%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC042+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 20:49:21 EDT 2023 % Result : Theorem 22.26s 3.68s % Output : Proof 27.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC042+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n022.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Mon Aug 28 16:14:24 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 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 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 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 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 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 % 6.40/1.57 Prover 3: Preprocessing ... % 6.40/1.57 Prover 6: Preprocessing ... % 6.40/1.57 Prover 5: Preprocessing ... % 6.40/1.57 Prover 2: Preprocessing ... % 6.92/1.59 Prover 0: Preprocessing ... % 6.92/1.59 Prover 1: Preprocessing ... % 6.92/1.60 Prover 4: Preprocessing ... % 16.08/2.80 Prover 2: Proving ... % 16.08/2.84 Prover 1: Constructing countermodel ... % 16.47/2.88 Prover 5: Constructing countermodel ... % 17.48/3.02 Prover 6: Proving ... % 17.87/3.04 Prover 3: Constructing countermodel ... % 22.26/3.68 Prover 3: proved (3053ms) % 22.26/3.68 % 22.26/3.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.26/3.68 % 22.26/3.68 Prover 2: stopped % 22.26/3.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.26/3.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.26/3.69 Prover 5: stopped % 22.69/3.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.69/3.70 Prover 6: stopped % 22.69/3.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.20/3.80 Prover 4: Constructing countermodel ... % 23.44/3.87 Prover 0: Proving ... % 24.21/3.92 Prover 0: stopped % 24.42/3.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.42/3.96 Prover 1: Found proof (size 23) % 24.42/3.96 Prover 1: proved (3336ms) % 24.42/3.96 Prover 4: stopped % 24.42/3.97 Prover 7: Preprocessing ... % 24.42/3.99 Prover 10: Preprocessing ... % 24.42/4.01 Prover 11: Preprocessing ... % 24.42/4.02 Prover 8: Preprocessing ... % 25.15/4.04 Prover 13: Preprocessing ... % 25.15/4.06 Prover 7: stopped % 25.62/4.10 Prover 10: stopped % 26.07/4.16 Prover 13: stopped % 26.26/4.22 Prover 11: stopped % 26.83/4.33 Prover 8: Warning: ignoring some quantifiers % 26.83/4.34 Prover 8: Constructing countermodel ... % 26.83/4.35 Prover 8: stopped % 26.83/4.35 % 26.83/4.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.83/4.35 % 26.83/4.35 % SZS output start Proof for theBenchmark % 26.83/4.36 Assumptions after simplification: % 26.83/4.36 --------------------------------- % 26.83/4.36 % 26.83/4.36 (ax83) % 27.11/4.40 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! % 27.11/4.40 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) % 27.11/4.40 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1 % 27.11/4.40 = nil) | ~ (v0 = nil) | v2 = nil)))) % 27.11/4.40 % 27.11/4.40 (co1) % 27.11/4.41 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 27.11/4.41 0 & $i(v1) & ? [v2: any] : (v1 = nil & ~ (v0 = nil) & totalorderedP(v0) % 27.11/4.41 = v2 & ssList(nil) = 0 & ? [v3: $i] : (v2 = 0 & ssList(v3) = 0 & % 27.11/4.41 app(v0, v3) = nil & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, % 27.11/4.41 nil) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & % 27.11/4.41 ssItem(v4) = v6) | ! [v6: $i] : ( ~ (app(v5, v6) = v3) | ~ % 27.11/4.41 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & ssList(v6) = v7) | ! [v7: % 27.11/4.41 $i] : ! [v8: $i] : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ? % 27.11/4.41 [v9: any] : ? [v10: any] : (leq(v7, v4) = v10 & ssItem(v7) = v9 % 27.11/4.41 & ( ~ (v9 = 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ (app(v11, % 27.11/4.41 v8) = v0) | ~ $i(v11) | ? [v12: int] : ( ~ (v12 = 0) % 27.11/4.41 & ssList(v11) = v12))))))))))) % 27.11/4.41 % 27.11/4.41 (function-axioms) % 27.11/4.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 27.11/4.42 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 27.11/4.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 27.11/4.42 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 27.11/4.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 27.11/4.42 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 27.11/4.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 27.11/4.42 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 27.11/4.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 27.11/4.42 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 27.11/4.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 27.11/4.42 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 27.11/4.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 27.11/4.42 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 27.11/4.42 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 27.11/4.42 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 27.11/4.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 27.11/4.42 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 27.11/4.42 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 27.11/4.42 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 27.11/4.42 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 27.11/4.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 27.11/4.42 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 27.11/4.42 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 27.11/4.42 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 27.11/4.42 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.11/4.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 27.11/4.42 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.11/4.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 27.11/4.42 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.11/4.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 27.11/4.42 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.11/4.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 27.11/4.42 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.11/4.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 27.11/4.42 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.11/4.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 27.11/4.42 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.11/4.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 27.11/4.42 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 27.11/4.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 27.11/4.42 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 27.11/4.42 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 27.11/4.42 % 27.11/4.42 Further assumptions not needed in the proof: % 27.11/4.42 -------------------------------------------- % 27.11/4.42 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20, % 27.11/4.42 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, % 27.11/4.42 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, % 27.11/4.42 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, % 27.11/4.42 ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, % 27.11/4.42 ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, % 27.11/4.42 ax80, ax81, ax82, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, % 27.11/4.42 ax93, ax94, ax95 % 27.11/4.42 % 27.11/4.42 Those formulas are unsatisfiable: % 27.11/4.42 --------------------------------- % 27.11/4.42 % 27.11/4.42 Begin of proof % 27.11/4.42 | % 27.11/4.42 | ALPHA: (ax83) implies: % 27.11/4.42 | (1) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: % 27.11/4.42 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = % 27.11/4.42 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = % 27.11/4.42 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil)))) % 27.11/4.42 | % 27.11/4.42 | ALPHA: (co1) implies: % 27.11/4.43 | (2) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 27.11/4.43 | & $i(v1) & ? [v2: any] : (v1 = nil & ~ (v0 = nil) & % 27.11/4.43 | totalorderedP(v0) = v2 & ssList(nil) = 0 & ? [v3: $i] : (v2 = 0 % 27.11/4.43 | & ssList(v3) = 0 & app(v0, v3) = nil & $i(v3) & ! [v4: $i] : % 27.11/4.43 | ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: % 27.11/4.43 | int] : ( ~ (v6 = 0) & ssItem(v4) = v6) | ! [v6: $i] : ( ~ % 27.11/4.43 | (app(v5, v6) = v3) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = % 27.11/4.43 | 0) & ssList(v6) = v7) | ! [v7: $i] : ! [v8: $i] : ( ~ % 27.11/4.43 | (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: any] : ? % 27.11/4.43 | [v10: any] : (leq(v7, v4) = v10 & ssItem(v7) = v9 & ( ~ % 27.11/4.43 | (v9 = 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ % 27.11/4.43 | (app(v11, v8) = v0) | ~ $i(v11) | ? [v12: int] : % 27.11/4.43 | ( ~ (v12 = 0) & ssList(v11) = v12))))))))))) % 27.11/4.43 | % 27.11/4.43 | ALPHA: (function-axioms) implies: % 27.11/4.43 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 27.11/4.43 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 27.11/4.43 | % 27.11/4.43 | DELTA: instantiating (2) with fresh symbol all_93_0 gives: % 27.11/4.43 | (4) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 27.11/4.43 | $i(v0) & ? [v1: any] : (v0 = nil & ~ (all_93_0 = nil) & % 27.11/4.43 | totalorderedP(all_93_0) = v1 & ssList(nil) = 0 & ? [v2: $i] : (v1 % 27.11/4.43 | = 0 & ssList(v2) = 0 & app(all_93_0, v2) = nil & $i(v2) & ! [v3: % 27.11/4.43 | $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? % 27.11/4.43 | [v5: int] : ( ~ (v5 = 0) & ssItem(v3) = v5) | ! [v5: $i] : ( ~ % 27.11/4.43 | (app(v4, v5) = v2) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) % 27.11/4.43 | & ssList(v5) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~ % 27.11/4.43 | (cons(v6, nil) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: % 27.11/4.43 | any] : (leq(v6, v3) = v9 & ssItem(v6) = v8 & ( ~ (v8 = 0) % 27.11/4.43 | | ! [v10: $i] : ( ~ (v9 = 0) | ~ (app(v10, v7) = % 27.11/4.43 | all_93_0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = % 27.11/4.43 | 0) & ssList(v10) = v11)))))))))) % 27.11/4.43 | % 27.11/4.43 | ALPHA: (4) implies: % 27.11/4.43 | (5) $i(all_93_0) % 27.11/4.43 | (6) ssList(all_93_0) = 0 % 27.11/4.44 | (7) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: any] : (v0 = nil & ~ % 27.11/4.44 | (all_93_0 = nil) & totalorderedP(all_93_0) = v1 & ssList(nil) = 0 & % 27.11/4.44 | ? [v2: $i] : (v1 = 0 & ssList(v2) = 0 & app(all_93_0, v2) = nil & % 27.11/4.44 | $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | % 27.11/4.44 | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssItem(v3) = v5) | ! % 27.11/4.44 | [v5: $i] : ( ~ (app(v4, v5) = v2) | ~ $i(v5) | ? [v6: int] : % 27.11/4.44 | ( ~ (v6 = 0) & ssList(v5) = v6) | ! [v6: $i] : ! [v7: $i] : % 27.11/4.44 | ( ~ (cons(v6, nil) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9: % 27.11/4.44 | any] : (leq(v6, v3) = v9 & ssItem(v6) = v8 & ( ~ (v8 = 0) % 27.11/4.44 | | ! [v10: $i] : ( ~ (v9 = 0) | ~ (app(v10, v7) = % 27.11/4.44 | all_93_0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = % 27.11/4.44 | 0) & ssList(v10) = v11)))))))))) % 27.11/4.44 | % 27.11/4.44 | DELTA: instantiating (7) with fresh symbol all_97_0 gives: % 27.11/4.44 | (8) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: any] : (all_97_0 = nil & % 27.11/4.44 | ~ (all_93_0 = nil) & totalorderedP(all_93_0) = v0 & ssList(nil) = 0 & % 27.11/4.44 | ? [v1: $i] : (v0 = 0 & ssList(v1) = 0 & app(all_93_0, v1) = nil & % 27.11/4.44 | $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ % 27.11/4.44 | $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: % 27.11/4.44 | $i] : ( ~ (app(v3, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ % 27.11/4.44 | (v5 = 0) & ssList(v4) = v5) | ! [v5: $i] : ! [v6: $i] : ( ~ % 27.11/4.44 | (cons(v5, nil) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: % 27.11/4.44 | any] : (leq(v5, v2) = v8 & ssItem(v5) = v7 & ( ~ (v7 = 0) | % 27.11/4.44 | ! [v9: $i] : ( ~ (v8 = 0) | ~ (app(v9, v6) = all_93_0) % 27.11/4.44 | | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & % 27.11/4.44 | ssList(v9) = v10))))))))) % 27.11/4.44 | % 27.11/4.44 | ALPHA: (8) implies: % 27.11/4.44 | (9) ? [v0: any] : (all_97_0 = nil & ~ (all_93_0 = nil) & % 27.11/4.44 | totalorderedP(all_93_0) = v0 & ssList(nil) = 0 & ? [v1: $i] : (v0 = % 27.11/4.44 | 0 & ssList(v1) = 0 & app(all_93_0, v1) = nil & $i(v1) & ! [v2: $i] % 27.11/4.44 | : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) | ? [v4: int] % 27.11/4.44 | : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, % 27.11/4.44 | v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 27.11/4.44 | ssList(v4) = v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v5, % 27.11/4.44 | nil) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : % 27.11/4.44 | (leq(v5, v2) = v8 & ssItem(v5) = v7 & ( ~ (v7 = 0) | ! [v9: % 27.11/4.44 | $i] : ( ~ (v8 = 0) | ~ (app(v9, v6) = all_93_0) | ~ % 27.11/4.44 | $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & ssList(v9) = % 27.11/4.44 | v10))))))))) % 27.11/4.44 | % 27.11/4.44 | DELTA: instantiating (9) with fresh symbol all_99_0 gives: % 27.11/4.44 | (10) all_97_0 = nil & ~ (all_93_0 = nil) & totalorderedP(all_93_0) = % 27.11/4.44 | all_99_0 & ssList(nil) = 0 & ? [v0: $i] : (all_99_0 = 0 & ssList(v0) % 27.11/4.44 | = 0 & app(all_93_0, v0) = nil & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 27.11/4.44 | ( ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 27.11/4.45 | ssItem(v1) = v3) | ! [v3: $i] : ( ~ (app(v2, v3) = v0) | ~ % 27.11/4.45 | $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) = v4) | ! % 27.11/4.45 | [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | % 27.11/4.45 | ? [v6: any] : ? [v7: any] : (leq(v4, v1) = v7 & ssItem(v4) = % 27.11/4.45 | v6 & ( ~ (v6 = 0) | ! [v8: $i] : ( ~ (v7 = 0) | ~ (app(v8, % 27.11/4.45 | v5) = all_93_0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 % 27.11/4.45 | = 0) & ssList(v8) = v9)))))))) % 27.11/4.45 | % 27.11/4.45 | ALPHA: (10) implies: % 27.11/4.45 | (11) ~ (all_93_0 = nil) % 27.11/4.45 | (12) ? [v0: $i] : (all_99_0 = 0 & ssList(v0) = 0 & app(all_93_0, v0) = nil % 27.11/4.45 | & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~ % 27.11/4.45 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: % 27.11/4.45 | $i] : ( ~ (app(v2, v3) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ % 27.11/4.45 | (v4 = 0) & ssList(v3) = v4) | ! [v4: $i] : ! [v5: $i] : ( ~ % 27.11/4.45 | (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] % 27.11/4.45 | : (leq(v4, v1) = v7 & ssItem(v4) = v6 & ( ~ (v6 = 0) | ! [v8: % 27.11/4.45 | $i] : ( ~ (v7 = 0) | ~ (app(v8, v5) = all_93_0) | ~ % 27.11/4.45 | $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v8) = % 27.11/4.45 | v9)))))))) % 27.11/4.45 | % 27.11/4.45 | DELTA: instantiating (12) with fresh symbol all_101_0 gives: % 27.11/4.45 | (13) all_99_0 = 0 & ssList(all_101_0) = 0 & app(all_93_0, all_101_0) = nil % 27.11/4.45 | & $i(all_101_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) % 27.11/4.45 | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | ! % 27.11/4.45 | [v2: $i] : ( ~ (app(v1, v2) = all_101_0) | ~ $i(v2) | ? [v3: int] % 27.11/4.45 | : ( ~ (v3 = 0) & ssList(v2) = v3) | ! [v3: $i] : ! [v4: $i] : ( % 27.11/4.45 | ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] % 27.11/4.45 | : (leq(v3, v0) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7: % 27.11/4.45 | $i] : ( ~ (v6 = 0) | ~ (app(v7, v4) = all_93_0) | ~ % 27.11/4.45 | $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v7) = % 27.11/4.45 | v8))))))) % 27.11/4.45 | % 27.11/4.45 | ALPHA: (13) implies: % 27.11/4.45 | (14) $i(all_101_0) % 27.11/4.45 | (15) app(all_93_0, all_101_0) = nil % 27.11/4.45 | (16) ssList(all_101_0) = 0 % 27.11/4.45 | % 27.11/4.45 | GROUND_INST: instantiating (1) with all_93_0, simplifying with (5), (6) gives: % 27.11/4.45 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_93_0, v0) = v1) | ~ $i(v0) | % 27.11/4.45 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) | % 27.11/4.45 | (v0 = nil & all_93_0 = nil)) & ( ~ (v0 = nil) | ~ (all_93_0 = % 27.11/4.45 | nil) | v1 = nil))) % 27.11/4.45 | % 27.11/4.45 | GROUND_INST: instantiating (17) with all_101_0, nil, simplifying with (14), % 27.11/4.45 | (15) gives: % 27.11/4.45 | (18) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) | (all_101_0 = % 27.11/4.45 | nil & all_93_0 = nil) % 27.11/4.45 | % 27.11/4.45 | BETA: splitting (18) gives: % 27.11/4.45 | % 27.11/4.45 | Case 1: % 27.11/4.45 | | % 27.11/4.45 | | (19) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) % 27.11/4.45 | | % 27.11/4.45 | | DELTA: instantiating (19) with fresh symbol all_249_0 gives: % 27.11/4.45 | | (20) ~ (all_249_0 = 0) & ssList(all_101_0) = all_249_0 % 27.11/4.45 | | % 27.11/4.46 | | ALPHA: (20) implies: % 27.11/4.46 | | (21) ~ (all_249_0 = 0) % 27.11/4.46 | | (22) ssList(all_101_0) = all_249_0 % 27.11/4.46 | | % 27.11/4.46 | | GROUND_INST: instantiating (3) with 0, all_249_0, all_101_0, simplifying % 27.11/4.46 | | with (16), (22) gives: % 27.11/4.46 | | (23) all_249_0 = 0 % 27.11/4.46 | | % 27.11/4.46 | | REDUCE: (21), (23) imply: % 27.11/4.46 | | (24) $false % 27.11/4.46 | | % 27.11/4.46 | | CLOSE: (24) is inconsistent. % 27.11/4.46 | | % 27.11/4.46 | Case 2: % 27.11/4.46 | | % 27.11/4.46 | | (25) all_101_0 = nil & all_93_0 = nil % 27.11/4.46 | | % 27.11/4.46 | | ALPHA: (25) implies: % 27.11/4.46 | | (26) all_93_0 = nil % 27.11/4.46 | | % 27.11/4.46 | | REDUCE: (11), (26) imply: % 27.11/4.46 | | (27) $false % 27.11/4.46 | | % 27.11/4.46 | | CLOSE: (27) is inconsistent. % 27.11/4.46 | | % 27.11/4.46 | End of split % 27.11/4.46 | % 27.11/4.46 End of proof % 27.11/4.46 % SZS output end Proof for theBenchmark % 27.11/4.46 % 27.11/4.46 3859ms %------------------------------------------------------------------------------