%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC207+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 : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 20:50:14 EDT 2023 % Result : Theorem 23.87s 3.98s % Output : Proof 38.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC207+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n022.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 14:59:39 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.63/1.53 Prover 4: Preprocessing ... % 5.63/1.53 Prover 1: Preprocessing ... % 5.63/1.56 Prover 2: Preprocessing ... % 5.63/1.56 Prover 0: Preprocessing ... % 5.63/1.56 Prover 3: Preprocessing ... % 6.19/1.57 Prover 6: Preprocessing ... % 6.19/1.57 Prover 5: Preprocessing ... % 15.21/2.81 Prover 2: Proving ... % 15.84/2.88 Prover 5: Constructing countermodel ... % 16.16/2.94 Prover 1: Constructing countermodel ... % 16.71/2.99 Prover 3: Constructing countermodel ... % 17.12/3.04 Prover 6: Proving ... % 23.87/3.93 Prover 4: Constructing countermodel ... % 23.87/3.96 Prover 0: Proving ... % 23.87/3.98 Prover 3: proved (3362ms) % 23.87/3.98 % 23.87/3.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.87/3.98 % 23.87/3.98 Prover 5: stopped % 23.87/3.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.87/3.98 Prover 6: stopped % 23.87/3.99 Prover 2: stopped % 23.87/3.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.87/3.99 Prover 0: stopped % 24.63/4.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 24.63/4.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.63/4.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.14/4.21 Prover 8: Preprocessing ... % 26.14/4.26 Prover 13: Preprocessing ... % 26.14/4.29 Prover 7: Preprocessing ... % 26.92/4.34 Prover 10: Preprocessing ... % 26.92/4.35 Prover 11: Preprocessing ... % 27.68/4.51 Prover 10: Constructing countermodel ... % 28.72/4.56 Prover 13: Constructing countermodel ... % 28.72/4.57 Prover 7: Constructing countermodel ... % 29.67/4.68 Prover 8: Warning: ignoring some quantifiers % 29.67/4.70 Prover 8: Constructing countermodel ... % 35.84/5.50 Prover 11: Constructing countermodel ... % 37.90/5.81 Prover 1: Found proof (size 66) % 37.90/5.81 Prover 1: proved (5201ms) % 37.90/5.81 Prover 11: stopped % 37.90/5.81 Prover 10: stopped % 37.90/5.81 Prover 7: stopped % 37.90/5.81 Prover 8: stopped % 37.90/5.81 Prover 4: stopped % 37.90/5.81 Prover 13: stopped % 37.90/5.81 % 37.90/5.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 37.90/5.81 % 37.90/5.82 % SZS output start Proof for theBenchmark % 37.90/5.83 Assumptions after simplification: % 37.90/5.83 --------------------------------- % 37.90/5.83 % 37.90/5.83 (ax15) % 38.43/5.85 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 38.43/5.85 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 38.43/5.85 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 38.43/5.85 % 38.43/5.86 (ax17) % 38.43/5.86 ssList(nil) = 0 & $i(nil) % 38.43/5.86 % 38.43/5.86 (ax18) % 38.43/5.86 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1, % 38.43/5.86 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) = % 38.43/5.86 v2))) % 38.43/5.86 % 38.43/5.86 (ax20) % 38.43/5.86 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 38.43/5.86 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 38.43/5.86 ssItem(v2) = 0 & $i(v2)))) % 38.43/5.86 % 38.43/5.86 (ax23) % 38.43/5.86 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 38.43/5.86 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 38.43/5.86 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 38.43/5.86 % 38.43/5.86 (ax25) % 38.43/5.86 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 38.43/5.86 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 38.43/5.86 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 38.43/5.86 % 38.43/5.86 (co1) % 38.43/5.87 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 38.43/5.87 $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) = 0 & % 38.43/5.87 $i(v2) & ( ? [v3: $i] : (memberP(v2, v3) = 0 & cons(v3, nil) = v0 & % 38.43/5.87 ssItem(v3) = 0 & $i(v3) & ! [v4: $i] : (v4 = v3 | ~ (memberP(v2, v4) % 38.43/5.87 = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (leq(v3, v4) = v6 % 38.43/5.87 & ssItem(v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) | (v2 = nil & % 38.43/5.87 v0 = nil)))) % 38.43/5.87 % 38.43/5.87 (function-axioms) % 38.43/5.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 38.43/5.87 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 38.43/5.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.43/5.87 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 38.43/5.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.43/5.87 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 38.43/5.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.43/5.87 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 38.43/5.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 38.43/5.87 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 38.43/5.87 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 38.43/5.87 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 38.43/5.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 38.43/5.87 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 38.43/5.87 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 38.43/5.87 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 38.43/5.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 38.43/5.87 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 38.43/5.87 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 38.43/5.87 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 38.43/5.87 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 38.43/5.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 38.43/5.87 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 38.43/5.87 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 38.43/5.87 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 38.43/5.87 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 38.43/5.87 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 38.43/5.87 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 38.43/5.87 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 38.43/5.87 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 38.43/5.87 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 38.43/5.87 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 38.43/5.87 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 38.43/5.87 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 38.43/5.87 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 38.43/5.87 % 38.43/5.87 Further assumptions not needed in the proof: % 38.43/5.87 -------------------------------------------- % 38.43/5.88 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax19, ax2, ax21, ax22, ax24, ax26, % 38.43/5.88 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, % 38.43/5.88 ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, % 38.43/5.88 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60, ax61, % 38.43/5.88 ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73, % 38.43/5.88 ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, % 38.43/5.88 ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 38.43/5.88 % 38.43/5.88 Those formulas are unsatisfiable: % 38.43/5.88 --------------------------------- % 38.43/5.88 % 38.43/5.88 Begin of proof % 38.43/5.88 | % 38.43/5.88 | ALPHA: (ax17) implies: % 38.43/5.88 | (1) ssList(nil) = 0 % 38.43/5.88 | % 38.43/5.88 | ALPHA: (ax20) implies: % 38.43/5.88 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 38.43/5.88 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 38.43/5.88 | ssItem(v2) = 0 & $i(v2)))) % 38.43/5.88 | % 38.43/5.88 | ALPHA: (co1) implies: % 38.43/5.88 | (3) $i(nil) % 38.43/5.88 | (4) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 38.43/5.88 | $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) = % 38.43/5.88 | 0 & $i(v2) & ( ? [v3: $i] : (memberP(v2, v3) = 0 & cons(v3, nil) = % 38.43/5.88 | v0 & ssItem(v3) = 0 & $i(v3) & ! [v4: $i] : (v4 = v3 | ~ % 38.43/5.88 | (memberP(v2, v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: % 38.43/5.88 | any] : (leq(v3, v4) = v6 & ssItem(v4) = v5 & ( ~ (v6 = 0) | % 38.43/5.88 | ~ (v5 = 0))))) | (v2 = nil & v0 = nil)))) % 38.43/5.88 | % 38.43/5.88 | ALPHA: (function-axioms) implies: % 38.43/5.88 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 38.43/5.88 | (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 38.43/5.88 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 38.43/5.88 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 38.43/5.88 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 38.43/5.88 | ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0)) % 38.43/5.88 | % 38.43/5.88 | DELTA: instantiating (4) with fresh symbols all_93_0, all_93_1 gives: % 38.43/5.89 | (8) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) & % 38.43/5.89 | ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 & % 38.43/5.89 | $i(v0) & ( ? [v1: $i] : (memberP(v0, v1) = 0 & cons(v1, nil) = % 38.43/5.89 | all_93_1 & ssItem(v1) = 0 & $i(v1) & ! [v2: $i] : (v2 = v1 | ~ % 38.43/5.89 | (memberP(v0, v2) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4: any] % 38.43/5.89 | : (leq(v1, v2) = v4 & ssItem(v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 38.43/5.89 | 0))))) | (v0 = nil & all_93_1 = nil))) % 38.43/5.89 | % 38.43/5.89 | ALPHA: (8) implies: % 38.43/5.89 | (9) $i(all_93_1) % 38.43/5.89 | (10) neq(all_93_1, nil) = all_93_0 % 38.43/5.89 | (11) ssList(all_93_1) = 0 % 38.43/5.89 | (12) ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 & % 38.43/5.89 | $i(v0) & ( ? [v1: $i] : (memberP(v0, v1) = 0 & cons(v1, nil) = % 38.43/5.89 | all_93_1 & ssItem(v1) = 0 & $i(v1) & ! [v2: $i] : (v2 = v1 | ~ % 38.43/5.89 | (memberP(v0, v2) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4: % 38.43/5.89 | any] : (leq(v1, v2) = v4 & ssItem(v2) = v3 & ( ~ (v4 = 0) | % 38.43/5.89 | ~ (v3 = 0))))) | (v0 = nil & all_93_1 = nil))) % 38.43/5.89 | % 38.43/5.89 | DELTA: instantiating (12) with fresh symbol all_97_0 gives: % 38.43/5.89 | (13) ~ (all_93_0 = 0) & ssList(all_97_0) = 0 & neq(all_97_0, nil) = 0 & % 38.43/5.89 | $i(all_97_0) & ( ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, % 38.43/5.89 | nil) = all_93_1 & ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = % 38.43/5.89 | v0 | ~ (memberP(all_97_0, v1) = 0) | ~ $i(v1) | ? [v2: any] : % 38.43/5.89 | ? [v3: any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = % 38.43/5.89 | 0) | ~ (v2 = 0))))) | (all_97_0 = nil & all_93_1 = nil)) % 38.43/5.89 | % 38.43/5.89 | ALPHA: (13) implies: % 38.43/5.89 | (14) ~ (all_93_0 = 0) % 38.43/5.89 | (15) $i(all_97_0) % 38.43/5.89 | (16) neq(all_97_0, nil) = 0 % 38.43/5.89 | (17) ssList(all_97_0) = 0 % 38.43/5.89 | (18) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) = all_93_1 & % 38.43/5.89 | ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~ % 38.43/5.89 | (memberP(all_97_0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: % 38.43/5.89 | any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ % 38.43/5.89 | (v2 = 0))))) | (all_97_0 = nil & all_93_1 = nil) % 38.43/5.89 | % 38.43/5.89 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (3) gives: % 38.43/5.89 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 38.43/5.89 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 38.43/5.89 | ( ~ (v2 = 0) | v3 = nil))) % 38.43/5.89 | % 38.43/5.89 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (3) gives: % 38.81/5.89 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 38.81/5.89 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 38.81/5.89 | ( ~ (v2 = 0) | v3 = v0))) % 38.81/5.89 | % 38.81/5.89 | GROUND_INST: instantiating (ax18) with nil, simplifying with (1), (3) gives: % 38.81/5.90 | (21) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : ( % 38.81/5.90 | ~ (v1 = 0) & ssItem(v0) = v1)) % 38.81/5.90 | % 38.81/5.90 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (9), (11) % 38.81/5.90 | gives: % 38.81/5.90 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0) % 38.81/5.90 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 38.81/5.90 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1))) % 38.81/5.90 | % 38.81/5.90 | GROUND_INST: instantiating (2) with all_97_0, simplifying with (15), (17) % 38.81/5.90 | gives: % 38.81/5.90 | (23) all_97_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 38.81/5.90 | : (cons(v1, v0) = all_97_0 & ssItem(v1) = 0 & $i(v1))) % 38.81/5.90 | % 38.81/5.90 | GROUND_INST: instantiating (22) with nil, all_93_0, simplifying with (3), (10) % 38.81/5.90 | gives: % 38.81/5.90 | (24) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0) % 38.81/5.90 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil)) % 38.81/5.90 | % 38.81/5.90 | BETA: splitting (24) gives: % 38.81/5.90 | % 38.81/5.90 | Case 1: % 38.81/5.90 | | % 38.81/5.90 | | (25) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 38.81/5.90 | | % 38.81/5.90 | | DELTA: instantiating (25) with fresh symbol all_274_0 gives: % 38.81/5.90 | | (26) ~ (all_274_0 = 0) & ssList(nil) = all_274_0 % 38.81/5.90 | | % 38.81/5.90 | | ALPHA: (26) implies: % 38.81/5.90 | | (27) ~ (all_274_0 = 0) % 38.81/5.90 | | (28) ssList(nil) = all_274_0 % 38.81/5.90 | | % 38.81/5.90 | | DELTA: instantiating (25) with fresh symbol all_276_0 gives: % 38.81/5.90 | | (29) ~ (all_276_0 = 0) & ssList(nil) = all_276_0 % 38.81/5.90 | | % 38.81/5.90 | | ALPHA: (29) implies: % 38.81/5.90 | | (30) ssList(nil) = all_276_0 % 38.81/5.90 | | % 38.81/5.90 | | GROUND_INST: instantiating (6) with 0, all_276_0, nil, simplifying with (1), % 38.81/5.90 | | (30) gives: % 38.81/5.90 | | (31) all_276_0 = 0 % 38.81/5.90 | | % 38.81/5.90 | | GROUND_INST: instantiating (6) with all_274_0, all_276_0, nil, simplifying % 38.81/5.90 | | with (28), (30) gives: % 38.81/5.90 | | (32) all_276_0 = all_274_0 % 38.81/5.90 | | % 38.81/5.90 | | COMBINE_EQS: (31), (32) imply: % 38.81/5.90 | | (33) all_274_0 = 0 % 38.81/5.90 | | % 38.81/5.90 | | REDUCE: (27), (33) imply: % 38.81/5.90 | | (34) $false % 38.81/5.90 | | % 38.81/5.90 | | CLOSE: (34) is inconsistent. % 38.81/5.90 | | % 38.81/5.90 | Case 2: % 38.81/5.90 | | % 38.81/5.90 | | (35) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 % 38.81/5.90 | | = nil) % 38.81/5.90 | | % 38.81/5.90 | | ALPHA: (35) implies: % 38.81/5.90 | | (36) all_93_0 = 0 | all_93_1 = nil % 38.81/5.90 | | % 38.81/5.90 | | BETA: splitting (36) gives: % 38.81/5.90 | | % 38.81/5.90 | | Case 1: % 38.81/5.90 | | | % 38.81/5.90 | | | (37) all_93_1 = nil % 38.81/5.90 | | | % 38.81/5.90 | | | REDUCE: (10), (37) imply: % 38.81/5.90 | | | (38) neq(nil, nil) = all_93_0 % 38.81/5.90 | | | % 38.81/5.90 | | | BETA: splitting (18) gives: % 38.81/5.90 | | | % 38.81/5.90 | | | Case 1: % 38.81/5.90 | | | | % 38.81/5.91 | | | | (39) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) = % 38.81/5.91 | | | | all_93_1 & ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | % 38.81/5.91 | | | | ~ (memberP(all_97_0, v1) = 0) | ~ $i(v1) | ? [v2: any] : % 38.81/5.91 | | | | ? [v3: any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 % 38.81/5.91 | | | | = 0) | ~ (v2 = 0))))) % 38.81/5.91 | | | | % 38.81/5.91 | | | | DELTA: instantiating (39) with fresh symbol all_299_0 gives: % 38.81/5.91 | | | | (40) memberP(all_97_0, all_299_0) = 0 & cons(all_299_0, nil) = % 38.81/5.91 | | | | all_93_1 & ssItem(all_299_0) = 0 & $i(all_299_0) & ! [v0: any] % 38.81/5.91 | | | | : (v0 = all_299_0 | ~ (memberP(all_97_0, v0) = 0) | ~ $i(v0) | % 38.81/5.91 | | | | ? [v1: any] : ? [v2: any] : (leq(all_299_0, v0) = v2 & % 38.81/5.91 | | | | ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 38.81/5.91 | | | | % 38.81/5.91 | | | | ALPHA: (40) implies: % 38.81/5.91 | | | | (41) $i(all_299_0) % 38.81/5.91 | | | | (42) ssItem(all_299_0) = 0 % 38.81/5.91 | | | | (43) cons(all_299_0, nil) = all_93_1 % 38.81/5.91 | | | | % 38.81/5.91 | | | | REDUCE: (37), (43) imply: % 38.81/5.91 | | | | (44) cons(all_299_0, nil) = nil % 38.81/5.91 | | | | % 38.81/5.91 | | | | BETA: splitting (23) gives: % 38.81/5.91 | | | | % 38.81/5.91 | | | | Case 1: % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | (45) all_97_0 = nil % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | REDUCE: (16), (45) imply: % 38.81/5.91 | | | | | (46) neq(nil, nil) = 0 % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | GROUND_INST: instantiating (7) with all_93_0, 0, nil, nil, simplifying % 38.81/5.91 | | | | | with (38), (46) gives: % 38.81/5.91 | | | | | (47) all_93_0 = 0 % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | REDUCE: (14), (47) imply: % 38.81/5.91 | | | | | (48) $false % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | CLOSE: (48) is inconsistent. % 38.81/5.91 | | | | | % 38.81/5.91 | | | | Case 2: % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | GROUND_INST: instantiating (21) with all_299_0, simplifying with (41), % 38.81/5.91 | | | | | (44) gives: % 38.81/5.91 | | | | | (49) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_299_0) = v0) % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | GROUND_INST: instantiating (19) with all_299_0, nil, simplifying with % 38.81/5.91 | | | | | (41), (44) gives: % 38.81/5.91 | | | | | (50) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 & ssItem(all_299_0) % 38.81/5.91 | | | | | = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | GROUND_INST: instantiating (20) with all_299_0, nil, simplifying with % 38.81/5.91 | | | | | (41), (44) gives: % 38.81/5.91 | | | | | (51) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 & ssItem(all_299_0) % 38.81/5.91 | | | | | = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = all_299_0)) % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | DELTA: instantiating (49) with fresh symbol all_518_0 gives: % 38.81/5.91 | | | | | (52) ~ (all_518_0 = 0) & ssItem(all_299_0) = all_518_0 % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | ALPHA: (52) implies: % 38.81/5.91 | | | | | (53) ~ (all_518_0 = 0) % 38.81/5.91 | | | | | (54) ssItem(all_299_0) = all_518_0 % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | DELTA: instantiating (50) with fresh symbols all_520_0, all_520_1 % 38.81/5.91 | | | | | gives: % 38.81/5.91 | | | | | (55) tl(nil) = all_520_0 & ssItem(all_299_0) = all_520_1 & % 38.81/5.91 | | | | | $i(all_520_0) & ( ~ (all_520_1 = 0) | all_520_0 = nil) % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | ALPHA: (55) implies: % 38.81/5.91 | | | | | (56) ssItem(all_299_0) = all_520_1 % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | DELTA: instantiating (51) with fresh symbols all_522_0, all_522_1 % 38.81/5.91 | | | | | gives: % 38.81/5.91 | | | | | (57) hd(nil) = all_522_0 & ssItem(all_299_0) = all_522_1 & % 38.81/5.91 | | | | | $i(all_522_0) & ( ~ (all_522_1 = 0) | all_522_0 = all_299_0) % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | ALPHA: (57) implies: % 38.81/5.91 | | | | | (58) ssItem(all_299_0) = all_522_1 % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | GROUND_INST: instantiating (5) with all_518_0, all_520_1, all_299_0, % 38.81/5.91 | | | | | simplifying with (54), (56) gives: % 38.81/5.91 | | | | | (59) all_520_1 = all_518_0 % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | GROUND_INST: instantiating (5) with 0, all_522_1, all_299_0, % 38.81/5.91 | | | | | simplifying with (42), (58) gives: % 38.81/5.91 | | | | | (60) all_522_1 = 0 % 38.81/5.91 | | | | | % 38.81/5.91 | | | | | GROUND_INST: instantiating (5) with all_520_1, all_522_1, all_299_0, % 38.81/5.91 | | | | | simplifying with (56), (58) gives: % 38.81/5.91 | | | | | (61) all_522_1 = all_520_1 % 38.81/5.91 | | | | | % 38.81/5.92 | | | | | COMBINE_EQS: (60), (61) imply: % 38.81/5.92 | | | | | (62) all_520_1 = 0 % 38.81/5.92 | | | | | % 38.81/5.92 | | | | | SIMP: (62) implies: % 38.81/5.92 | | | | | (63) all_520_1 = 0 % 38.81/5.92 | | | | | % 38.81/5.92 | | | | | COMBINE_EQS: (59), (63) imply: % 38.81/5.92 | | | | | (64) all_518_0 = 0 % 38.81/5.92 | | | | | % 38.81/5.92 | | | | | SIMP: (64) implies: % 38.81/5.92 | | | | | (65) all_518_0 = 0 % 38.81/5.92 | | | | | % 38.81/5.92 | | | | | REDUCE: (53), (65) imply: % 38.81/5.92 | | | | | (66) $false % 38.81/5.92 | | | | | % 38.81/5.92 | | | | | CLOSE: (66) is inconsistent. % 38.81/5.92 | | | | | % 38.81/5.92 | | | | End of split % 38.81/5.92 | | | | % 38.81/5.92 | | | Case 2: % 38.81/5.92 | | | | % 38.81/5.92 | | | | (67) all_97_0 = nil & all_93_1 = nil % 38.81/5.92 | | | | % 38.81/5.92 | | | | ALPHA: (67) implies: % 38.81/5.92 | | | | (68) all_97_0 = nil % 38.81/5.92 | | | | % 38.81/5.92 | | | | REDUCE: (16), (68) imply: % 38.81/5.92 | | | | (69) neq(nil, nil) = 0 % 38.81/5.92 | | | | % 38.81/5.92 | | | | GROUND_INST: instantiating (7) with all_93_0, 0, nil, nil, simplifying % 38.81/5.92 | | | | with (38), (69) gives: % 38.81/5.92 | | | | (70) all_93_0 = 0 % 38.81/5.92 | | | | % 38.93/5.92 | | | | REDUCE: (14), (70) imply: % 38.93/5.92 | | | | (71) $false % 38.93/5.92 | | | | % 38.93/5.92 | | | | CLOSE: (71) is inconsistent. % 38.93/5.92 | | | | % 38.93/5.92 | | | End of split % 38.93/5.92 | | | % 38.93/5.92 | | Case 2: % 38.93/5.92 | | | % 38.93/5.92 | | | (72) all_93_0 = 0 % 38.93/5.92 | | | % 38.93/5.92 | | | REDUCE: (14), (72) imply: % 38.93/5.92 | | | (73) $false % 38.93/5.92 | | | % 38.93/5.92 | | | CLOSE: (73) is inconsistent. % 38.93/5.92 | | | % 38.93/5.92 | | End of split % 38.93/5.92 | | % 38.93/5.92 | End of split % 38.93/5.92 | % 38.93/5.92 End of proof % 38.93/5.92 % SZS output end Proof for theBenchmark % 38.93/5.92 % 38.93/5.92 5326ms %------------------------------------------------------------------------------