%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC132+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 : n024.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 20:49:50 EDT 2023 % Result : Theorem 23.33s 3.91s % Output : Proof 28.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWC132+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 18:15:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.55/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.55/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.55/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.55/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.55/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.55/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.55/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.46/1.63 Prover 1: Preprocessing ... % 6.46/1.63 Prover 4: Preprocessing ... % 6.46/1.65 Prover 6: Preprocessing ... % 6.46/1.65 Prover 5: Preprocessing ... % 6.46/1.65 Prover 2: Preprocessing ... % 6.46/1.65 Prover 3: Preprocessing ... % 6.46/1.66 Prover 0: Preprocessing ... % 16.40/2.97 Prover 2: Proving ... % 16.74/3.00 Prover 1: Constructing countermodel ... % 16.74/3.00 Prover 5: Constructing countermodel ... % 17.34/3.07 Prover 6: Proving ... % 17.66/3.12 Prover 3: Constructing countermodel ... % 23.33/3.91 Prover 3: proved (3264ms) % 23.33/3.91 % 23.33/3.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.33/3.91 % 23.33/3.91 Prover 4: Constructing countermodel ... % 23.33/3.91 Prover 5: stopped % 23.33/3.92 Prover 6: stopped % 23.33/3.92 Prover 2: stopped % 23.86/3.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.86/3.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.86/3.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.86/3.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 25.33/4.11 Prover 7: Preprocessing ... % 25.50/4.13 Prover 0: Proving ... % 25.50/4.14 Prover 10: Preprocessing ... % 25.50/4.14 Prover 0: stopped % 25.50/4.14 Prover 8: Preprocessing ... % 25.50/4.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 25.50/4.20 Prover 11: Preprocessing ... % 26.73/4.29 Prover 13: Preprocessing ... % 26.73/4.37 Prover 10: Constructing countermodel ... % 27.38/4.41 Prover 1: Found proof (size 30) % 27.38/4.41 Prover 1: proved (3775ms) % 27.38/4.42 Prover 4: stopped % 27.38/4.42 Prover 11: stopped % 27.38/4.42 Prover 10: stopped % 27.38/4.43 Prover 13: stopped % 27.38/4.45 Prover 7: Constructing countermodel ... % 27.38/4.47 Prover 7: stopped % 28.11/4.57 Prover 8: Warning: ignoring some quantifiers % 28.11/4.58 Prover 8: Constructing countermodel ... % 28.11/4.59 Prover 8: stopped % 28.11/4.59 % 28.11/4.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 28.11/4.59 % 28.11/4.60 % SZS output start Proof for theBenchmark % 28.50/4.60 Assumptions after simplification: % 28.50/4.60 --------------------------------- % 28.50/4.60 % 28.50/4.60 (ax15) % 28.50/4.63 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 28.50/4.63 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 28.50/4.63 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 28.50/4.63 % 28.50/4.63 (ax17) % 28.50/4.63 ssList(nil) = 0 & $i(nil) % 28.50/4.63 % 28.50/4.63 (ax60) % 28.50/4.63 cyclefreeP(nil) = 0 & $i(nil) % 28.50/4.63 % 28.50/4.63 (co1) % 28.50/4.63 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] % 28.50/4.63 : (cyclefreeP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? [v3: $i] : (ssList(v3) % 28.50/4.63 = 0 & $i(v3) & ? [v4: int] : (v3 = v0 & ~ (v4 = 0) & ~ (v2 = 0) & % 28.50/4.63 neq(v1, nil) = v4)))) % 28.50/4.63 % 28.50/4.63 (function-axioms) % 28.50/4.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 28.50/4.65 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 28.50/4.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.50/4.65 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 28.50/4.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.50/4.65 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 28.50/4.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.50/4.65 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 28.50/4.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.50/4.65 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 28.50/4.65 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 28.50/4.65 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 28.50/4.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 28.50/4.65 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 28.50/4.65 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 28.50/4.65 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 28.50/4.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.50/4.65 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 28.50/4.65 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 28.50/4.65 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 28.50/4.65 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 28.50/4.65 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 28.50/4.65 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 28.50/4.65 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 28.50/4.65 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 28.50/4.65 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.50/4.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 28.50/4.65 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.50/4.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 28.50/4.65 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.50/4.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 28.50/4.65 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.50/4.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 28.50/4.65 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.50/4.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 28.50/4.65 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.50/4.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 28.50/4.65 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.50/4.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 28.50/4.65 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.50/4.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 28.50/4.65 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 28.50/4.65 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 28.50/4.65 % 28.50/4.65 Further assumptions not needed in the proof: % 28.50/4.65 -------------------------------------------- % 28.50/4.65 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 28.50/4.65 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, % 28.50/4.65 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, % 28.50/4.65 ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, % 28.50/4.65 ax59, ax6, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, % 28.50/4.65 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, % 28.50/4.65 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, % 28.50/4.65 ax95 % 28.50/4.65 % 28.50/4.65 Those formulas are unsatisfiable: % 28.50/4.65 --------------------------------- % 28.50/4.65 % 28.50/4.65 Begin of proof % 28.50/4.65 | % 28.50/4.65 | ALPHA: (ax17) implies: % 28.50/4.65 | (1) ssList(nil) = 0 % 28.50/4.65 | % 28.50/4.65 | ALPHA: (ax60) implies: % 28.50/4.65 | (2) cyclefreeP(nil) = 0 % 28.50/4.65 | % 28.50/4.65 | ALPHA: (co1) implies: % 28.50/4.65 | (3) $i(nil) % 28.50/4.65 | (4) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 28.50/4.65 | (cyclefreeP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? [v3: $i] : % 28.50/4.65 | (ssList(v3) = 0 & $i(v3) & ? [v4: int] : (v3 = v0 & ~ (v4 = 0) & % 28.50/4.65 | ~ (v2 = 0) & neq(v1, nil) = v4)))) % 28.50/4.65 | % 28.50/4.65 | ALPHA: (function-axioms) implies: % 28.50/4.66 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 28.50/4.66 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 28.50/4.66 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 28.50/4.66 | (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0)) % 28.50/4.66 | % 28.50/4.66 | DELTA: instantiating (4) with fresh symbol all_93_0 gives: % 28.50/4.66 | (7) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : ? [v1: any] : % 28.50/4.66 | (cyclefreeP(v0) = v1 & ssList(v0) = 0 & $i(v0) & ? [v2: $i] : % 28.50/4.66 | (ssList(v2) = 0 & $i(v2) & ? [v3: int] : (v2 = all_93_0 & ~ (v3 = % 28.50/4.66 | 0) & ~ (v1 = 0) & neq(v0, nil) = v3))) % 28.50/4.66 | % 28.50/4.66 | ALPHA: (7) implies: % 28.50/4.66 | (8) ? [v0: $i] : ? [v1: any] : (cyclefreeP(v0) = v1 & ssList(v0) = 0 & % 28.50/4.66 | $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: int] : (v2 % 28.50/4.66 | = all_93_0 & ~ (v3 = 0) & ~ (v1 = 0) & neq(v0, nil) = v3))) % 28.50/4.66 | % 28.50/4.66 | DELTA: instantiating (8) with fresh symbols all_97_0, all_97_1 gives: % 28.50/4.66 | (9) cyclefreeP(all_97_1) = all_97_0 & ssList(all_97_1) = 0 & $i(all_97_1) & % 28.50/4.66 | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: int] : (v0 = all_93_0 % 28.50/4.66 | & ~ (v1 = 0) & ~ (all_97_0 = 0) & neq(all_97_1, nil) = v1)) % 28.50/4.66 | % 28.50/4.66 | ALPHA: (9) implies: % 28.50/4.66 | (10) $i(all_97_1) % 28.50/4.66 | (11) ssList(all_97_1) = 0 % 28.50/4.66 | (12) cyclefreeP(all_97_1) = all_97_0 % 28.50/4.66 | (13) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: int] : (v0 = all_93_0 % 28.50/4.66 | & ~ (v1 = 0) & ~ (all_97_0 = 0) & neq(all_97_1, nil) = v1)) % 28.50/4.66 | % 28.50/4.66 | DELTA: instantiating (13) with fresh symbol all_99_0 gives: % 28.50/4.66 | (14) ssList(all_99_0) = 0 & $i(all_99_0) & ? [v0: int] : (all_99_0 = % 28.50/4.66 | all_93_0 & ~ (v0 = 0) & ~ (all_97_0 = 0) & neq(all_97_1, nil) = % 28.50/4.66 | v0) % 28.50/4.66 | % 28.50/4.66 | ALPHA: (14) implies: % 28.50/4.66 | (15) ? [v0: int] : (all_99_0 = all_93_0 & ~ (v0 = 0) & ~ (all_97_0 = 0) % 28.50/4.66 | & neq(all_97_1, nil) = v0) % 28.50/4.66 | % 28.50/4.66 | DELTA: instantiating (15) with fresh symbol all_101_0 gives: % 28.50/4.66 | (16) all_99_0 = all_93_0 & ~ (all_101_0 = 0) & ~ (all_97_0 = 0) & % 28.50/4.66 | neq(all_97_1, nil) = all_101_0 % 28.50/4.66 | % 28.50/4.66 | ALPHA: (16) implies: % 28.50/4.66 | (17) ~ (all_97_0 = 0) % 28.50/4.66 | (18) ~ (all_101_0 = 0) % 28.50/4.66 | (19) neq(all_97_1, nil) = all_101_0 % 28.50/4.66 | % 28.50/4.66 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (10), (11) % 28.50/4.66 | gives: % 28.50/4.66 | (20) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0) % 28.50/4.66 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 28.50/4.66 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1))) % 28.50/4.66 | % 28.50/4.66 | GROUND_INST: instantiating (20) with nil, all_101_0, simplifying with (3), % 28.50/4.66 | (19) gives: % 28.50/4.66 | (21) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_101_0 = 0) % 28.50/4.66 | | ~ (all_97_1 = nil)) & (all_101_0 = 0 | all_97_1 = nil)) % 28.50/4.66 | % 28.50/4.66 | BETA: splitting (21) gives: % 28.50/4.66 | % 28.50/4.66 | Case 1: % 28.50/4.67 | | % 28.50/4.67 | | (22) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 28.50/4.67 | | % 28.50/4.67 | | DELTA: instantiating (22) with fresh symbol all_261_0 gives: % 28.50/4.67 | | (23) ~ (all_261_0 = 0) & ssList(nil) = all_261_0 % 28.50/4.67 | | % 28.50/4.67 | | ALPHA: (23) implies: % 28.50/4.67 | | (24) ~ (all_261_0 = 0) % 28.50/4.67 | | (25) ssList(nil) = all_261_0 % 28.50/4.67 | | % 28.50/4.67 | | GROUND_INST: instantiating (5) with 0, all_261_0, nil, simplifying with (1), % 28.50/4.67 | | (25) gives: % 28.50/4.67 | | (26) all_261_0 = 0 % 28.50/4.67 | | % 28.50/4.67 | | REDUCE: (24), (26) imply: % 28.50/4.67 | | (27) $false % 28.50/4.67 | | % 28.50/4.67 | | CLOSE: (27) is inconsistent. % 28.50/4.67 | | % 28.50/4.67 | Case 2: % 28.50/4.67 | | % 28.50/4.67 | | (28) ( ~ (all_101_0 = 0) | ~ (all_97_1 = nil)) & (all_101_0 = 0 | % 28.50/4.67 | | all_97_1 = nil) % 28.50/4.67 | | % 28.50/4.67 | | ALPHA: (28) implies: % 28.50/4.67 | | (29) all_101_0 = 0 | all_97_1 = nil % 28.50/4.67 | | % 28.50/4.67 | | BETA: splitting (29) gives: % 28.50/4.67 | | % 28.50/4.67 | | Case 1: % 28.50/4.67 | | | % 28.50/4.67 | | | (30) all_97_1 = nil % 28.50/4.67 | | | % 28.50/4.67 | | | REDUCE: (12), (30) imply: % 28.50/4.67 | | | (31) cyclefreeP(nil) = all_97_0 % 28.50/4.67 | | | % 28.50/4.67 | | | GROUND_INST: instantiating (6) with 0, all_97_0, nil, simplifying with % 28.50/4.67 | | | (2), (31) gives: % 28.50/4.67 | | | (32) all_97_0 = 0 % 28.50/4.67 | | | % 28.50/4.67 | | | REDUCE: (17), (32) imply: % 28.50/4.67 | | | (33) $false % 28.50/4.67 | | | % 28.50/4.67 | | | CLOSE: (33) is inconsistent. % 28.50/4.67 | | | % 28.50/4.67 | | Case 2: % 28.50/4.67 | | | % 28.50/4.67 | | | (34) all_101_0 = 0 % 28.50/4.67 | | | % 28.50/4.67 | | | REDUCE: (18), (34) imply: % 28.50/4.67 | | | (35) $false % 28.50/4.67 | | | % 28.50/4.67 | | | CLOSE: (35) is inconsistent. % 28.50/4.67 | | | % 28.50/4.67 | | End of split % 28.50/4.67 | | % 28.50/4.67 | End of split % 28.50/4.67 | % 28.50/4.67 End of proof % 28.50/4.67 % SZS output end Proof for theBenchmark % 28.50/4.67 % 28.50/4.67 4048ms %------------------------------------------------------------------------------