%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC037+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 : n010.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 20:49:19 EDT 2023 % Result : Theorem 26.59s 4.36s % Output : Proof 31.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWC037+1 : TPTP v8.1.2. Released v2.4.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n010.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 14:35:19 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.21/1.62 Prover 1: Preprocessing ... % 6.88/1.64 Prover 6: Preprocessing ... % 6.88/1.64 Prover 5: Preprocessing ... % 6.88/1.64 Prover 3: Preprocessing ... % 6.88/1.64 Prover 2: Preprocessing ... % 6.88/1.64 Prover 0: Preprocessing ... % 6.88/1.64 Prover 4: Preprocessing ... % 16.98/3.06 Prover 2: Proving ... % 17.56/3.08 Prover 5: Constructing countermodel ... % 17.56/3.10 Prover 6: Proving ... % 17.56/3.12 Prover 1: Constructing countermodel ... % 18.32/3.19 Prover 3: Constructing countermodel ... % 23.63/3.96 Prover 4: Constructing countermodel ... % 23.63/3.99 Prover 0: Proving ... % 26.59/4.35 Prover 3: proved (3724ms) % 26.59/4.35 % 26.59/4.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 26.59/4.36 % 26.59/4.36 Prover 5: stopped % 26.59/4.36 Prover 2: stopped % 26.59/4.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 26.59/4.37 Prover 0: stopped % 26.59/4.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.59/4.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.59/4.37 Prover 6: stopped % 27.30/4.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 27.30/4.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 27.63/4.49 Prover 10: Preprocessing ... % 28.26/4.53 Prover 7: Preprocessing ... % 28.26/4.55 Prover 8: Preprocessing ... % 28.26/4.57 Prover 13: Preprocessing ... % 28.26/4.57 Prover 11: Preprocessing ... % 29.43/4.70 Prover 1: Found proof (size 77) % 29.43/4.70 Prover 1: proved (4071ms) % 29.43/4.70 Prover 4: stopped % 29.43/4.74 Prover 13: stopped % 29.43/4.74 Prover 10: Constructing countermodel ... % 29.43/4.76 Prover 10: stopped % 29.43/4.77 Prover 7: Constructing countermodel ... % 30.26/4.79 Prover 7: stopped % 30.26/4.79 Prover 11: stopped % 30.82/4.91 Prover 8: Warning: ignoring some quantifiers % 30.82/4.92 Prover 8: Constructing countermodel ... % 30.82/4.93 Prover 8: stopped % 30.82/4.93 % 30.82/4.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 30.82/4.93 % 30.82/4.93 % SZS output start Proof for theBenchmark % 30.82/4.94 Assumptions after simplification: % 30.82/4.94 --------------------------------- % 30.82/4.94 % 30.82/4.94 (ax15) % 30.82/4.96 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 30.82/4.96 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 30.82/4.96 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 30.82/4.96 % 30.82/4.96 (ax54) % 30.82/4.96 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~ % 30.82/4.96 (segmentP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : % 30.82/4.96 (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 30.82/4.96 % 30.82/4.96 (ax58) % 30.82/4.96 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ % 30.82/4.96 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 % 30.82/4.96 = nil) & ( ~ (v0 = nil) | v1 = 0))) % 30.82/4.96 % 30.82/4.96 (co1) % 30.82/4.97 $i(nil) & ? [v0: $i] : ( ~ (v0 = nil) & ssList(v0) = 0 & ssList(nil) = 0 & % 30.82/4.97 $i(v0) & ? [v1: $i] : (segmentP(v0, v1) = 0 & segmentP(nil, v1) = 0 & % 30.82/4.97 ssList(v1) = 0 & neq(v1, nil) = 0 & $i(v1))) % 30.82/4.97 % 30.82/4.97 (function-axioms) % 30.82/4.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 30.82/4.97 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 30.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 30.82/4.97 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 30.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 30.82/4.97 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 30.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 30.82/4.97 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 30.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 30.82/4.97 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 30.82/4.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 30.82/4.97 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 30.82/4.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 30.82/4.97 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 30.82/4.97 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 30.82/4.97 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 30.82/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.82/4.97 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 30.82/4.97 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 30.82/4.97 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 30.82/4.97 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 30.82/4.97 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 30.82/4.97 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 30.82/4.97 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 30.82/4.97 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 30.82/4.97 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 30.82/4.97 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 30.82/4.97 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 30.82/4.97 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 30.82/4.97 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 30.82/4.97 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.15/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 31.15/4.97 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.15/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 31.15/4.98 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 31.15/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 31.15/4.98 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 31.15/4.98 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 31.15/4.98 % 31.15/4.98 Further assumptions not needed in the proof: % 31.15/4.98 -------------------------------------------- % 31.15/4.98 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax17, ax18, ax19, ax2, ax20, ax21, % 31.15/4.98 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, % 31.15/4.98 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, % 31.15/4.98 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax55, ax56, ax57, ax59, % 31.15/4.98 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, % 31.15/4.98 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, % 31.15/4.98 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, % 31.15/4.98 ax95 % 31.15/4.98 % 31.15/4.98 Those formulas are unsatisfiable: % 31.15/4.98 --------------------------------- % 31.15/4.98 % 31.15/4.98 Begin of proof % 31.15/4.98 | % 31.15/4.98 | ALPHA: (ax58) implies: % 31.15/4.98 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ $i(v0) | % 31.15/4.98 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 = % 31.15/4.98 | nil) & ( ~ (v0 = nil) | v1 = 0))) % 31.15/4.98 | % 31.15/4.98 | ALPHA: (co1) implies: % 31.15/4.98 | (2) $i(nil) % 31.15/4.98 | (3) ? [v0: $i] : ( ~ (v0 = nil) & ssList(v0) = 0 & ssList(nil) = 0 & % 31.15/4.98 | $i(v0) & ? [v1: $i] : (segmentP(v0, v1) = 0 & segmentP(nil, v1) = 0 % 31.15/4.98 | & ssList(v1) = 0 & neq(v1, nil) = 0 & $i(v1))) % 31.15/4.98 | % 31.15/4.98 | ALPHA: (function-axioms) implies: % 31.15/4.98 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 31.15/4.98 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 31.15/4.98 | % 31.15/4.98 | DELTA: instantiating (3) with fresh symbol all_93_0 gives: % 31.15/4.98 | (5) ~ (all_93_0 = nil) & ssList(all_93_0) = 0 & ssList(nil) = 0 & % 31.15/4.98 | $i(all_93_0) & ? [v0: $i] : (segmentP(all_93_0, v0) = 0 & % 31.15/4.98 | segmentP(nil, v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0)) % 31.15/4.98 | % 31.15/4.98 | ALPHA: (5) implies: % 31.15/4.98 | (6) ~ (all_93_0 = nil) % 31.15/4.98 | (7) $i(all_93_0) % 31.15/4.98 | (8) ssList(nil) = 0 % 31.15/4.98 | (9) ssList(all_93_0) = 0 % 31.15/4.98 | (10) ? [v0: $i] : (segmentP(all_93_0, v0) = 0 & segmentP(nil, v0) = 0 & % 31.15/4.98 | ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0)) % 31.15/4.98 | % 31.15/4.98 | DELTA: instantiating (10) with fresh symbol all_97_0 gives: % 31.15/4.98 | (11) segmentP(all_93_0, all_97_0) = 0 & segmentP(nil, all_97_0) = 0 & % 31.15/4.98 | ssList(all_97_0) = 0 & neq(all_97_0, nil) = 0 & $i(all_97_0) % 31.15/4.98 | % 31.15/4.98 | ALPHA: (11) implies: % 31.15/4.98 | (12) $i(all_97_0) % 31.15/4.98 | (13) neq(all_97_0, nil) = 0 % 31.15/4.98 | (14) ssList(all_97_0) = 0 % 31.15/4.98 | (15) segmentP(nil, all_97_0) = 0 % 31.15/4.98 | (16) segmentP(all_93_0, all_97_0) = 0 % 31.15/4.98 | % 31.15/4.99 | GROUND_INST: instantiating (ax54) with nil, simplifying with (2), (8) gives: % 31.15/4.99 | (17) ! [v0: $i] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ~ $i(v0) | ? % 31.15/4.99 | [v1: any] : ? [v2: any] : (segmentP(v0, nil) = v2 & ssList(v0) = v1 % 31.15/4.99 | & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 31.15/4.99 | % 31.15/4.99 | GROUND_INST: instantiating (ax54) with all_93_0, simplifying with (7), (9) % 31.15/4.99 | gives: % 31.15/4.99 | (18) ! [v0: any] : (v0 = all_93_0 | ~ (segmentP(all_93_0, v0) = 0) | ~ % 31.15/4.99 | $i(v0) | ? [v1: any] : ? [v2: any] : (segmentP(v0, all_93_0) = v2 % 31.15/4.99 | & ssList(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 31.15/4.99 | % 31.15/4.99 | GROUND_INST: instantiating (ax15) with all_97_0, simplifying with (12), (14) % 31.15/4.99 | gives: % 31.15/4.99 | (19) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_0, v0) = v1) | ~ $i(v0) % 31.15/4.99 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 31.15/4.99 | ~ (v0 = all_97_0)) & (v1 = 0 | v0 = all_97_0))) % 31.15/4.99 | % 31.15/4.99 | GROUND_INST: instantiating (1) with all_97_0, 0, simplifying with (12), (15) % 31.15/4.99 | gives: % 31.15/4.99 | (20) all_97_0 = nil | ? [v0: int] : ( ~ (v0 = 0) & ssList(all_97_0) = v0) % 31.15/4.99 | % 31.15/4.99 | GROUND_INST: instantiating (17) with all_97_0, simplifying with (12), (15) % 31.15/4.99 | gives: % 31.15/4.99 | (21) all_97_0 = nil | ? [v0: any] : ? [v1: any] : (segmentP(all_97_0, % 31.15/4.99 | nil) = v1 & ssList(all_97_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.15/4.99 | % 31.15/4.99 | GROUND_INST: instantiating (18) with all_97_0, simplifying with (12), (16) % 31.15/4.99 | gives: % 31.15/4.99 | (22) all_97_0 = all_93_0 | ? [v0: any] : ? [v1: any] : % 31.15/4.99 | (segmentP(all_97_0, all_93_0) = v1 & ssList(all_97_0) = v0 & ( ~ (v1 = % 31.15/4.99 | 0) | ~ (v0 = 0))) % 31.15/4.99 | % 31.15/4.99 | GROUND_INST: instantiating (19) with nil, 0, simplifying with (2) gives: % 31.15/4.99 | (23) ~ (all_97_0 = nil) | ~ (neq(nil, nil) = 0) | ? [v0: int] : ( ~ (v0 % 31.15/4.99 | = 0) & ssList(nil) = v0) % 31.15/4.99 | % 31.15/4.99 | BETA: splitting (20) gives: % 31.15/4.99 | % 31.15/4.99 | Case 1: % 31.15/4.99 | | % 31.15/4.99 | | (24) all_97_0 = nil % 31.15/4.99 | | % 31.15/4.99 | | REDUCE: (13), (24) imply: % 31.15/4.99 | | (25) neq(nil, nil) = 0 % 31.15/4.99 | | % 31.15/4.99 | | BETA: splitting (23) gives: % 31.15/4.99 | | % 31.15/4.99 | | Case 1: % 31.15/4.99 | | | % 31.15/4.99 | | | (26) ~ (neq(nil, nil) = 0) % 31.15/4.99 | | | % 31.15/4.99 | | | PRED_UNIFY: (25), (26) imply: % 31.15/4.99 | | | (27) $false % 31.15/4.99 | | | % 31.15/4.99 | | | CLOSE: (27) is inconsistent. % 31.15/4.99 | | | % 31.15/4.99 | | Case 2: % 31.15/4.99 | | | % 31.15/4.99 | | | (28) ~ (all_97_0 = nil) | ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = % 31.15/4.99 | | | v0) % 31.15/4.99 | | | % 31.15/4.99 | | | BETA: splitting (28) gives: % 31.15/4.99 | | | % 31.15/4.99 | | | Case 1: % 31.15/4.99 | | | | % 31.15/4.99 | | | | (29) ~ (all_97_0 = nil) % 31.15/4.99 | | | | % 31.15/4.99 | | | | REDUCE: (24), (29) imply: % 31.15/4.99 | | | | (30) $false % 31.15/4.99 | | | | % 31.15/4.99 | | | | CLOSE: (30) is inconsistent. % 31.15/4.99 | | | | % 31.15/4.99 | | | Case 2: % 31.15/4.99 | | | | % 31.15/4.99 | | | | (31) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 31.15/5.00 | | | | % 31.15/5.00 | | | | DELTA: instantiating (31) with fresh symbol all_295_0 gives: % 31.15/5.00 | | | | (32) ~ (all_295_0 = 0) & ssList(nil) = all_295_0 % 31.15/5.00 | | | | % 31.15/5.00 | | | | ALPHA: (32) implies: % 31.15/5.00 | | | | (33) ~ (all_295_0 = 0) % 31.15/5.00 | | | | (34) ssList(nil) = all_295_0 % 31.15/5.00 | | | | % 31.15/5.00 | | | | DELTA: instantiating (31) with fresh symbol all_297_0 gives: % 31.15/5.00 | | | | (35) ~ (all_297_0 = 0) & ssList(nil) = all_297_0 % 31.15/5.00 | | | | % 31.15/5.00 | | | | ALPHA: (35) implies: % 31.15/5.00 | | | | (36) ssList(nil) = all_297_0 % 31.15/5.00 | | | | % 31.15/5.00 | | | | DELTA: instantiating (31) with fresh symbol all_299_0 gives: % 31.15/5.00 | | | | (37) ~ (all_299_0 = 0) & ssList(nil) = all_299_0 % 31.15/5.00 | | | | % 31.15/5.00 | | | | ALPHA: (37) implies: % 31.15/5.00 | | | | (38) ssList(nil) = all_299_0 % 31.15/5.00 | | | | % 31.15/5.00 | | | | BETA: splitting (22) gives: % 31.15/5.00 | | | | % 31.15/5.00 | | | | Case 1: % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | (39) all_97_0 = all_93_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | COMBINE_EQS: (24), (39) imply: % 31.15/5.00 | | | | | (40) all_93_0 = nil % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | SIMP: (40) implies: % 31.15/5.00 | | | | | (41) all_93_0 = nil % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | REDUCE: (6), (41) imply: % 31.15/5.00 | | | | | (42) $false % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | CLOSE: (42) is inconsistent. % 31.15/5.00 | | | | | % 31.15/5.00 | | | | Case 2: % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | (43) ? [v0: any] : ? [v1: any] : (segmentP(all_97_0, all_93_0) = % 31.15/5.00 | | | | | v1 & ssList(all_97_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | DELTA: instantiating (43) with fresh symbols all_304_0, all_304_1 % 31.15/5.00 | | | | | gives: % 31.15/5.00 | | | | | (44) segmentP(all_97_0, all_93_0) = all_304_0 & ssList(all_97_0) = % 31.15/5.00 | | | | | all_304_1 & ( ~ (all_304_0 = 0) | ~ (all_304_1 = 0)) % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | ALPHA: (44) implies: % 31.15/5.00 | | | | | (45) ssList(all_97_0) = all_304_1 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | REDUCE: (24), (45) imply: % 31.15/5.00 | | | | | (46) ssList(nil) = all_304_1 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | DELTA: instantiating (31) with fresh symbol all_316_0 gives: % 31.15/5.00 | | | | | (47) ~ (all_316_0 = 0) & ssList(nil) = all_316_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | ALPHA: (47) implies: % 31.15/5.00 | | | | | (48) ssList(nil) = all_316_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with 0, all_299_0, nil, simplifying % 31.15/5.00 | | | | | with (8), (38) gives: % 31.15/5.00 | | | | | (49) all_299_0 = 0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with all_299_0, all_304_1, nil, % 31.15/5.00 | | | | | simplifying with (38), (46) gives: % 31.15/5.00 | | | | | (50) all_304_1 = all_299_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with all_297_0, all_304_1, nil, % 31.15/5.00 | | | | | simplifying with (36), (46) gives: % 31.15/5.00 | | | | | (51) all_304_1 = all_297_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with all_304_1, all_316_0, nil, % 31.15/5.00 | | | | | simplifying with (46), (48) gives: % 31.15/5.00 | | | | | (52) all_316_0 = all_304_1 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with all_295_0, all_316_0, nil, % 31.15/5.00 | | | | | simplifying with (34), (48) gives: % 31.15/5.00 | | | | | (53) all_316_0 = all_295_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | COMBINE_EQS: (52), (53) imply: % 31.15/5.00 | | | | | (54) all_304_1 = all_295_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | SIMP: (54) implies: % 31.15/5.00 | | | | | (55) all_304_1 = all_295_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | COMBINE_EQS: (50), (51) imply: % 31.15/5.00 | | | | | (56) all_299_0 = all_297_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | SIMP: (56) implies: % 31.15/5.00 | | | | | (57) all_299_0 = all_297_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | COMBINE_EQS: (51), (55) imply: % 31.15/5.00 | | | | | (58) all_297_0 = all_295_0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | COMBINE_EQS: (49), (57) imply: % 31.15/5.00 | | | | | (59) all_297_0 = 0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | SIMP: (59) implies: % 31.15/5.00 | | | | | (60) all_297_0 = 0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | COMBINE_EQS: (58), (60) imply: % 31.15/5.00 | | | | | (61) all_295_0 = 0 % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | REDUCE: (33), (61) imply: % 31.15/5.00 | | | | | (62) $false % 31.15/5.00 | | | | | % 31.15/5.00 | | | | | CLOSE: (62) is inconsistent. % 31.15/5.00 | | | | | % 31.15/5.00 | | | | End of split % 31.15/5.00 | | | | % 31.15/5.00 | | | End of split % 31.15/5.00 | | | % 31.15/5.00 | | End of split % 31.15/5.00 | | % 31.15/5.00 | Case 2: % 31.15/5.00 | | % 31.15/5.00 | | (63) ~ (all_97_0 = nil) % 31.15/5.00 | | (64) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_97_0) = v0) % 31.15/5.00 | | % 31.15/5.00 | | DELTA: instantiating (64) with fresh symbol all_267_0 gives: % 31.15/5.00 | | (65) ~ (all_267_0 = 0) & ssList(all_97_0) = all_267_0 % 31.15/5.00 | | % 31.15/5.00 | | ALPHA: (65) implies: % 31.15/5.00 | | (66) ~ (all_267_0 = 0) % 31.15/5.00 | | (67) ssList(all_97_0) = all_267_0 % 31.15/5.00 | | % 31.15/5.00 | | DELTA: instantiating (64) with fresh symbol all_271_0 gives: % 31.15/5.00 | | (68) ~ (all_271_0 = 0) & ssList(all_97_0) = all_271_0 % 31.15/5.00 | | % 31.15/5.00 | | ALPHA: (68) implies: % 31.15/5.00 | | (69) ssList(all_97_0) = all_271_0 % 31.15/5.00 | | % 31.15/5.00 | | BETA: splitting (21) gives: % 31.15/5.00 | | % 31.15/5.00 | | Case 1: % 31.15/5.00 | | | % 31.15/5.00 | | | (70) all_97_0 = nil % 31.15/5.00 | | | % 31.15/5.00 | | | REDUCE: (63), (70) imply: % 31.15/5.01 | | | (71) $false % 31.15/5.01 | | | % 31.15/5.01 | | | CLOSE: (71) is inconsistent. % 31.15/5.01 | | | % 31.15/5.01 | | Case 2: % 31.15/5.01 | | | % 31.15/5.01 | | | (72) ? [v0: any] : ? [v1: any] : (segmentP(all_97_0, nil) = v1 & % 31.15/5.01 | | | ssList(all_97_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 31.15/5.01 | | | % 31.15/5.01 | | | DELTA: instantiating (72) with fresh symbols all_291_0, all_291_1 gives: % 31.15/5.01 | | | (73) segmentP(all_97_0, nil) = all_291_0 & ssList(all_97_0) = all_291_1 % 31.15/5.01 | | | & ( ~ (all_291_0 = 0) | ~ (all_291_1 = 0)) % 31.15/5.01 | | | % 31.15/5.01 | | | ALPHA: (73) implies: % 31.15/5.01 | | | (74) ssList(all_97_0) = all_291_1 % 31.15/5.01 | | | % 31.15/5.01 | | | GROUND_INST: instantiating (4) with 0, all_271_0, all_97_0, simplifying % 31.15/5.01 | | | with (14), (69) gives: % 31.15/5.01 | | | (75) all_271_0 = 0 % 31.15/5.01 | | | % 31.15/5.01 | | | GROUND_INST: instantiating (4) with all_271_0, all_291_1, all_97_0, % 31.15/5.01 | | | simplifying with (69), (74) gives: % 31.15/5.01 | | | (76) all_291_1 = all_271_0 % 31.15/5.01 | | | % 31.15/5.01 | | | GROUND_INST: instantiating (4) with all_267_0, all_291_1, all_97_0, % 31.15/5.01 | | | simplifying with (67), (74) gives: % 31.15/5.01 | | | (77) all_291_1 = all_267_0 % 31.15/5.01 | | | % 31.15/5.01 | | | COMBINE_EQS: (76), (77) imply: % 31.15/5.01 | | | (78) all_271_0 = all_267_0 % 31.15/5.01 | | | % 31.15/5.01 | | | SIMP: (78) implies: % 31.15/5.01 | | | (79) all_271_0 = all_267_0 % 31.15/5.01 | | | % 31.15/5.01 | | | COMBINE_EQS: (75), (79) imply: % 31.15/5.01 | | | (80) all_267_0 = 0 % 31.15/5.01 | | | % 31.15/5.01 | | | REDUCE: (66), (80) imply: % 31.15/5.01 | | | (81) $false % 31.15/5.01 | | | % 31.15/5.01 | | | CLOSE: (81) is inconsistent. % 31.15/5.01 | | | % 31.15/5.01 | | End of split % 31.15/5.01 | | % 31.15/5.01 | End of split % 31.15/5.01 | % 31.15/5.01 End of proof % 31.15/5.01 % SZS output end Proof for theBenchmark % 31.15/5.01 % 31.15/5.01 4402ms %------------------------------------------------------------------------------