%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC032+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 : n012.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 22.63s 3.79s % Output : Proof 30.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWC032+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n012.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Mon Aug 28 16:32:40 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.80/1.55 Prover 4: Preprocessing ... % 5.80/1.56 Prover 1: Preprocessing ... % 5.80/1.60 Prover 0: Preprocessing ... % 5.80/1.60 Prover 6: Preprocessing ... % 5.80/1.60 Prover 3: Preprocessing ... % 5.80/1.60 Prover 5: Preprocessing ... % 6.55/1.62 Prover 2: Preprocessing ... % 14.49/2.79 Prover 2: Proving ... % 14.49/2.81 Prover 5: Constructing countermodel ... % 16.09/2.90 Prover 1: Constructing countermodel ... % 16.09/2.94 Prover 6: Proving ... % 16.47/3.03 Prover 3: Constructing countermodel ... % 22.63/3.78 Prover 3: proved (3147ms) % 22.63/3.78 % 22.63/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.63/3.79 % 22.63/3.80 Prover 5: stopped % 22.63/3.80 Prover 2: stopped % 22.63/3.80 Prover 6: stopped % 23.00/3.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.00/3.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.00/3.81 Prover 4: Constructing countermodel ... % 23.00/3.81 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.00/3.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.02/3.95 Prover 0: Proving ... % 24.02/3.96 Prover 0: stopped % 24.02/3.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.93/4.06 Prover 10: Preprocessing ... % 24.93/4.07 Prover 8: Preprocessing ... % 24.93/4.07 Prover 7: Preprocessing ... % 24.93/4.08 Prover 11: Preprocessing ... % 25.31/4.12 Prover 13: Preprocessing ... % 26.35/4.38 Prover 10: Constructing countermodel ... % 27.06/4.42 Prover 7: Constructing countermodel ... % 28.43/4.55 Prover 8: Warning: ignoring some quantifiers % 28.43/4.56 Prover 8: Constructing countermodel ... % 29.16/4.67 Prover 13: Constructing countermodel ... % 29.69/4.70 Prover 1: Found proof (size 47) % 29.69/4.70 Prover 1: proved (4068ms) % 29.69/4.70 Prover 10: stopped % 29.69/4.70 Prover 13: stopped % 29.69/4.70 Prover 7: stopped % 29.69/4.70 Prover 4: stopped % 29.69/4.71 Prover 11: stopped % 29.69/4.71 Prover 8: stopped % 29.69/4.71 % 29.69/4.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.69/4.71 % 29.69/4.71 % SZS output start Proof for theBenchmark % 29.69/4.72 Assumptions after simplification: % 29.69/4.72 --------------------------------- % 29.69/4.72 % 29.69/4.72 (ax83) % 29.69/4.74 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 29.69/4.74 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 29.69/4.74 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1 % 29.69/4.74 = nil) | ~ (v0 = nil) | v2 = nil)))) % 29.69/4.74 % 29.69/4.74 (co1) % 29.69/4.75 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 29.69/4.75 0 & $i(v1) & ? [v2: any] : (strictorderedP(v0) = v2 & ? [v3: $i] : (v2 = % 29.69/4.75 0 & ssList(v3) = 0 & app(v0, v3) = v1 & $i(v3) & ! [v4: $i] : ! [v5: % 29.69/4.75 $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 % 29.69/4.75 = 0) & ssItem(v4) = v6) | ! [v6: $i] : ( ~ (app(v5, v6) = v3) | % 29.69/4.75 ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & ssList(v6) = v7) | ! % 29.69/4.75 [v7: $i] : ! [v8: $i] : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ? % 29.69/4.75 [v9: any] : ? [v10: any] : (lt(v7, v4) = v10 & ssItem(v7) = v9 % 29.69/4.75 & ( ~ (v9 = 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ (app(v11, % 29.69/4.75 v8) = v0) | ~ $i(v11) | ? [v12: int] : ( ~ (v12 = 0) % 29.69/4.75 & ssList(v11) = v12)))))))) & ( ~ (v0 = nil) | v1 = nil) % 29.69/4.75 & ((v1 = nil & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = nil)))))) % 29.69/4.75 % 29.69/4.75 (function-axioms) % 29.69/4.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 29.69/4.76 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 29.69/4.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.69/4.76 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 29.69/4.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.69/4.76 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 29.69/4.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.69/4.76 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 29.69/4.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.69/4.76 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 29.69/4.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 29.69/4.76 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 29.69/4.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 29.69/4.76 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 29.69/4.76 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 29.69/4.76 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 29.69/4.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.69/4.76 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 29.69/4.76 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 29.69/4.76 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 29.69/4.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 29.69/4.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 29.69/4.76 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 29.69/4.76 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 29.69/4.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 29.69/4.76 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.69/4.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 29.69/4.76 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.69/4.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 29.69/4.76 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.69/4.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 29.69/4.76 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.69/4.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 29.69/4.76 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.69/4.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 29.69/4.76 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.69/4.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 29.69/4.76 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.69/4.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 29.69/4.76 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.69/4.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 29.69/4.76 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 29.69/4.76 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 29.69/4.76 % 29.69/4.76 Further assumptions not needed in the proof: % 29.69/4.76 -------------------------------------------- % 29.69/4.76 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20, % 29.69/4.76 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, % 29.69/4.76 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, % 29.69/4.76 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, % 29.69/4.76 ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, % 29.69/4.76 ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, % 29.69/4.76 ax80, ax81, ax82, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, % 29.69/4.76 ax93, ax94, ax95 % 29.69/4.76 % 29.69/4.76 Those formulas are unsatisfiable: % 29.69/4.76 --------------------------------- % 29.69/4.76 % 29.69/4.76 Begin of proof % 29.69/4.76 | % 29.69/4.76 | ALPHA: (ax83) implies: % 29.69/4.76 | (1) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 29.69/4.76 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 29.69/4.76 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = % 29.69/4.76 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil)))) % 29.69/4.76 | % 29.69/4.76 | ALPHA: (co1) implies: % 29.69/4.77 | (2) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 29.69/4.77 | & $i(v1) & ? [v2: any] : (strictorderedP(v0) = v2 & ? [v3: $i] : % 29.69/4.77 | (v2 = 0 & ssList(v3) = 0 & app(v0, v3) = v1 & $i(v3) & ! [v4: % 29.69/4.77 | $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? % 29.69/4.77 | [v6: int] : ( ~ (v6 = 0) & ssItem(v4) = v6) | ! [v6: $i] : ( % 29.69/4.77 | ~ (app(v5, v6) = v3) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = % 29.69/4.77 | 0) & ssList(v6) = v7) | ! [v7: $i] : ! [v8: $i] : ( ~ % 29.69/4.77 | (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: any] : ? % 29.69/4.77 | [v10: any] : (lt(v7, v4) = v10 & ssItem(v7) = v9 & ( ~ % 29.69/4.77 | (v9 = 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ % 29.69/4.77 | (app(v11, v8) = v0) | ~ $i(v11) | ? [v12: int] : % 29.69/4.77 | ( ~ (v12 = 0) & ssList(v11) = v12)))))))) & ( ~ (v0 % 29.69/4.77 | = nil) | v1 = nil) & ((v1 = nil & ~ (v0 = nil)) | (v0 = nil % 30.05/4.77 | & ~ (v1 = nil)))))) % 30.05/4.77 | % 30.05/4.77 | ALPHA: (function-axioms) implies: % 30.05/4.77 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 30.05/4.77 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 30.05/4.77 | % 30.05/4.77 | DELTA: instantiating (2) with fresh symbol all_93_0 gives: % 30.05/4.77 | (4) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 30.05/4.77 | $i(v0) & ? [v1: any] : (strictorderedP(all_93_0) = v1 & ? [v2: $i] % 30.05/4.77 | : (v1 = 0 & ssList(v2) = 0 & app(all_93_0, v2) = v0 & $i(v2) & ! % 30.05/4.77 | [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | % 30.05/4.77 | ? [v5: int] : ( ~ (v5 = 0) & ssItem(v3) = v5) | ! [v5: $i] : ( % 30.05/4.77 | ~ (app(v4, v5) = v2) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = % 30.05/4.77 | 0) & ssList(v5) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 30.05/4.77 | (cons(v6, nil) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: % 30.05/4.77 | any] : (lt(v6, v3) = v9 & ssItem(v6) = v8 & ( ~ (v8 = 0) % 30.05/4.77 | | ! [v10: $i] : ( ~ (v9 = 0) | ~ (app(v10, v7) = % 30.05/4.77 | all_93_0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = % 30.05/4.77 | 0) & ssList(v10) = v11)))))))) & ( ~ (all_93_0 = % 30.05/4.77 | nil) | v0 = nil) & ((v0 = nil & ~ (all_93_0 = nil)) | % 30.05/4.77 | (all_93_0 = nil & ~ (v0 = nil))))) % 30.05/4.77 | % 30.05/4.77 | ALPHA: (4) implies: % 30.05/4.77 | (5) $i(all_93_0) % 30.05/4.77 | (6) ssList(all_93_0) = 0 % 30.05/4.78 | (7) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: any] : % 30.05/4.78 | (strictorderedP(all_93_0) = v1 & ? [v2: $i] : (v1 = 0 & ssList(v2) = % 30.05/4.78 | 0 & app(all_93_0, v2) = v0 & $i(v2) & ! [v3: $i] : ! [v4: $i] : % 30.05/4.78 | ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = % 30.05/4.78 | 0) & ssItem(v3) = v5) | ! [v5: $i] : ( ~ (app(v4, v5) = % 30.05/4.78 | v2) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v5) % 30.05/4.78 | = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v6, nil) = % 30.05/4.78 | v7) | ~ $i(v6) | ? [v8: any] : ? [v9: any] : (lt(v6, % 30.05/4.78 | v3) = v9 & ssItem(v6) = v8 & ( ~ (v8 = 0) | ! [v10: % 30.05/4.78 | $i] : ( ~ (v9 = 0) | ~ (app(v10, v7) = all_93_0) | % 30.05/4.78 | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & % 30.05/4.78 | ssList(v10) = v11)))))))) & ( ~ (all_93_0 = nil) | % 30.05/4.78 | v0 = nil) & ((v0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & % 30.05/4.78 | ~ (v0 = nil))))) % 30.05/4.78 | % 30.05/4.78 | DELTA: instantiating (7) with fresh symbol all_97_0 gives: % 30.05/4.78 | (8) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: any] : % 30.05/4.78 | (strictorderedP(all_93_0) = v0 & ? [v1: $i] : (v0 = 0 & ssList(v1) = 0 % 30.05/4.78 | & app(all_93_0, v1) = all_97_0 & $i(v1) & ! [v2: $i] : ! [v3: $i] % 30.05/4.78 | : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 30.05/4.78 | 0) & ssItem(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, v4) = v1) % 30.05/4.78 | | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v4) = v5) | % 30.05/4.78 | ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v5, nil) = v6) | ~ $i(v5) % 30.05/4.78 | | ? [v7: any] : ? [v8: any] : (lt(v5, v2) = v8 & ssItem(v5) % 30.05/4.78 | = v7 & ( ~ (v7 = 0) | ! [v9: $i] : ( ~ (v8 = 0) | ~ % 30.05/4.78 | (app(v9, v6) = all_93_0) | ~ $i(v9) | ? [v10: int] : % 30.05/4.78 | ( ~ (v10 = 0) & ssList(v9) = v10)))))))) & ( ~ % 30.05/4.78 | (all_93_0 = nil) | all_97_0 = nil) & ((all_97_0 = nil & ~ % 30.05/4.78 | (all_93_0 = nil)) | (all_93_0 = nil & ~ (all_97_0 = nil)))) % 30.05/4.78 | % 30.05/4.78 | ALPHA: (8) implies: % 30.05/4.78 | (9) ? [v0: any] : (strictorderedP(all_93_0) = v0 & ? [v1: $i] : (v0 = 0 & % 30.05/4.78 | ssList(v1) = 0 & app(all_93_0, v1) = all_97_0 & $i(v1) & ! [v2: % 30.05/4.78 | $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) | ? % 30.05/4.78 | [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : ( ~ % 30.05/4.78 | (app(v3, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 30.05/4.78 | ssList(v4) = v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v5, % 30.05/4.78 | nil) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : % 30.05/4.78 | (lt(v5, v2) = v8 & ssItem(v5) = v7 & ( ~ (v7 = 0) | ! [v9: % 30.05/4.78 | $i] : ( ~ (v8 = 0) | ~ (app(v9, v6) = all_93_0) | ~ % 30.05/4.78 | $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & ssList(v9) = % 30.05/4.78 | v10)))))))) & ( ~ (all_93_0 = nil) | all_97_0 = nil) % 30.05/4.78 | & ((all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 30.05/4.78 | (all_97_0 = nil)))) % 30.05/4.78 | % 30.05/4.78 | DELTA: instantiating (9) with fresh symbol all_99_0 gives: % 30.05/4.79 | (10) strictorderedP(all_93_0) = all_99_0 & ? [v0: $i] : (all_99_0 = 0 & % 30.05/4.79 | ssList(v0) = 0 & app(all_93_0, v0) = all_97_0 & $i(v0) & ! [v1: $i] % 30.05/4.79 | : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int] % 30.05/4.79 | : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: $i] : ( ~ (app(v2, v3) % 30.05/4.79 | = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) = % 30.05/4.79 | v4) | ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | % 30.05/4.79 | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (lt(v4, v1) = v7 & % 30.05/4.79 | ssItem(v4) = v6 & ( ~ (v6 = 0) | ! [v8: $i] : ( ~ (v7 = 0) % 30.05/4.79 | | ~ (app(v8, v5) = all_93_0) | ~ $i(v8) | ? [v9: int] % 30.05/4.79 | : ( ~ (v9 = 0) & ssList(v8) = v9)))))))) & ( ~ (all_93_0 % 30.05/4.79 | = nil) | all_97_0 = nil) & ((all_97_0 = nil & ~ (all_93_0 = nil)) % 30.05/4.79 | | (all_93_0 = nil & ~ (all_97_0 = nil))) % 30.05/4.79 | % 30.05/4.79 | ALPHA: (10) implies: % 30.05/4.79 | (11) (all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 30.05/4.79 | (all_97_0 = nil)) % 30.05/4.79 | (12) ~ (all_93_0 = nil) | all_97_0 = nil % 30.05/4.79 | (13) ? [v0: $i] : (all_99_0 = 0 & ssList(v0) = 0 & app(all_93_0, v0) = % 30.05/4.79 | all_97_0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = % 30.05/4.79 | v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) % 30.05/4.79 | | ! [v3: $i] : ( ~ (app(v2, v3) = v0) | ~ $i(v3) | ? [v4: int] % 30.05/4.79 | : ( ~ (v4 = 0) & ssList(v3) = v4) | ! [v4: $i] : ! [v5: $i] : % 30.05/4.79 | ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: % 30.05/4.79 | any] : (lt(v4, v1) = v7 & ssItem(v4) = v6 & ( ~ (v6 = 0) | % 30.05/4.79 | ! [v8: $i] : ( ~ (v7 = 0) | ~ (app(v8, v5) = all_93_0) | % 30.05/4.79 | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v8) = % 30.05/4.79 | v9)))))))) % 30.05/4.79 | % 30.05/4.79 | DELTA: instantiating (13) with fresh symbol all_101_0 gives: % 30.05/4.79 | (14) all_99_0 = 0 & ssList(all_101_0) = 0 & app(all_93_0, all_101_0) = % 30.05/4.79 | all_97_0 & $i(all_101_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, % 30.05/4.79 | nil) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 30.05/4.79 | ssItem(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = all_101_0) | % 30.05/4.79 | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3) | ! % 30.05/4.79 | [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? % 30.05/4.79 | [v5: any] : ? [v6: any] : (lt(v3, v0) = v6 & ssItem(v3) = v5 & % 30.05/4.79 | ( ~ (v5 = 0) | ! [v7: $i] : ( ~ (v6 = 0) | ~ (app(v7, v4) = % 30.05/4.79 | all_93_0) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & % 30.05/4.79 | ssList(v7) = v8))))))) % 30.05/4.79 | % 30.05/4.79 | ALPHA: (14) implies: % 30.05/4.79 | (15) $i(all_101_0) % 30.05/4.79 | (16) app(all_93_0, all_101_0) = all_97_0 % 30.05/4.79 | (17) ssList(all_101_0) = 0 % 30.05/4.79 | % 30.05/4.79 | GROUND_INST: instantiating (1) with all_93_0, simplifying with (5), (6) gives: % 30.05/4.79 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_93_0, v0) = v1) | ~ $i(v0) | % 30.05/4.79 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) | % 30.05/4.79 | (v0 = nil & all_93_0 = nil)) & ( ~ (v0 = nil) | ~ (all_93_0 = % 30.05/4.79 | nil) | v1 = nil))) % 30.05/4.79 | % 30.05/4.79 | GROUND_INST: instantiating (18) with all_101_0, all_97_0, simplifying with % 30.05/4.79 | (15), (16) gives: % 30.05/4.80 | (19) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) | (( ~ % 30.05/4.80 | (all_101_0 = nil) | ~ (all_93_0 = nil) | all_97_0 = nil) & ( ~ % 30.05/4.80 | (all_97_0 = nil) | (all_101_0 = nil & all_93_0 = nil))) % 30.05/4.80 | % 30.05/4.80 | BETA: splitting (12) gives: % 30.05/4.80 | % 30.05/4.80 | Case 1: % 30.05/4.80 | | % 30.05/4.80 | | (20) ~ (all_93_0 = nil) % 30.05/4.80 | | % 30.05/4.80 | | BETA: splitting (11) gives: % 30.05/4.80 | | % 30.05/4.80 | | Case 1: % 30.05/4.80 | | | % 30.05/4.80 | | | (21) all_97_0 = nil & ~ (all_93_0 = nil) % 30.05/4.80 | | | % 30.05/4.80 | | | ALPHA: (21) implies: % 30.05/4.80 | | | (22) all_97_0 = nil % 30.19/4.80 | | | % 30.19/4.80 | | | BETA: splitting (19) gives: % 30.19/4.80 | | | % 30.19/4.80 | | | Case 1: % 30.19/4.80 | | | | % 30.19/4.80 | | | | (23) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) % 30.19/4.80 | | | | % 30.19/4.80 | | | | DELTA: instantiating (23) with fresh symbol all_357_0 gives: % 30.19/4.80 | | | | (24) ~ (all_357_0 = 0) & ssList(all_101_0) = all_357_0 % 30.19/4.80 | | | | % 30.19/4.80 | | | | ALPHA: (24) implies: % 30.19/4.80 | | | | (25) ~ (all_357_0 = 0) % 30.19/4.80 | | | | (26) ssList(all_101_0) = all_357_0 % 30.19/4.80 | | | | % 30.19/4.80 | | | | GROUND_INST: instantiating (3) with 0, all_357_0, all_101_0, simplifying % 30.19/4.80 | | | | with (17), (26) gives: % 30.19/4.80 | | | | (27) all_357_0 = 0 % 30.19/4.80 | | | | % 30.19/4.80 | | | | REDUCE: (25), (27) imply: % 30.19/4.80 | | | | (28) $false % 30.19/4.80 | | | | % 30.19/4.80 | | | | CLOSE: (28) is inconsistent. % 30.19/4.80 | | | | % 30.19/4.80 | | | Case 2: % 30.19/4.80 | | | | % 30.19/4.80 | | | | (29) ( ~ (all_101_0 = nil) | ~ (all_93_0 = nil) | all_97_0 = nil) & % 30.19/4.80 | | | | ( ~ (all_97_0 = nil) | (all_101_0 = nil & all_93_0 = nil)) % 30.19/4.80 | | | | % 30.19/4.80 | | | | ALPHA: (29) implies: % 30.19/4.80 | | | | (30) ~ (all_97_0 = nil) | (all_101_0 = nil & all_93_0 = nil) % 30.19/4.80 | | | | % 30.19/4.80 | | | | BETA: splitting (30) gives: % 30.19/4.80 | | | | % 30.19/4.80 | | | | Case 1: % 30.19/4.80 | | | | | % 30.19/4.80 | | | | | (31) ~ (all_97_0 = nil) % 30.19/4.80 | | | | | % 30.19/4.80 | | | | | REDUCE: (22), (31) imply: % 30.19/4.80 | | | | | (32) $false % 30.19/4.80 | | | | | % 30.19/4.80 | | | | | CLOSE: (32) is inconsistent. % 30.19/4.80 | | | | | % 30.19/4.80 | | | | Case 2: % 30.19/4.80 | | | | | % 30.19/4.80 | | | | | (33) all_101_0 = nil & all_93_0 = nil % 30.19/4.80 | | | | | % 30.19/4.80 | | | | | ALPHA: (33) implies: % 30.19/4.80 | | | | | (34) all_93_0 = nil % 30.19/4.80 | | | | | % 30.19/4.80 | | | | | REF_CLOSE: (11), (22), (34) are inconsistent by sub-proof #1. % 30.19/4.80 | | | | | % 30.19/4.80 | | | | End of split % 30.19/4.80 | | | | % 30.19/4.80 | | | End of split % 30.19/4.80 | | | % 30.19/4.80 | | Case 2: % 30.19/4.80 | | | % 30.19/4.80 | | | (35) all_93_0 = nil & ~ (all_97_0 = nil) % 30.19/4.80 | | | % 30.19/4.80 | | | ALPHA: (35) implies: % 30.19/4.80 | | | (36) all_93_0 = nil % 30.19/4.80 | | | % 30.19/4.80 | | | REDUCE: (20), (36) imply: % 30.19/4.80 | | | (37) $false % 30.19/4.80 | | | % 30.19/4.80 | | | CLOSE: (37) is inconsistent. % 30.19/4.80 | | | % 30.19/4.80 | | End of split % 30.19/4.80 | | % 30.19/4.80 | Case 2: % 30.19/4.80 | | % 30.19/4.80 | | (38) all_93_0 = nil % 30.19/4.80 | | (39) all_97_0 = nil % 30.19/4.80 | | % 30.19/4.80 | | REF_CLOSE: (11), (38), (39) are inconsistent by sub-proof #1. % 30.19/4.80 | | % 30.19/4.80 | End of split % 30.19/4.80 | % 30.19/4.80 End of proof % 30.19/4.80 % 30.19/4.80 Sub-proof #1 shows that the following formulas are inconsistent: % 30.19/4.80 ---------------------------------------------------------------- % 30.19/4.80 (1) (all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ (all_97_0 = % 30.19/4.80 nil)) % 30.19/4.80 (2) all_93_0 = nil % 30.19/4.80 (3) all_97_0 = nil % 30.19/4.80 % 30.19/4.80 Begin of proof % 30.19/4.80 | % 30.19/4.80 | BETA: splitting (1) gives: % 30.19/4.80 | % 30.19/4.80 | Case 1: % 30.19/4.80 | | % 30.19/4.80 | | (4) all_97_0 = nil & ~ (all_93_0 = nil) % 30.19/4.80 | | % 30.19/4.80 | | ALPHA: (4) implies: % 30.19/4.80 | | (5) ~ (all_93_0 = nil) % 30.19/4.80 | | % 30.19/4.80 | | REDUCE: (2), (5) imply: % 30.19/4.80 | | (6) $false % 30.19/4.80 | | % 30.19/4.80 | | CLOSE: (6) is inconsistent. % 30.19/4.80 | | % 30.19/4.80 | Case 2: % 30.19/4.80 | | % 30.19/4.80 | | (7) all_93_0 = nil & ~ (all_97_0 = nil) % 30.19/4.80 | | % 30.19/4.81 | | ALPHA: (7) implies: % 30.19/4.81 | | (8) ~ (all_97_0 = nil) % 30.19/4.81 | | % 30.19/4.81 | | REDUCE: (3), (8) imply: % 30.19/4.81 | | (9) $false % 30.19/4.81 | | % 30.19/4.81 | | CLOSE: (9) is inconsistent. % 30.19/4.81 | | % 30.19/4.81 | End of split % 30.19/4.81 | % 30.19/4.81 End of proof % 30.19/4.81 % SZS output end Proof for theBenchmark % 30.19/4.81 % 30.19/4.81 4192ms %------------------------------------------------------------------------------