % 110.31/15.34 | | | % 110.31/15.34 | | | BETA: splitting (23) gives: % 110.31/15.34 | | | % 110.31/15.34 | | | Case 1: % 110.31/15.34 | | | | % 110.31/15.34 | | | | (176) ~ (all_97_0 = nil) % 110.31/15.34 | | | | % 110.31/15.34 | | | | REDUCE: (174), (176) imply: % 110.31/15.34 | | | | (177) $false % 110.31/15.34 | | | | % 110.31/15.34 | | | | CLOSE: (177) is inconsistent. % 110.31/15.34 | | | | % 110.31/15.34 | | | Case 2: % 110.31/15.34 | | | | % 110.31/15.34 | | | | (178) all_93_0 = nil % 110.31/15.34 | | | | % 110.31/15.34 | | | | REDUCE: (175), (178) imply: % 110.31/15.34 | | | | (179) $false % 110.31/15.34 | | | | % 110.31/15.34 | | | | CLOSE: (179) is inconsistent. % 110.31/15.34 | | | | % 110.31/15.34 | | | End of split % 110.31/15.34 | | | % 110.31/15.34 | | End of split % 110.31/15.34 | | % 110.31/15.34 | End of split % 110.31/15.34 | % 110.31/15.34 End of proof % 110.31/15.34 % 110.31/15.34 Sub-proof #1 shows that the following formulas are inconsistent: % 110.31/15.34 ---------------------------------------------------------------- % 110.31/15.35 (1) ~ (all_337_0 = 0) & ssList(all_93_0) = all_337_0 % 110.31/15.35 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 110.31/15.35 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 110.31/15.35 (3) ssList(all_93_0) = 0 % 110.31/15.35 % 110.31/15.35 Begin of proof % 110.31/15.35 | % 110.31/15.35 | ALPHA: (1) implies: % 110.31/15.35 | (4) ~ (all_337_0 = 0) % 110.31/15.35 | (5) ssList(all_93_0) = all_337_0 % 110.31/15.35 | % 110.31/15.35 | GROUND_INST: instantiating (2) with 0, all_337_0, all_93_0, simplifying with % 110.31/15.35 | (3), (5) gives: % 110.31/15.35 | (6) all_337_0 = 0 % 110.31/15.35 | % 110.31/15.35 | REDUCE: (4), (6) imply: % 110.31/15.35 | (7) $false % 110.31/15.35 | % 110.31/15.35 | CLOSE: (7) is inconsistent. % 110.31/15.35 | % 110.31/15.35 End of proof % 110.31/15.35 % SZS output end Proof for theBenchmark % 110.31/15.35 % 110.31/15.35 14733ms %------------------------------------------------------------------------------