%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC028+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 : n014.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 20:49:16 EDT 2023 % Result : Theorem 24.26s 4.01s % Output : Proof 39.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWC028+1 : TPTP v8.1.2. Released v2.4.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n014.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 16:08:30 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 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 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 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 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 % 6.36/1.63 Prover 1: Preprocessing ... % 6.36/1.64 Prover 4: Preprocessing ... % 6.36/1.66 Prover 3: Preprocessing ... % 6.36/1.66 Prover 2: Preprocessing ... % 6.94/1.67 Prover 6: Preprocessing ... % 6.94/1.67 Prover 0: Preprocessing ... % 6.94/1.67 Prover 5: Preprocessing ... % 15.62/2.89 Prover 2: Proving ... % 15.62/2.89 Prover 5: Constructing countermodel ... % 16.16/2.94 Prover 1: Constructing countermodel ... % 16.67/3.02 Prover 3: Constructing countermodel ... % 16.67/3.04 Prover 6: Proving ... % 21.94/3.71 Prover 4: Constructing countermodel ... % 22.67/3.77 Prover 0: Proving ... % 24.26/4.01 Prover 3: proved (3382ms) % 24.26/4.01 % 24.26/4.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.26/4.01 % 24.26/4.02 Prover 5: stopped % 24.26/4.02 Prover 0: stopped % 24.26/4.02 Prover 2: stopped % 24.26/4.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.26/4.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.26/4.02 Prover 6: stopped % 24.26/4.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 24.26/4.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.26/4.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.25/4.26 Prover 10: Preprocessing ... % 26.25/4.26 Prover 8: Preprocessing ... % 26.25/4.31 Prover 13: Preprocessing ... % 26.25/4.31 Prover 7: Preprocessing ... % 26.25/4.33 Prover 11: Preprocessing ... % 28.04/4.54 Prover 10: Constructing countermodel ... % 28.04/4.54 Prover 7: Constructing countermodel ... % 28.04/4.56 Prover 13: Constructing countermodel ... % 28.84/4.59 Prover 8: Warning: ignoring some quantifiers % 29.11/4.61 Prover 8: Constructing countermodel ... % 35.41/5.42 Prover 11: Constructing countermodel ... % 38.56/5.87 Prover 1: Found proof (size 87) % 38.56/5.87 Prover 1: proved (5242ms) % 38.56/5.87 Prover 11: stopped % 38.56/5.87 Prover 7: stopped % 38.56/5.87 Prover 8: stopped % 38.56/5.87 Prover 10: stopped % 38.56/5.87 Prover 4: stopped % 38.56/5.87 Prover 13: stopped % 38.56/5.87 % 38.56/5.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 38.56/5.87 % 38.98/5.88 % SZS output start Proof for theBenchmark % 38.98/5.88 Assumptions after simplification: % 38.98/5.88 --------------------------------- % 38.98/5.88 % 38.98/5.88 (ax15) % 38.98/5.91 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 38.98/5.91 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 38.98/5.91 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 38.98/5.91 % 38.98/5.91 (ax6) % 38.98/5.91 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 38.98/5.91 ( ~ (rearsegP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 38.98/5.91 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : (ssList(v3) = 0 & % 38.98/5.91 app(v3, v1) = v0 & $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (app(v3, % 38.98/5.91 v1) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) % 38.98/5.91 = v4)))))) % 38.98/5.91 % 38.98/5.91 (ax83) % 38.98/5.91 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 38.98/5.91 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 38.98/5.91 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1 % 38.98/5.91 = nil) | ~ (v0 = nil) | v2 = nil)))) % 38.98/5.91 % 38.98/5.91 (co1) % 38.98/5.92 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 38.98/5.92 0 & $i(v1) & ? [v2: $i] : ? [v3: any] : (ssList(v2) = 0 & neq(v2, nil) = % 38.98/5.92 v3 & $i(v2) & ? [v4: any] : (v2 = v0 & rearsegP(v1, v0) = v4 & ((v4 = 0 % 38.98/5.92 & v3 = 0) | (v1 = nil & v0 = nil)) & ((v1 = nil & ~ (v0 = nil)) | % 38.98/5.92 (v0 = nil & ~ (v1 = nil))))))) % 38.98/5.92 % 38.98/5.92 (function-axioms) % 38.98/5.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 38.98/5.92 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 38.98/5.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.98/5.92 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 38.98/5.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.98/5.92 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 38.98/5.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.98/5.92 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 38.98/5.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.98/5.92 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 38.98/5.92 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 38.98/5.92 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 38.98/5.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 38.98/5.92 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 38.98/5.92 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 38.98/5.92 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 38.98/5.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.98/5.92 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 38.98/5.92 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 38.98/5.92 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 38.98/5.92 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 38.98/5.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 38.98/5.92 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 38.98/5.92 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 38.98/5.92 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 38.98/5.92 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.98/5.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 38.98/5.92 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.98/5.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 38.98/5.92 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.98/5.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 38.98/5.93 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.98/5.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 38.98/5.93 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.98/5.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 38.98/5.93 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.98/5.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 38.98/5.93 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.98/5.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 38.98/5.93 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.98/5.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 38.98/5.93 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 38.98/5.93 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 38.98/5.93 % 38.98/5.93 Further assumptions not needed in the proof: % 38.98/5.93 -------------------------------------------- % 38.98/5.93 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax17, ax18, ax19, ax2, ax20, ax21, % 38.98/5.93 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, % 38.98/5.93 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, % 38.98/5.93 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, % 38.98/5.93 ax58, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, % 38.98/5.93 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 38.98/5.93 ax82, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, % 38.98/5.93 ax95 % 38.98/5.93 % 38.98/5.93 Those formulas are unsatisfiable: % 38.98/5.93 --------------------------------- % 38.98/5.93 % 38.98/5.93 Begin of proof % 38.98/5.93 | % 38.98/5.93 | ALPHA: (ax83) implies: % 38.98/5.93 | (1) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 38.98/5.93 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 38.98/5.93 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = % 38.98/5.93 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil)))) % 38.98/5.93 | % 38.98/5.93 | ALPHA: (co1) implies: % 38.98/5.93 | (2) $i(nil) % 38.98/5.93 | (3) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 38.98/5.93 | & $i(v1) & ? [v2: $i] : ? [v3: any] : (ssList(v2) = 0 & neq(v2, % 38.98/5.93 | nil) = v3 & $i(v2) & ? [v4: any] : (v2 = v0 & rearsegP(v1, v0) % 38.98/5.93 | = v4 & ((v4 = 0 & v3 = 0) | (v1 = nil & v0 = nil)) & ((v1 = nil % 38.98/5.93 | & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = nil))))))) % 38.98/5.93 | % 38.98/5.93 | ALPHA: (function-axioms) implies: % 38.98/5.93 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 38.98/5.93 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 38.98/5.93 | % 38.98/5.93 | DELTA: instantiating (3) with fresh symbol all_93_0 gives: % 38.98/5.93 | (5) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 38.98/5.93 | $i(v0) & ? [v1: $i] : ? [v2: any] : (ssList(v1) = 0 & neq(v1, nil) % 38.98/5.93 | = v2 & $i(v1) & ? [v3: any] : (v1 = all_93_0 & rearsegP(v0, % 38.98/5.93 | all_93_0) = v3 & ((v3 = 0 & v2 = 0) | (v0 = nil & all_93_0 = % 38.98/5.93 | nil)) & ((v0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & % 38.98/5.93 | ~ (v0 = nil)))))) % 38.98/5.93 | % 38.98/5.93 | ALPHA: (5) implies: % 38.98/5.94 | (6) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 38.98/5.94 | (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ? [v3: any] : (v1 = % 38.98/5.94 | all_93_0 & rearsegP(v0, all_93_0) = v3 & ((v3 = 0 & v2 = 0) | (v0 % 38.98/5.94 | = nil & all_93_0 = nil)) & ((v0 = nil & ~ (all_93_0 = nil)) % 38.98/5.94 | | (all_93_0 = nil & ~ (v0 = nil)))))) % 38.98/5.94 | % 38.98/5.94 | DELTA: instantiating (6) with fresh symbol all_97_0 gives: % 38.98/5.94 | (7) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: $i] : ? [v1: any] : % 38.98/5.94 | (ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v2: any] : (v0 = % 38.98/5.94 | all_93_0 & rearsegP(all_97_0, all_93_0) = v2 & ((v2 = 0 & v1 = 0) | % 38.98/5.94 | (all_97_0 = nil & all_93_0 = nil)) & ((all_97_0 = nil & ~ % 38.98/5.94 | (all_93_0 = nil)) | (all_93_0 = nil & ~ (all_97_0 = nil))))) % 38.98/5.94 | % 38.98/5.94 | ALPHA: (7) implies: % 38.98/5.94 | (8) $i(all_97_0) % 38.98/5.94 | (9) ssList(all_97_0) = 0 % 38.98/5.94 | (10) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 38.98/5.94 | $i(v0) & ? [v2: any] : (v0 = all_93_0 & rearsegP(all_97_0, % 38.98/5.94 | all_93_0) = v2 & ((v2 = 0 & v1 = 0) | (all_97_0 = nil & all_93_0 % 38.98/5.94 | = nil)) & ((all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 % 38.98/5.94 | = nil & ~ (all_97_0 = nil))))) % 38.98/5.94 | % 38.98/5.94 | DELTA: instantiating (10) with fresh symbols all_99_0, all_99_1 gives: % 38.98/5.94 | (11) ssList(all_99_1) = 0 & neq(all_99_1, nil) = all_99_0 & $i(all_99_1) & % 38.98/5.94 | ? [v0: any] : (all_99_1 = all_93_0 & rearsegP(all_97_0, all_93_0) = v0 % 38.98/5.94 | & ((v0 = 0 & all_99_0 = 0) | (all_97_0 = nil & all_93_0 = nil)) & % 38.98/5.94 | ((all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 38.98/5.94 | (all_97_0 = nil)))) % 38.98/5.94 | % 38.98/5.94 | ALPHA: (11) implies: % 38.98/5.94 | (12) $i(all_99_1) % 38.98/5.94 | (13) neq(all_99_1, nil) = all_99_0 % 38.98/5.94 | (14) ssList(all_99_1) = 0 % 38.98/5.94 | (15) ? [v0: any] : (all_99_1 = all_93_0 & rearsegP(all_97_0, all_93_0) = % 38.98/5.94 | v0 & ((v0 = 0 & all_99_0 = 0) | (all_97_0 = nil & all_93_0 = nil)) & % 38.98/5.94 | ((all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 38.98/5.94 | (all_97_0 = nil)))) % 38.98/5.94 | % 38.98/5.94 | DELTA: instantiating (15) with fresh symbol all_101_0 gives: % 38.98/5.94 | (16) all_99_1 = all_93_0 & rearsegP(all_97_0, all_93_0) = all_101_0 & % 38.98/5.94 | ((all_101_0 = 0 & all_99_0 = 0) | (all_97_0 = nil & all_93_0 = nil)) & % 38.98/5.94 | ((all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 38.98/5.94 | (all_97_0 = nil))) % 38.98/5.94 | % 38.98/5.94 | ALPHA: (16) implies: % 38.98/5.94 | (17) all_99_1 = all_93_0 % 38.98/5.94 | (18) rearsegP(all_97_0, all_93_0) = all_101_0 % 38.98/5.94 | (19) (all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 38.98/5.94 | (all_97_0 = nil)) % 38.98/5.94 | (20) (all_101_0 = 0 & all_99_0 = 0) | (all_97_0 = nil & all_93_0 = nil) % 38.98/5.94 | % 38.98/5.94 | REDUCE: (14), (17) imply: % 38.98/5.94 | (21) ssList(all_93_0) = 0 % 38.98/5.94 | % 38.98/5.94 | REDUCE: (13), (17) imply: % 38.98/5.94 | (22) neq(all_93_0, nil) = all_99_0 % 38.98/5.94 | % 38.98/5.94 | REDUCE: (12), (17) imply: % 38.98/5.94 | (23) $i(all_93_0) % 38.98/5.94 | % 38.98/5.94 | GROUND_INST: instantiating (ax15) with all_93_0, simplifying with (21), (23) % 38.98/5.94 | gives: % 38.98/5.95 | (24) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_0, v0) = v1) | ~ $i(v0) % 38.98/5.95 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 38.98/5.95 | ~ (v0 = all_93_0)) & (v1 = 0 | v0 = all_93_0))) % 38.98/5.95 | % 38.98/5.95 | GROUND_INST: instantiating (ax6) with all_97_0, simplifying with (8), (9) % 38.98/5.95 | gives: % 38.98/5.95 | (25) ! [v0: $i] : ! [v1: any] : ( ~ (rearsegP(all_97_0, v0) = v1) | ~ % 38.98/5.95 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = % 38.98/5.95 | 0) | ? [v2: $i] : (ssList(v2) = 0 & app(v2, v0) = all_97_0 & % 38.98/5.95 | $i(v2))) & (v1 = 0 | ! [v2: $i] : ( ~ (app(v2, v0) = % 38.98/5.95 | all_97_0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 38.98/5.95 | ssList(v2) = v3))))) % 38.98/5.95 | % 38.98/5.95 | GROUND_INST: instantiating (24) with nil, all_99_0, simplifying with (2), (22) % 38.98/5.95 | gives: % 38.98/5.95 | (26) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_99_0 = 0) % 38.98/5.95 | | ~ (all_93_0 = nil)) & (all_99_0 = 0 | all_93_0 = nil)) % 38.98/5.95 | % 38.98/5.95 | GROUND_INST: instantiating (25) with all_93_0, all_101_0, simplifying with % 38.98/5.95 | (18), (23) gives: % 38.98/5.95 | (27) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_0) = v0) | (( ~ (all_101_0 % 38.98/5.95 | = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_93_0) = % 38.98/5.95 | all_97_0 & $i(v0))) & (all_101_0 = 0 | ! [v0: $i] : ( ~ % 38.98/5.95 | (app(v0, all_93_0) = all_97_0) | ~ $i(v0) | ? [v1: int] : ( ~ % 38.98/5.95 | (v1 = 0) & ssList(v0) = v1)))) % 38.98/5.95 | % 38.98/5.95 | BETA: splitting (19) gives: % 38.98/5.95 | % 38.98/5.95 | Case 1: % 38.98/5.95 | | % 38.98/5.95 | | (28) all_97_0 = nil & ~ (all_93_0 = nil) % 38.98/5.95 | | % 38.98/5.95 | | ALPHA: (28) implies: % 38.98/5.95 | | (29) all_97_0 = nil % 38.98/5.95 | | (30) ~ (all_93_0 = nil) % 38.98/5.95 | | % 38.98/5.95 | | REDUCE: (9), (29) imply: % 38.98/5.95 | | (31) ssList(nil) = 0 % 38.98/5.95 | | % 38.98/5.95 | | BETA: splitting (20) gives: % 38.98/5.95 | | % 38.98/5.95 | | Case 1: % 38.98/5.95 | | | % 38.98/5.95 | | | (32) all_101_0 = 0 & all_99_0 = 0 % 38.98/5.95 | | | % 38.98/5.95 | | | ALPHA: (32) implies: % 38.98/5.95 | | | (33) all_99_0 = 0 % 38.98/5.95 | | | (34) all_101_0 = 0 % 38.98/5.95 | | | % 38.98/5.95 | | | BETA: splitting (27) gives: % 38.98/5.95 | | | % 38.98/5.95 | | | Case 1: % 38.98/5.95 | | | | % 38.98/5.95 | | | | (35) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_0) = v0) % 38.98/5.95 | | | | % 38.98/5.95 | | | | DELTA: instantiating (35) with fresh symbol all_317_0 gives: % 38.98/5.95 | | | | (36) ~ (all_317_0 = 0) & ssList(all_93_0) = all_317_0 % 38.98/5.95 | | | | % 39.35/5.95 | | | | REF_CLOSE: (4), (21), (36) are inconsistent by sub-proof #2. % 39.35/5.95 | | | | % 39.35/5.95 | | | Case 2: % 39.35/5.95 | | | | % 39.35/5.95 | | | | (37) ( ~ (all_101_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0, % 39.35/5.95 | | | | all_93_0) = all_97_0 & $i(v0))) & (all_101_0 = 0 | ! [v0: % 39.35/5.95 | | | | $i] : ( ~ (app(v0, all_93_0) = all_97_0) | ~ $i(v0) | ? % 39.35/5.95 | | | | [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1))) % 39.35/5.95 | | | | % 39.35/5.95 | | | | ALPHA: (37) implies: % 39.35/5.96 | | | | (38) ~ (all_101_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0, % 39.35/5.96 | | | | all_93_0) = all_97_0 & $i(v0)) % 39.35/5.96 | | | | % 39.35/5.96 | | | | BETA: splitting (38) gives: % 39.35/5.96 | | | | % 39.35/5.96 | | | | Case 1: % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | (39) ~ (all_101_0 = 0) % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | REDUCE: (34), (39) imply: % 39.35/5.96 | | | | | (40) $false % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | CLOSE: (40) is inconsistent. % 39.35/5.96 | | | | | % 39.35/5.96 | | | | Case 2: % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | (41) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_93_0) = all_97_0 & % 39.35/5.96 | | | | | $i(v0)) % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | DELTA: instantiating (41) with fresh symbol all_320_0 gives: % 39.35/5.96 | | | | | (42) ssList(all_320_0) = 0 & app(all_320_0, all_93_0) = all_97_0 & % 39.35/5.96 | | | | | $i(all_320_0) % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | ALPHA: (42) implies: % 39.35/5.96 | | | | | (43) $i(all_320_0) % 39.35/5.96 | | | | | (44) app(all_320_0, all_93_0) = all_97_0 % 39.35/5.96 | | | | | (45) ssList(all_320_0) = 0 % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | REDUCE: (29), (44) imply: % 39.35/5.96 | | | | | (46) app(all_320_0, all_93_0) = nil % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | GROUND_INST: instantiating (1) with all_320_0, simplifying with (43), % 39.35/5.96 | | | | | (45) gives: % 39.35/5.96 | | | | | (47) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_320_0, v0) = v1) | ~ % 39.35/5.96 | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( % 39.35/5.96 | | | | | ~ (v1 = nil) | (v0 = nil & all_320_0 = nil)) & ( ~ (v0 = % 39.35/5.96 | | | | | nil) | ~ (all_320_0 = nil) | v1 = nil))) % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | GROUND_INST: instantiating (47) with all_93_0, nil, simplifying with % 39.35/5.96 | | | | | (23), (46) gives: % 39.35/5.96 | | | | | (48) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_0) = v0) | % 39.35/5.96 | | | | | (all_320_0 = nil & all_93_0 = nil) % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | BETA: splitting (48) gives: % 39.35/5.96 | | | | | % 39.35/5.96 | | | | | Case 1: % 39.35/5.96 | | | | | | % 39.35/5.96 | | | | | | (49) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_0) = v0) % 39.35/5.96 | | | | | | % 39.35/5.96 | | | | | | DELTA: instantiating (49) with fresh symbol all_317_0 gives: % 39.35/5.96 | | | | | | (50) ~ (all_317_0 = 0) & ssList(all_93_0) = all_317_0 % 39.35/5.96 | | | | | | % 39.35/5.96 | | | | | | REF_CLOSE: (4), (21), (50) are inconsistent by sub-proof #2. % 39.35/5.96 | | | | | | % 39.35/5.96 | | | | | Case 2: % 39.35/5.96 | | | | | | % 39.35/5.96 | | | | | | (51) all_320_0 = nil & all_93_0 = nil % 39.35/5.96 | | | | | | % 39.35/5.96 | | | | | | ALPHA: (51) implies: % 39.35/5.96 | | | | | | (52) all_93_0 = nil % 39.35/5.96 | | | | | | % 39.35/5.96 | | | | | | REF_CLOSE: (4), (26), (31), (33), (52) are inconsistent by sub-proof % 39.35/5.96 | | | | | | #1. % 39.35/5.96 | | | | | | % 39.35/5.96 | | | | | End of split % 39.35/5.96 | | | | | % 39.35/5.96 | | | | End of split % 39.35/5.96 | | | | % 39.35/5.96 | | | End of split % 39.35/5.96 | | | % 39.35/5.96 | | Case 2: % 39.35/5.96 | | | % 39.35/5.96 | | | (53) all_97_0 = nil & all_93_0 = nil % 39.35/5.96 | | | % 39.35/5.96 | | | ALPHA: (53) implies: % 39.35/5.96 | | | (54) all_93_0 = nil % 39.35/5.96 | | | % 39.35/5.96 | | | REDUCE: (30), (54) imply: % 39.35/5.96 | | | (55) $false % 39.35/5.96 | | | % 39.35/5.96 | | | CLOSE: (55) is inconsistent. % 39.35/5.96 | | | % 39.35/5.96 | | End of split % 39.35/5.96 | | % 39.35/5.96 | Case 2: % 39.35/5.96 | | % 39.35/5.96 | | (56) all_93_0 = nil & ~ (all_97_0 = nil) % 39.35/5.96 | | % 39.35/5.96 | | ALPHA: (56) implies: % 39.35/5.96 | | (57) all_93_0 = nil % 39.35/5.96 | | (58) ~ (all_97_0 = nil) % 39.35/5.96 | | % 39.35/5.96 | | REDUCE: (21), (57) imply: % 39.35/5.96 | | (59) ssList(nil) = 0 % 39.35/5.96 | | % 39.35/5.96 | | BETA: splitting (20) gives: % 39.35/5.96 | | % 39.35/5.96 | | Case 1: % 39.35/5.96 | | | % 39.35/5.96 | | | (60) all_101_0 = 0 & all_99_0 = 0 % 39.35/5.96 | | | % 39.35/5.96 | | | ALPHA: (60) implies: % 39.35/5.96 | | | (61) all_99_0 = 0 % 39.35/5.96 | | | % 39.35/5.96 | | | REF_CLOSE: (4), (26), (57), (59), (61) are inconsistent by sub-proof #1. % 39.35/5.96 | | | % 39.35/5.96 | | Case 2: % 39.35/5.96 | | | % 39.35/5.96 | | | (62) all_97_0 = nil & all_93_0 = nil % 39.35/5.96 | | | % 39.35/5.96 | | | ALPHA: (62) implies: % 39.35/5.96 | | | (63) all_97_0 = nil % 39.35/5.96 | | | % 39.35/5.96 | | | REDUCE: (58), (63) imply: % 39.35/5.96 | | | (64) $false % 39.35/5.96 | | | % 39.35/5.96 | | | CLOSE: (64) is inconsistent. % 39.35/5.96 | | | % 39.35/5.96 | | End of split % 39.35/5.96 | | % 39.35/5.96 | End of split % 39.35/5.96 | % 39.35/5.96 End of proof % 39.35/5.96 % 39.35/5.96 Sub-proof #1 shows that the following formulas are inconsistent: % 39.35/5.96 ---------------------------------------------------------------- % 39.35/5.97 (1) all_99_0 = 0 % 39.35/5.97 (2) all_93_0 = nil % 39.35/5.97 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 39.35/5.97 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 39.35/5.97 (4) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_99_0 = 0) | % 39.35/5.97 ~ (all_93_0 = nil)) & (all_99_0 = 0 | all_93_0 = nil)) % 39.35/5.97 (5) ssList(nil) = 0 % 39.35/5.97 % 39.35/5.97 Begin of proof % 39.35/5.97 | % 39.35/5.97 | BETA: splitting (4) gives: % 39.35/5.97 | % 39.35/5.97 | Case 1: % 39.35/5.97 | | % 39.35/5.97 | | (6) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 39.35/5.97 | | % 39.35/5.97 | | DELTA: instantiating (6) with fresh symbol all_310_0 gives: % 39.35/5.97 | | (7) ~ (all_310_0 = 0) & ssList(nil) = all_310_0 % 39.35/5.97 | | % 39.35/5.97 | | ALPHA: (7) implies: % 39.35/5.97 | | (8) ~ (all_310_0 = 0) % 39.35/5.97 | | (9) ssList(nil) = all_310_0 % 39.35/5.97 | | % 39.35/5.97 | | GROUND_INST: instantiating (3) with 0, all_310_0, nil, simplifying with (5), % 39.35/5.97 | | (9) gives: % 39.35/5.97 | | (10) all_310_0 = 0 % 39.35/5.97 | | % 39.35/5.97 | | REDUCE: (8), (10) imply: % 39.35/5.97 | | (11) $false % 39.35/5.97 | | % 39.35/5.97 | | CLOSE: (11) is inconsistent. % 39.35/5.97 | | % 39.35/5.97 | Case 2: % 39.35/5.97 | | % 39.35/5.97 | | (12) ( ~ (all_99_0 = 0) | ~ (all_93_0 = nil)) & (all_99_0 = 0 | all_93_0 % 39.35/5.97 | | = nil) % 39.35/5.97 | | % 39.35/5.97 | | ALPHA: (12) implies: % 39.35/5.97 | | (13) ~ (all_99_0 = 0) | ~ (all_93_0 = nil) % 39.35/5.97 | | % 39.35/5.97 | | BETA: splitting (13) gives: % 39.35/5.97 | | % 39.35/5.97 | | Case 1: % 39.35/5.97 | | | % 39.35/5.97 | | | (14) ~ (all_93_0 = nil) % 39.35/5.97 | | | % 39.35/5.97 | | | REDUCE: (2), (14) imply: % 39.35/5.97 | | | (15) $false % 39.35/5.97 | | | % 39.35/5.97 | | | CLOSE: (15) is inconsistent. % 39.35/5.97 | | | % 39.35/5.97 | | Case 2: % 39.35/5.97 | | | % 39.35/5.97 | | | (16) ~ (all_99_0 = 0) % 39.35/5.97 | | | % 39.35/5.97 | | | REDUCE: (1), (16) imply: % 39.35/5.97 | | | (17) $false % 39.35/5.97 | | | % 39.35/5.97 | | | CLOSE: (17) is inconsistent. % 39.35/5.97 | | | % 39.35/5.97 | | End of split % 39.35/5.97 | | % 39.35/5.97 | End of split % 39.35/5.97 | % 39.35/5.97 End of proof % 39.35/5.97 % 39.35/5.97 Sub-proof #2 shows that the following formulas are inconsistent: % 39.35/5.97 ---------------------------------------------------------------- % 39.35/5.97 (1) ~ (all_317_0 = 0) & ssList(all_93_0) = all_317_0 % 39.35/5.97 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 39.35/5.97 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 39.35/5.97 (3) ssList(all_93_0) = 0 % 39.35/5.97 % 39.35/5.97 Begin of proof % 39.35/5.97 | % 39.35/5.97 | ALPHA: (1) implies: % 39.35/5.97 | (4) ~ (all_317_0 = 0) % 39.35/5.97 | (5) ssList(all_93_0) = all_317_0 % 39.35/5.97 | % 39.35/5.97 | GROUND_INST: instantiating (2) with 0, all_317_0, all_93_0, simplifying with % 39.35/5.97 | (3), (5) gives: % 39.35/5.97 | (6) all_317_0 = 0 % 39.35/5.97 | % 39.35/5.97 | REDUCE: (4), (6) imply: % 39.35/5.97 | (7) $false % 39.35/5.97 | % 39.35/5.97 | CLOSE: (7) is inconsistent. % 39.35/5.97 | % 39.35/5.97 End of proof % 39.35/5.97 % SZS output end Proof for theBenchmark % 39.35/5.97 % 39.35/5.97 5363ms %------------------------------------------------------------------------------