%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC205+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 : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 20:50:13 EDT 2023 % Result : Theorem 21.67s 3.71s % Output : Proof 27.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC205+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n001.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Mon Aug 28 19:05:50 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 4.72/1.39 Prover 4: Preprocessing ... % 4.72/1.42 Prover 1: Preprocessing ... % 4.72/1.46 Prover 2: Preprocessing ... % 4.72/1.46 Prover 3: Preprocessing ... % 4.72/1.46 Prover 5: Preprocessing ... % 4.72/1.46 Prover 6: Preprocessing ... % 4.72/1.46 Prover 0: Preprocessing ... % 14.39/2.84 Prover 2: Proving ... % 14.39/2.84 Prover 1: Constructing countermodel ... % 14.39/2.84 Prover 5: Constructing countermodel ... % 15.65/2.87 Prover 6: Proving ... % 16.07/2.94 Prover 3: Constructing countermodel ... % 21.67/3.66 Prover 4: Constructing countermodel ... % 21.67/3.71 Prover 3: proved (3081ms) % 21.67/3.71 % 21.67/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.67/3.71 % 22.13/3.72 Prover 0: Proving ... % 22.13/3.72 Prover 6: stopped % 22.13/3.73 Prover 5: stopped % 22.13/3.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.13/3.74 Prover 0: stopped % 22.13/3.74 Prover 2: stopped % 22.13/3.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.13/3.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.13/3.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.13/3.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.00/3.97 Prover 10: Preprocessing ... % 24.41/4.04 Prover 13: Preprocessing ... % 24.41/4.06 Prover 11: Preprocessing ... % 24.73/4.06 Prover 7: Preprocessing ... % 24.73/4.08 Prover 8: Preprocessing ... % 25.65/4.29 Prover 1: Found proof (size 49) % 25.65/4.29 Prover 1: proved (3666ms) % 25.65/4.29 Prover 4: stopped % 26.59/4.33 Prover 11: stopped % 26.59/4.36 Prover 7: Constructing countermodel ... % 27.03/4.37 Prover 10: Constructing countermodel ... % 27.03/4.38 Prover 7: stopped % 27.03/4.38 Prover 10: stopped % 27.03/4.39 Prover 13: Constructing countermodel ... % 27.03/4.41 Prover 13: stopped % 27.03/4.45 Prover 8: Warning: ignoring some quantifiers % 27.49/4.46 Prover 8: Constructing countermodel ... % 27.49/4.47 Prover 8: stopped % 27.49/4.47 % 27.49/4.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 27.49/4.47 % 27.49/4.48 % SZS output start Proof for theBenchmark % 27.49/4.48 Assumptions after simplification: % 27.49/4.48 --------------------------------- % 27.49/4.48 % 27.49/4.48 (ax15) % 27.60/4.50 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 27.60/4.50 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 27.60/4.50 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 27.60/4.50 % 27.60/4.51 (ax17) % 27.60/4.51 ssList(nil) = 0 & $i(nil) % 27.60/4.51 % 27.60/4.51 (co1) % 27.60/4.51 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 27.60/4.51 $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) = 0 & % 27.60/4.51 $i(v2) & ( ~ (v2 = nil) | v0 = nil) & ( ~ (v0 = nil) | v2 = nil))) % 27.60/4.51 % 27.60/4.51 (function-axioms) % 27.60/4.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 27.60/4.52 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 27.60/4.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 27.60/4.52 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 27.60/4.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 27.60/4.52 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 27.60/4.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 27.60/4.52 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 27.60/4.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 27.60/4.52 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 27.60/4.52 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 27.60/4.52 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 27.60/4.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 27.60/4.52 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 27.60/4.52 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 27.60/4.52 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 27.60/4.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 27.60/4.52 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 27.60/4.52 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 27.60/4.52 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 27.60/4.52 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 27.60/4.52 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 27.60/4.52 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 27.60/4.52 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 27.60/4.52 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 27.60/4.52 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 27.60/4.52 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 27.60/4.52 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 27.60/4.52 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 27.60/4.52 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 27.60/4.52 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 27.60/4.52 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 27.60/4.52 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 27.60/4.52 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 27.60/4.52 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 27.60/4.52 % 27.60/4.52 Further assumptions not needed in the proof: % 27.60/4.52 -------------------------------------------- % 27.60/4.52 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 27.60/4.52 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, % 27.60/4.52 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, % 27.60/4.52 ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, % 27.60/4.52 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, % 27.60/4.52 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 27.60/4.52 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 27.60/4.52 ax94, ax95 % 27.60/4.52 % 27.60/4.52 Those formulas are unsatisfiable: % 27.60/4.52 --------------------------------- % 27.60/4.52 % 27.60/4.52 Begin of proof % 27.60/4.52 | % 27.60/4.52 | ALPHA: (ax17) implies: % 27.60/4.52 | (1) ssList(nil) = 0 % 27.60/4.52 | % 27.60/4.52 | ALPHA: (co1) implies: % 27.60/4.52 | (2) $i(nil) % 27.60/4.52 | (3) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 27.60/4.52 | $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) = % 27.60/4.52 | 0 & $i(v2) & ( ~ (v2 = nil) | v0 = nil) & ( ~ (v0 = nil) | v2 = % 27.60/4.52 | nil))) % 27.60/4.52 | % 27.60/4.52 | ALPHA: (function-axioms) implies: % 27.60/4.52 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 27.60/4.52 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 27.60/4.52 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 27.60/4.52 | ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0)) % 27.60/4.52 | % 27.60/4.52 | DELTA: instantiating (3) with fresh symbols all_93_0, all_93_1 gives: % 27.60/4.52 | (6) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) & % 27.60/4.52 | ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 & % 27.60/4.53 | $i(v0) & ( ~ (v0 = nil) | all_93_1 = nil) & ( ~ (all_93_1 = nil) | v0 % 27.60/4.53 | = nil)) % 27.60/4.53 | % 27.60/4.53 | ALPHA: (6) implies: % 27.79/4.53 | (7) $i(all_93_1) % 27.79/4.53 | (8) neq(all_93_1, nil) = all_93_0 % 27.79/4.53 | (9) ssList(all_93_1) = 0 % 27.79/4.53 | (10) ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 & % 27.79/4.53 | $i(v0) & ( ~ (v0 = nil) | all_93_1 = nil) & ( ~ (all_93_1 = nil) | % 27.79/4.53 | v0 = nil)) % 27.79/4.53 | % 27.79/4.53 | DELTA: instantiating (10) with fresh symbol all_97_0 gives: % 27.79/4.53 | (11) ~ (all_93_0 = 0) & ssList(all_97_0) = 0 & neq(all_97_0, nil) = 0 & % 27.79/4.53 | $i(all_97_0) & ( ~ (all_97_0 = nil) | all_93_1 = nil) & ( ~ (all_93_1 % 27.79/4.53 | = nil) | all_97_0 = nil) % 27.79/4.53 | % 27.79/4.53 | ALPHA: (11) implies: % 27.79/4.53 | (12) ~ (all_93_0 = 0) % 27.79/4.53 | (13) neq(all_97_0, nil) = 0 % 27.79/4.53 | (14) ~ (all_93_1 = nil) | all_97_0 = nil % 27.79/4.53 | % 27.79/4.53 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (7), (9) % 27.79/4.53 | gives: % 27.79/4.53 | (15) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0) % 27.79/4.53 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 27.79/4.53 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1))) % 27.79/4.53 | % 27.79/4.53 | GROUND_INST: instantiating (15) with nil, all_93_0, simplifying with (2), (8) % 27.79/4.53 | gives: % 27.79/4.53 | (16) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0) % 27.79/4.53 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil)) % 27.79/4.53 | % 27.79/4.53 | BETA: splitting (16) gives: % 27.79/4.53 | % 27.79/4.53 | Case 1: % 27.79/4.53 | | % 27.79/4.53 | | (17) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 27.79/4.53 | | % 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_258_0 gives: % 27.79/4.53 | | (18) ~ (all_258_0 = 0) & ssList(nil) = all_258_0 % 27.79/4.53 | | % 27.79/4.53 | | ALPHA: (18) implies: % 27.79/4.53 | | (19) ~ (all_258_0 = 0) % 27.79/4.53 | | (20) ssList(nil) = all_258_0 % 27.79/4.53 | | % 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_260_0 gives: % 27.79/4.53 | | (21) ~ (all_260_0 = 0) & ssList(nil) = all_260_0 % 27.79/4.53 | | % 27.79/4.53 | | ALPHA: (21) implies: % 27.79/4.53 | | (22) ssList(nil) = all_260_0 % 27.79/4.53 | | % 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_262_0 gives: % 27.79/4.53 | | (23) ~ (all_262_0 = 0) & ssList(nil) = all_262_0 % 27.79/4.53 | | % 27.79/4.53 | | ALPHA: (23) implies: % 27.79/4.53 | | (24) ssList(nil) = all_262_0 % 27.79/4.53 | | % 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_264_0 gives: % 27.79/4.53 | | (25) ~ (all_264_0 = 0) & ssList(nil) = all_264_0 % 27.79/4.53 | | % 27.79/4.53 | | ALPHA: (25) implies: % 27.79/4.53 | | (26) ssList(nil) = all_264_0 % 27.79/4.53 | | % 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_266_0 gives: % 27.79/4.53 | | (27) ~ (all_266_0 = 0) & ssList(nil) = all_266_0 % 27.79/4.53 | | % 27.79/4.53 | | ALPHA: (27) implies: % 27.79/4.53 | | (28) ssList(nil) = all_266_0 % 27.79/4.53 | | % 27.79/4.53 | | GROUND_INST: instantiating (4) with all_260_0, all_262_0, nil, simplifying % 27.79/4.53 | | with (22), (24) gives: % 27.79/4.53 | | (29) all_262_0 = all_260_0 % 27.79/4.53 | | % 27.79/4.53 | | GROUND_INST: instantiating (4) with 0, all_264_0, nil, simplifying with (1), % 27.79/4.53 | | (26) gives: % 27.79/4.53 | | (30) all_264_0 = 0 % 27.79/4.53 | | % 27.79/4.53 | | GROUND_INST: instantiating (4) with all_260_0, all_264_0, nil, simplifying % 27.79/4.53 | | with (22), (26) gives: % 27.79/4.53 | | (31) all_264_0 = all_260_0 % 27.79/4.53 | | % 27.79/4.53 | | GROUND_INST: instantiating (4) with all_262_0, all_266_0, nil, simplifying % 27.79/4.53 | | with (24), (28) gives: % 27.79/4.53 | | (32) all_266_0 = all_262_0 % 27.79/4.53 | | % 27.79/4.53 | | GROUND_INST: instantiating (4) with all_258_0, all_266_0, nil, simplifying % 27.79/4.53 | | with (20), (28) gives: % 27.79/4.53 | | (33) all_266_0 = all_258_0 % 27.79/4.53 | | % 27.79/4.53 | | COMBINE_EQS: (32), (33) imply: % 27.79/4.54 | | (34) all_262_0 = all_258_0 % 27.79/4.54 | | % 27.79/4.54 | | SIMP: (34) implies: % 27.79/4.54 | | (35) all_262_0 = all_258_0 % 27.79/4.54 | | % 27.79/4.54 | | COMBINE_EQS: (30), (31) imply: % 27.79/4.54 | | (36) all_260_0 = 0 % 27.79/4.54 | | % 27.79/4.54 | | SIMP: (36) implies: % 27.79/4.54 | | (37) all_260_0 = 0 % 27.79/4.54 | | % 27.79/4.54 | | COMBINE_EQS: (29), (35) imply: % 27.79/4.54 | | (38) all_260_0 = all_258_0 % 27.79/4.54 | | % 27.79/4.54 | | SIMP: (38) implies: % 27.79/4.54 | | (39) all_260_0 = all_258_0 % 27.79/4.54 | | % 27.79/4.54 | | COMBINE_EQS: (37), (39) imply: % 27.79/4.54 | | (40) all_258_0 = 0 % 27.79/4.54 | | % 27.79/4.54 | | REDUCE: (19), (40) imply: % 27.79/4.54 | | (41) $false % 27.79/4.54 | | % 27.79/4.54 | | CLOSE: (41) is inconsistent. % 27.79/4.54 | | % 27.79/4.54 | Case 2: % 27.79/4.54 | | % 27.85/4.54 | | (42) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 % 27.85/4.54 | | = nil) % 27.85/4.54 | | % 27.85/4.54 | | ALPHA: (42) implies: % 27.85/4.54 | | (43) all_93_0 = 0 | all_93_1 = nil % 27.85/4.54 | | % 27.85/4.54 | | BETA: splitting (43) gives: % 27.85/4.54 | | % 27.85/4.54 | | Case 1: % 27.85/4.54 | | | % 27.85/4.54 | | | (44) all_93_1 = nil % 27.85/4.54 | | | % 27.85/4.54 | | | REDUCE: (8), (44) imply: % 27.85/4.54 | | | (45) neq(nil, nil) = all_93_0 % 27.85/4.54 | | | % 27.85/4.54 | | | BETA: splitting (14) gives: % 27.85/4.54 | | | % 27.85/4.54 | | | Case 1: % 27.85/4.54 | | | | % 27.85/4.54 | | | | (46) ~ (all_93_1 = nil) % 27.85/4.54 | | | | % 27.85/4.54 | | | | REDUCE: (44), (46) imply: % 27.85/4.54 | | | | (47) $false % 27.85/4.54 | | | | % 27.85/4.54 | | | | CLOSE: (47) is inconsistent. % 27.85/4.54 | | | | % 27.85/4.54 | | | Case 2: % 27.85/4.54 | | | | % 27.85/4.54 | | | | (48) all_97_0 = nil % 27.85/4.54 | | | | % 27.85/4.54 | | | | REDUCE: (13), (48) imply: % 27.85/4.54 | | | | (49) neq(nil, nil) = 0 % 27.85/4.54 | | | | % 27.85/4.54 | | | | GROUND_INST: instantiating (5) with 0, all_93_0, nil, nil, simplifying % 27.85/4.54 | | | | with (45), (49) gives: % 27.85/4.54 | | | | (50) all_93_0 = 0 % 27.85/4.54 | | | | % 27.85/4.54 | | | | REDUCE: (12), (50) imply: % 27.85/4.54 | | | | (51) $false % 27.85/4.54 | | | | % 27.85/4.54 | | | | CLOSE: (51) is inconsistent. % 27.85/4.54 | | | | % 27.85/4.54 | | | End of split % 27.85/4.54 | | | % 27.85/4.54 | | Case 2: % 27.85/4.54 | | | % 27.85/4.54 | | | (52) all_93_0 = 0 % 27.85/4.54 | | | % 27.85/4.54 | | | REDUCE: (12), (52) imply: % 27.85/4.54 | | | (53) $false % 27.85/4.54 | | | % 27.85/4.54 | | | CLOSE: (53) is inconsistent. % 27.85/4.54 | | | % 27.85/4.54 | | End of split % 27.85/4.54 | | % 27.85/4.54 | End of split % 27.85/4.54 | % 27.85/4.54 End of proof % 27.85/4.54 % SZS output end Proof for theBenchmark % 27.85/4.54 % 27.85/4.54 3940ms %------------------------------------------------------------------------------