%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC030+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 20:49:17 EDT 2023 % Result : Theorem 21.68s 3.78s % Output : Proof 34.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC030+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n001.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 15:55:35 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.64 (2023-06-19) % 0.20/0.64 % 0.20/0.64 (c) Philipp Rümmer, 2009-2023 % 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.64 Amanda Stjerna. % 0.20/0.64 Free software under BSD-3-Clause. % 0.20/0.64 % 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.64 % 0.20/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 4.18/1.49 Prover 1: Preprocessing ... % 4.18/1.49 Prover 4: Preprocessing ... % 4.18/1.53 Prover 0: Preprocessing ... % 4.18/1.53 Prover 3: Preprocessing ... % 4.18/1.53 Prover 2: Preprocessing ... % 4.18/1.53 Prover 6: Preprocessing ... % 4.18/1.54 Prover 5: Preprocessing ... % 14.63/2.80 Prover 2: Proving ... % 15.62/2.87 Prover 5: Constructing countermodel ... % 15.62/2.89 Prover 6: Proving ... % 15.62/2.91 Prover 1: Constructing countermodel ... % 16.24/2.98 Prover 3: Constructing countermodel ... % 21.68/3.73 Prover 4: Constructing countermodel ... % 21.68/3.78 Prover 0: Proving ... % 21.68/3.78 Prover 3: proved (3112ms) % 21.68/3.78 % 21.68/3.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.68/3.78 % 21.68/3.80 Prover 5: stopped % 21.68/3.80 Prover 6: stopped % 21.68/3.80 Prover 2: stopped % 21.68/3.82 Prover 0: stopped % 21.68/3.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.68/3.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.68/3.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.68/3.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.68/3.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.62/4.14 Prover 8: Preprocessing ... % 24.62/4.15 Prover 13: Preprocessing ... % 24.62/4.17 Prover 11: Preprocessing ... % 25.22/4.20 Prover 10: Preprocessing ... % 25.22/4.21 Prover 7: Preprocessing ... % 27.13/4.43 Prover 7: Constructing countermodel ... % 27.13/4.46 Prover 10: Constructing countermodel ... % 27.74/4.55 Prover 13: Constructing countermodel ... % 27.74/4.63 Prover 8: Warning: ignoring some quantifiers % 27.74/4.64 Prover 8: Constructing countermodel ... % 33.24/5.24 Prover 11: Constructing countermodel ... % 33.97/5.33 Prover 1: Found proof (size 59) % 33.97/5.33 Prover 1: proved (4657ms) % 33.97/5.33 Prover 4: stopped % 33.97/5.33 Prover 7: stopped % 33.97/5.33 Prover 10: stopped % 33.97/5.33 Prover 8: stopped % 33.97/5.33 Prover 11: stopped % 33.97/5.33 Prover 13: stopped % 33.97/5.33 % 33.97/5.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 33.97/5.33 % 33.97/5.33 % SZS output start Proof for theBenchmark % 33.97/5.34 Assumptions after simplification: % 33.97/5.34 --------------------------------- % 33.97/5.34 % 33.97/5.34 (ax83) % 33.97/5.36 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 33.97/5.36 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 33.97/5.36 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1 % 33.97/5.36 = nil) | ~ (v0 = nil) | v2 = nil)))) % 33.97/5.36 % 33.97/5.36 (co1) % 33.97/5.36 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 33.97/5.36 0 & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : % 33.97/5.36 (ssList(v3) = 0 & app(v3, v2) = v0 & app(v2, v3) = v1 & $i(v3))) & ((v1 % 33.97/5.36 = nil & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = nil))))) % 33.97/5.36 % 33.97/5.37 (function-axioms) % 33.97/5.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 33.97/5.38 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 33.97/5.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.97/5.38 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 33.97/5.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.97/5.38 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 33.97/5.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.97/5.38 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 33.97/5.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.97/5.38 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 33.97/5.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 33.97/5.38 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 33.97/5.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 33.97/5.38 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 33.97/5.38 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 33.97/5.38 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 33.97/5.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.97/5.38 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 33.97/5.38 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 33.97/5.38 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 33.97/5.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 33.97/5.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 33.97/5.38 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 33.97/5.38 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 33.97/5.38 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 33.97/5.38 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 33.97/5.38 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 33.97/5.38 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 33.97/5.38 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 33.97/5.38 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 33.97/5.38 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 33.97/5.38 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 33.97/5.38 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 33.97/5.38 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 33.97/5.38 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 33.97/5.38 % 33.97/5.38 Further assumptions not needed in the proof: % 33.97/5.38 -------------------------------------------- % 33.97/5.38 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20, % 33.97/5.38 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, % 33.97/5.38 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, % 33.97/5.38 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, % 33.97/5.38 ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, % 33.97/5.38 ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, % 33.97/5.38 ax80, ax81, ax82, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, % 33.97/5.38 ax93, ax94, ax95 % 33.97/5.38 % 33.97/5.38 Those formulas are unsatisfiable: % 33.97/5.38 --------------------------------- % 33.97/5.38 % 33.97/5.38 Begin of proof % 33.97/5.38 | % 33.97/5.38 | ALPHA: (ax83) implies: % 33.97/5.38 | (1) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 33.97/5.38 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 33.97/5.38 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = % 33.97/5.38 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil)))) % 33.97/5.38 | % 33.97/5.38 | ALPHA: (co1) implies: % 33.97/5.38 | (2) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 33.97/5.38 | & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : % 33.97/5.38 | (ssList(v3) = 0 & app(v3, v2) = v0 & app(v2, v3) = v1 & $i(v3))) % 33.97/5.38 | & ((v1 = nil & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = nil))))) % 33.97/5.38 | % 33.97/5.38 | ALPHA: (function-axioms) implies: % 33.97/5.39 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 33.97/5.39 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 33.97/5.39 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.97/5.39 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 33.97/5.39 | % 33.97/5.39 | DELTA: instantiating (2) with fresh symbol all_93_0 gives: % 33.97/5.39 | (5) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 33.97/5.39 | $i(v0) & ? [v1: $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : % 33.97/5.39 | (ssList(v2) = 0 & app(v2, v1) = all_93_0 & app(v1, v2) = v0 & % 34.32/5.39 | $i(v2))) & ((v0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & % 34.32/5.39 | ~ (v0 = nil)))) % 34.32/5.39 | % 34.32/5.39 | ALPHA: (5) implies: % 34.32/5.39 | (6) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 34.32/5.39 | & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & app(v2, v1) = all_93_0 & % 34.32/5.39 | app(v1, v2) = v0 & $i(v2))) & ((v0 = nil & ~ (all_93_0 = nil)) | % 34.32/5.39 | (all_93_0 = nil & ~ (v0 = nil)))) % 34.32/5.39 | % 34.32/5.39 | DELTA: instantiating (6) with fresh symbol all_97_0 gives: % 34.32/5.39 | (7) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: $i] : (ssList(v0) = 0 & % 34.32/5.39 | $i(v0) & ? [v1: $i] : (ssList(v1) = 0 & app(v1, v0) = all_93_0 & % 34.32/5.39 | app(v0, v1) = all_97_0 & $i(v1))) & ((all_97_0 = nil & ~ (all_93_0 % 34.32/5.39 | = nil)) | (all_93_0 = nil & ~ (all_97_0 = nil))) % 34.32/5.39 | % 34.32/5.39 | ALPHA: (7) implies: % 34.32/5.39 | (8) (all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ (all_97_0 % 34.32/5.39 | = nil)) % 34.32/5.39 | (9) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 34.32/5.39 | & app(v1, v0) = all_93_0 & app(v0, v1) = all_97_0 & $i(v1))) % 34.32/5.39 | % 34.32/5.39 | DELTA: instantiating (9) with fresh symbol all_99_0 gives: % 34.32/5.39 | (10) ssList(all_99_0) = 0 & $i(all_99_0) & ? [v0: $i] : (ssList(v0) = 0 & % 34.32/5.39 | app(v0, all_99_0) = all_93_0 & app(all_99_0, v0) = all_97_0 & % 34.32/5.39 | $i(v0)) % 34.32/5.39 | % 34.32/5.39 | ALPHA: (10) implies: % 34.32/5.39 | (11) $i(all_99_0) % 34.32/5.39 | (12) ssList(all_99_0) = 0 % 34.32/5.39 | (13) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_99_0) = all_93_0 & % 34.32/5.39 | app(all_99_0, v0) = all_97_0 & $i(v0)) % 34.32/5.39 | % 34.32/5.39 | DELTA: instantiating (13) with fresh symbol all_101_0 gives: % 34.32/5.39 | (14) ssList(all_101_0) = 0 & app(all_101_0, all_99_0) = all_93_0 & % 34.32/5.39 | app(all_99_0, all_101_0) = all_97_0 & $i(all_101_0) % 34.32/5.39 | % 34.32/5.39 | ALPHA: (14) implies: % 34.32/5.39 | (15) $i(all_101_0) % 34.32/5.39 | (16) app(all_99_0, all_101_0) = all_97_0 % 34.32/5.39 | (17) app(all_101_0, all_99_0) = all_93_0 % 34.32/5.39 | (18) ssList(all_101_0) = 0 % 34.32/5.39 | % 34.32/5.39 | GROUND_INST: instantiating (1) with all_99_0, simplifying with (11), (12) % 34.32/5.39 | gives: % 34.32/5.39 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_99_0, v0) = v1) | ~ $i(v0) | % 34.32/5.39 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) | % 34.32/5.39 | (v0 = nil & all_99_0 = nil)) & ( ~ (v0 = nil) | ~ (all_99_0 = % 34.32/5.39 | nil) | v1 = nil))) % 34.32/5.40 | % 34.32/5.40 | GROUND_INST: instantiating (1) with all_101_0, simplifying with (15), (18) % 34.32/5.40 | gives: % 34.32/5.40 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_101_0, v0) = v1) | ~ $i(v0) % 34.32/5.40 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) | % 34.32/5.40 | (v0 = nil & all_101_0 = nil)) & ( ~ (v0 = nil) | ~ (all_101_0 = % 34.32/5.40 | nil) | v1 = nil))) % 34.32/5.40 | % 34.32/5.40 | GROUND_INST: instantiating (20) with all_99_0, all_93_0, simplifying with % 34.32/5.40 | (11), (17) gives: % 34.32/5.40 | (21) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_99_0) = v0) | (( ~ (all_101_0 % 34.32/5.40 | = nil) | ~ (all_99_0 = nil) | all_93_0 = nil) & ( ~ (all_93_0 = % 34.32/5.40 | nil) | (all_101_0 = nil & all_99_0 = nil))) % 34.32/5.40 | % 34.32/5.40 | GROUND_INST: instantiating (19) with all_101_0, all_97_0, simplifying with % 34.32/5.40 | (15), (16) gives: % 34.32/5.40 | (22) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) | (( ~ % 34.32/5.40 | (all_101_0 = nil) | ~ (all_99_0 = nil) | all_97_0 = nil) & ( ~ % 34.32/5.40 | (all_97_0 = nil) | (all_101_0 = nil & all_99_0 = nil))) % 34.32/5.40 | % 34.32/5.40 | BETA: splitting (8) gives: % 34.32/5.40 | % 34.32/5.40 | Case 1: % 34.32/5.40 | | % 34.32/5.40 | | (23) all_97_0 = nil & ~ (all_93_0 = nil) % 34.32/5.40 | | % 34.32/5.40 | | ALPHA: (23) implies: % 34.32/5.40 | | (24) all_97_0 = nil % 34.32/5.40 | | (25) ~ (all_93_0 = nil) % 34.32/5.40 | | % 34.32/5.40 | | REDUCE: (16), (24) imply: % 34.32/5.40 | | (26) app(all_99_0, all_101_0) = nil % 34.32/5.40 | | % 34.32/5.40 | | BETA: splitting (22) gives: % 34.32/5.40 | | % 34.32/5.40 | | Case 1: % 34.32/5.40 | | | % 34.32/5.40 | | | (27) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) % 34.32/5.40 | | | % 34.32/5.40 | | | DELTA: instantiating (27) with fresh symbol all_396_0 gives: % 34.32/5.40 | | | (28) ~ (all_396_0 = 0) & ssList(all_101_0) = all_396_0 % 34.32/5.40 | | | % 34.32/5.40 | | | ALPHA: (28) implies: % 34.32/5.40 | | | (29) ~ (all_396_0 = 0) % 34.32/5.40 | | | (30) ssList(all_101_0) = all_396_0 % 34.32/5.40 | | | % 34.32/5.40 | | | GROUND_INST: instantiating (3) with 0, all_396_0, all_101_0, simplifying % 34.32/5.40 | | | with (18), (30) gives: % 34.32/5.40 | | | (31) all_396_0 = 0 % 34.32/5.40 | | | % 34.32/5.40 | | | REDUCE: (29), (31) imply: % 34.32/5.40 | | | (32) $false % 34.32/5.40 | | | % 34.32/5.40 | | | CLOSE: (32) is inconsistent. % 34.32/5.40 | | | % 34.32/5.40 | | Case 2: % 34.32/5.40 | | | % 34.32/5.40 | | | (33) ( ~ (all_101_0 = nil) | ~ (all_99_0 = nil) | all_97_0 = nil) & ( % 34.32/5.40 | | | ~ (all_97_0 = nil) | (all_101_0 = nil & all_99_0 = nil)) % 34.32/5.40 | | | % 34.32/5.40 | | | ALPHA: (33) implies: % 34.32/5.40 | | | (34) ~ (all_97_0 = nil) | (all_101_0 = nil & all_99_0 = nil) % 34.32/5.40 | | | % 34.32/5.40 | | | BETA: splitting (34) gives: % 34.32/5.40 | | | % 34.32/5.40 | | | Case 1: % 34.32/5.40 | | | | % 34.32/5.40 | | | | (35) ~ (all_97_0 = nil) % 34.32/5.40 | | | | % 34.32/5.40 | | | | REDUCE: (24), (35) imply: % 34.32/5.40 | | | | (36) $false % 34.32/5.40 | | | | % 34.32/5.40 | | | | CLOSE: (36) is inconsistent. % 34.32/5.40 | | | | % 34.32/5.40 | | | Case 2: % 34.32/5.40 | | | | % 34.32/5.40 | | | | (37) all_101_0 = nil & all_99_0 = nil % 34.32/5.40 | | | | % 34.32/5.40 | | | | ALPHA: (37) implies: % 34.32/5.40 | | | | (38) all_99_0 = nil % 34.32/5.40 | | | | (39) all_101_0 = nil % 34.32/5.40 | | | | % 34.32/5.40 | | | | REDUCE: (17), (38), (39) imply: % 34.32/5.40 | | | | (40) app(nil, nil) = all_93_0 % 34.32/5.40 | | | | % 34.32/5.40 | | | | REDUCE: (26), (38), (39) imply: % 34.32/5.40 | | | | (41) app(nil, nil) = nil % 34.32/5.40 | | | | % 34.32/5.40 | | | | GROUND_INST: instantiating (4) with nil, all_93_0, nil, nil, simplifying % 34.32/5.40 | | | | with (40), (41) gives: % 34.32/5.40 | | | | (42) all_93_0 = nil % 34.32/5.40 | | | | % 34.32/5.40 | | | | REDUCE: (25), (42) imply: % 34.32/5.40 | | | | (43) $false % 34.32/5.40 | | | | % 34.32/5.40 | | | | CLOSE: (43) is inconsistent. % 34.32/5.40 | | | | % 34.32/5.40 | | | End of split % 34.32/5.40 | | | % 34.32/5.40 | | End of split % 34.32/5.40 | | % 34.32/5.40 | Case 2: % 34.32/5.40 | | % 34.32/5.40 | | (44) all_93_0 = nil & ~ (all_97_0 = nil) % 34.32/5.40 | | % 34.32/5.40 | | ALPHA: (44) implies: % 34.32/5.40 | | (45) all_93_0 = nil % 34.32/5.40 | | (46) ~ (all_97_0 = nil) % 34.32/5.40 | | % 34.32/5.41 | | REDUCE: (17), (45) imply: % 34.32/5.41 | | (47) app(all_101_0, all_99_0) = nil % 34.32/5.41 | | % 34.32/5.41 | | BETA: splitting (21) gives: % 34.32/5.41 | | % 34.32/5.41 | | Case 1: % 34.32/5.41 | | | % 34.32/5.41 | | | (48) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_99_0) = v0) % 34.32/5.41 | | | % 34.32/5.41 | | | DELTA: instantiating (48) with fresh symbol all_396_0 gives: % 34.32/5.41 | | | (49) ~ (all_396_0 = 0) & ssList(all_99_0) = all_396_0 % 34.32/5.41 | | | % 34.32/5.41 | | | ALPHA: (49) implies: % 34.32/5.41 | | | (50) ~ (all_396_0 = 0) % 34.32/5.41 | | | (51) ssList(all_99_0) = all_396_0 % 34.32/5.41 | | | % 34.32/5.41 | | | GROUND_INST: instantiating (3) with 0, all_396_0, all_99_0, simplifying % 34.32/5.41 | | | with (12), (51) gives: % 34.32/5.41 | | | (52) all_396_0 = 0 % 34.32/5.41 | | | % 34.32/5.41 | | | REDUCE: (50), (52) imply: % 34.32/5.41 | | | (53) $false % 34.32/5.41 | | | % 34.32/5.41 | | | CLOSE: (53) is inconsistent. % 34.32/5.41 | | | % 34.32/5.41 | | Case 2: % 34.32/5.41 | | | % 34.32/5.41 | | | (54) ( ~ (all_101_0 = nil) | ~ (all_99_0 = nil) | all_93_0 = nil) & ( % 34.32/5.41 | | | ~ (all_93_0 = nil) | (all_101_0 = nil & all_99_0 = nil)) % 34.32/5.41 | | | % 34.32/5.41 | | | ALPHA: (54) implies: % 34.32/5.41 | | | (55) ~ (all_93_0 = nil) | (all_101_0 = nil & all_99_0 = nil) % 34.32/5.41 | | | % 34.32/5.41 | | | BETA: splitting (55) gives: % 34.32/5.41 | | | % 34.32/5.41 | | | Case 1: % 34.32/5.41 | | | | % 34.32/5.41 | | | | (56) ~ (all_93_0 = nil) % 34.32/5.41 | | | | % 34.32/5.41 | | | | REDUCE: (45), (56) imply: % 34.32/5.41 | | | | (57) $false % 34.32/5.41 | | | | % 34.32/5.41 | | | | CLOSE: (57) is inconsistent. % 34.32/5.41 | | | | % 34.32/5.41 | | | Case 2: % 34.32/5.41 | | | | % 34.32/5.41 | | | | (58) all_101_0 = nil & all_99_0 = nil % 34.32/5.41 | | | | % 34.32/5.41 | | | | ALPHA: (58) implies: % 34.32/5.41 | | | | (59) all_99_0 = nil % 34.32/5.41 | | | | (60) all_101_0 = nil % 34.32/5.41 | | | | % 34.32/5.41 | | | | REDUCE: (47), (59), (60) imply: % 34.32/5.41 | | | | (61) app(nil, nil) = nil % 34.32/5.41 | | | | % 34.32/5.41 | | | | REDUCE: (16), (59), (60) imply: % 34.32/5.41 | | | | (62) app(nil, nil) = all_97_0 % 34.32/5.41 | | | | % 34.32/5.41 | | | | GROUND_INST: instantiating (4) with nil, all_97_0, nil, nil, simplifying % 34.32/5.41 | | | | with (61), (62) gives: % 34.32/5.41 | | | | (63) all_97_0 = nil % 34.32/5.41 | | | | % 34.32/5.41 | | | | REDUCE: (46), (63) imply: % 34.32/5.41 | | | | (64) $false % 34.32/5.41 | | | | % 34.32/5.41 | | | | CLOSE: (64) is inconsistent. % 34.32/5.41 | | | | % 34.32/5.41 | | | End of split % 34.32/5.41 | | | % 34.32/5.41 | | End of split % 34.32/5.41 | | % 34.32/5.41 | End of split % 34.32/5.41 | % 34.32/5.41 End of proof % 34.32/5.41 % SZS output end Proof for theBenchmark % 34.32/5.41 % 34.32/5.41 4770ms %------------------------------------------------------------------------------