%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC027+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 : n006.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 20:49:16 EDT 2023 % Result : Theorem 41.53s 6.44s % Output : Proof 80.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.12 % Problem : SWC027+1 : TPTP v8.1.2. Released v2.4.0. % 0.09/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n006.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 17:37:21 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.62 ________ _____ % 0.18/0.62 ___ __ \_________(_)________________________________ % 0.18/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.62 % 0.18/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.62 (2023-06-19) % 0.18/0.62 % 0.18/0.62 (c) Philipp Rümmer, 2009-2023 % 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.62 Amanda Stjerna. % 0.18/0.62 Free software under BSD-3-Clause. % 0.18/0.62 % 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.62 % 0.18/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.64 Running up to 7 provers in parallel. % 0.18/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.18/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 6.38/1.68 Prover 1: Preprocessing ... % 6.38/1.70 Prover 4: Preprocessing ... % 6.38/1.72 Prover 5: Preprocessing ... % 6.38/1.72 Prover 3: Preprocessing ... % 6.38/1.72 Prover 2: Preprocessing ... % 6.38/1.72 Prover 0: Preprocessing ... % 6.38/1.72 Prover 6: Preprocessing ... % 21.37/3.79 Prover 2: Proving ... % 21.37/3.85 Prover 5: Constructing countermodel ... % 21.37/3.88 Prover 3: Constructing countermodel ... % 21.37/3.90 Prover 1: Constructing countermodel ... % 22.48/3.97 Prover 6: Proving ... % 33.09/5.36 Prover 4: Constructing countermodel ... % 35.43/5.64 Prover 0: Proving ... % 41.53/6.44 Prover 3: proved (5778ms) % 41.53/6.44 % 41.53/6.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 41.53/6.44 % 41.53/6.45 Prover 2: stopped % 41.53/6.46 Prover 5: stopped % 41.53/6.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 41.53/6.47 Prover 6: stopped % 41.53/6.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 41.53/6.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 41.53/6.47 Prover 0: stopped % 41.53/6.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 41.53/6.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 44.34/6.83 Prover 8: Preprocessing ... % 44.34/6.86 Prover 10: Preprocessing ... % 45.13/6.95 Prover 13: Preprocessing ... % 45.13/6.98 Prover 7: Preprocessing ... % 45.70/7.00 Prover 11: Preprocessing ... % 47.44/7.23 Prover 10: Constructing countermodel ... % 47.44/7.31 Prover 13: Constructing countermodel ... % 48.21/7.32 Prover 7: Constructing countermodel ... % 48.86/7.43 Prover 8: Warning: ignoring some quantifiers % 48.86/7.46 Prover 8: Constructing countermodel ... % 59.11/8.74 Prover 11: Constructing countermodel ... % 78.16/11.23 Prover 13: stopped % 78.16/11.24 Prover 1: Found proof (size 127) % 78.16/11.24 Prover 1: proved (10598ms) % 78.16/11.24 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 78.16/11.24 Prover 8: stopped % 78.16/11.24 Prover 7: stopped % 78.16/11.24 Prover 11: stopped % 78.41/11.25 Prover 10: stopped % 78.41/11.25 Prover 4: stopped % 78.76/11.35 Prover 16: Preprocessing ... % 78.97/11.40 Prover 16: stopped % 78.97/11.40 % 78.97/11.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 78.97/11.40 % 78.97/11.43 % SZS output start Proof for theBenchmark % 78.97/11.44 Assumptions after simplification: % 78.97/11.44 --------------------------------- % 78.97/11.44 % 78.97/11.44 (ax17) % 79.28/11.47 ssList(nil) = 0 & $i(nil) % 79.28/11.47 % 79.28/11.47 (ax18) % 79.28/11.48 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1, % 79.28/11.48 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) = % 79.28/11.48 v2))) % 79.28/11.48 % 79.28/11.48 (ax20) % 79.28/11.48 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 79.28/11.48 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 79.28/11.48 ssItem(v2) = 0 & $i(v2)))) % 79.28/11.48 % 79.28/11.48 (ax23) % 79.28/11.49 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 79.28/11.49 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) = % 79.28/11.49 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1)))) % 79.28/11.49 % 79.28/11.49 (ax25) % 79.28/11.49 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ( % 79.28/11.49 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) = % 79.28/11.49 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0)))) % 79.28/11.49 % 79.28/11.49 (ax38) % 79.28/11.49 $i(nil) & ! [v0: $i] : ( ~ (memberP(nil, v0) = 0) | ~ $i(v0) | ? [v1: int] % 79.28/11.49 : ( ~ (v1 = 0) & ssItem(v0) = v1)) % 79.28/11.49 % 79.28/11.49 (ax59) % 79.28/11.49 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 79.28/11.49 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 79.28/11.49 (v2 = 0) | v3 = 0))) % 79.28/11.49 % 79.28/11.49 (ax61) % 79.28/11.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 79.28/11.50 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 79.28/11.50 (v2 = 0) | v3 = 0))) % 79.28/11.50 % 79.28/11.50 (ax63) % 79.28/11.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 79.28/11.50 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 79.28/11.50 (v2 = 0) | v3 = 0))) % 79.28/11.50 % 79.28/11.50 (ax65) % 79.28/11.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 79.28/11.50 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 79.28/11.50 (v2 = 0) | v3 = 0))) % 79.28/11.50 % 79.28/11.50 (ax68) % 79.28/11.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 79.28/11.50 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( % 79.28/11.50 ~ (v2 = 0) | v3 = 0))) % 79.28/11.50 % 79.28/11.50 (ax71) % 79.28/11.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 79.28/11.50 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 79.28/11.50 ~ (v2 = 0) | v3 = 0))) % 79.28/11.50 % 79.28/11.50 (ax73) % 79.28/11.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | % 79.28/11.50 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ % 79.28/11.50 (v2 = 0) | v3 = 0))) % 79.28/11.50 % 79.28/11.50 (co1) % 79.28/11.51 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = % 79.28/11.51 0 & $i(v1) & ( ? [v2: $i] : (memberP(v1, v2) = 0 & cons(v2, nil) = v0 & % 79.28/11.51 ssItem(v2) = 0 & $i(v2) & ! [v3: $i] : (v3 = v2 | ~ (memberP(v1, v3) % 79.28/11.51 = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (leq(v2, v3) = v5 % 79.28/11.51 & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) | (v1 = nil & % 79.28/11.51 v0 = nil)) & ((v1 = nil & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = % 79.28/11.51 nil))))) % 79.28/11.51 % 79.28/11.51 (function-axioms) % 79.28/11.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 79.28/11.52 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 79.28/11.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 79.28/11.52 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 79.28/11.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 79.28/11.52 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 79.28/11.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 79.28/11.52 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 79.28/11.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 79.28/11.52 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 79.28/11.52 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 79.28/11.52 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 79.28/11.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 79.28/11.52 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 79.28/11.52 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 79.28/11.52 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 79.28/11.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.28/11.52 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 79.28/11.52 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 79.28/11.52 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 79.28/11.52 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 79.28/11.52 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 79.28/11.52 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 79.28/11.52 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 79.28/11.52 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 79.28/11.52 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.28/11.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 79.28/11.52 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.28/11.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 79.28/11.52 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.28/11.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 79.28/11.52 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.28/11.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 79.28/11.52 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.28/11.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 79.28/11.52 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.28/11.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 79.28/11.52 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.28/11.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 79.28/11.52 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.28/11.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 79.28/11.52 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 79.28/11.52 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 79.28/11.52 % 79.28/11.52 Further assumptions not needed in the proof: % 79.28/11.52 -------------------------------------------- % 79.28/11.52 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax19, ax2, ax21, ax22, ax24, % 79.28/11.52 ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, % 79.28/11.52 ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, % 79.28/11.52 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, % 79.28/11.52 ax66, ax67, ax69, ax7, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax8, % 79.28/11.52 ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, % 79.28/11.52 ax92, ax93, ax94, ax95 % 79.28/11.52 % 79.28/11.52 Those formulas are unsatisfiable: % 79.28/11.52 --------------------------------- % 79.28/11.52 % 79.28/11.52 Begin of proof % 79.28/11.52 | % 79.28/11.52 | ALPHA: (ax17) implies: % 79.28/11.52 | (1) ssList(nil) = 0 % 79.28/11.52 | % 79.28/11.52 | ALPHA: (ax20) implies: % 79.28/11.52 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 79.28/11.52 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 79.28/11.52 | ssItem(v2) = 0 & $i(v2)))) % 79.28/11.52 | % 79.28/11.52 | ALPHA: (ax38) implies: % 79.28/11.52 | (3) ! [v0: $i] : ( ~ (memberP(nil, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( % 79.28/11.52 | ~ (v1 = 0) & ssItem(v0) = v1)) % 79.28/11.52 | % 79.28/11.52 | ALPHA: (ax59) implies: % 79.28/11.53 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.28/11.53 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( % 79.28/11.53 | ~ (v2 = 0) | v3 = 0))) % 79.28/11.53 | % 79.28/11.53 | ALPHA: (ax61) implies: % 79.28/11.53 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.28/11.53 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & % 79.28/11.53 | ( ~ (v2 = 0) | v3 = 0))) % 79.28/11.53 | % 79.28/11.53 | ALPHA: (ax63) implies: % 79.28/11.53 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.28/11.53 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & % 79.28/11.53 | ( ~ (v2 = 0) | v3 = 0))) % 79.28/11.53 | % 79.28/11.53 | ALPHA: (ax65) implies: % 79.28/11.53 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.28/11.53 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 % 79.28/11.53 | & ( ~ (v2 = 0) | v3 = 0))) % 79.28/11.53 | % 79.28/11.53 | ALPHA: (ax68) implies: % 79.28/11.53 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.28/11.53 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 % 79.28/11.53 | & ( ~ (v2 = 0) | v3 = 0))) % 79.28/11.53 | % 79.28/11.53 | ALPHA: (ax71) implies: % 79.28/11.53 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.28/11.53 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 % 79.28/11.53 | & ( ~ (v2 = 0) | v3 = 0))) % 79.28/11.53 | % 79.28/11.53 | ALPHA: (ax73) implies: % 79.28/11.53 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.28/11.53 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & % 79.28/11.53 | ( ~ (v2 = 0) | v3 = 0))) % 79.28/11.53 | % 79.28/11.53 | ALPHA: (co1) implies: % 79.28/11.53 | (11) $i(nil) % 79.28/11.54 | (12) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0 % 79.28/11.54 | & $i(v1) & ( ? [v2: $i] : (memberP(v1, v2) = 0 & cons(v2, nil) = % 79.28/11.54 | v0 & ssItem(v2) = 0 & $i(v2) & ! [v3: $i] : (v3 = v2 | ~ % 79.28/11.54 | (memberP(v1, v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: % 79.28/11.54 | any] : (leq(v2, v3) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) % 79.28/11.54 | | ~ (v4 = 0))))) | (v1 = nil & v0 = nil)) & ((v1 = nil % 79.28/11.54 | & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = nil))))) % 79.28/11.54 | % 79.28/11.54 | ALPHA: (function-axioms) implies: % 79.28/11.54 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 79.28/11.54 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 79.28/11.54 | % 79.28/11.54 | DELTA: instantiating (12) with fresh symbol all_93_0 gives: % 79.28/11.54 | (14) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 & % 79.28/11.54 | $i(v0) & ( ? [v1: $i] : (memberP(v0, v1) = 0 & cons(v1, nil) = % 79.28/11.54 | all_93_0 & ssItem(v1) = 0 & $i(v1) & ! [v2: $i] : (v2 = v1 | ~ % 79.28/11.54 | (memberP(v0, v2) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4: % 79.28/11.54 | any] : (leq(v1, v2) = v4 & ssItem(v2) = v3 & ( ~ (v4 = 0) | % 79.28/11.54 | ~ (v3 = 0))))) | (v0 = nil & all_93_0 = nil)) & ((v0 = nil % 79.28/11.54 | & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ (v0 = nil)))) % 79.28/11.54 | % 79.28/11.54 | ALPHA: (14) implies: % 79.28/11.54 | (15) $i(all_93_0) % 79.28/11.54 | (16) ssList(all_93_0) = 0 % 79.28/11.54 | (17) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ( ? [v1: $i] : (memberP(v0, % 79.28/11.54 | v1) = 0 & cons(v1, nil) = all_93_0 & ssItem(v1) = 0 & $i(v1) & % 79.28/11.54 | ! [v2: $i] : (v2 = v1 | ~ (memberP(v0, v2) = 0) | ~ $i(v2) | % 79.28/11.54 | ? [v3: any] : ? [v4: any] : (leq(v1, v2) = v4 & ssItem(v2) = % 79.28/11.54 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) | (v0 = nil & all_93_0 = % 79.28/11.54 | nil)) & ((v0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 79.28/11.54 | (v0 = nil)))) % 79.28/11.54 | % 79.28/11.54 | DELTA: instantiating (17) with fresh symbol all_97_0 gives: % 79.28/11.54 | (18) ssList(all_97_0) = 0 & $i(all_97_0) & ( ? [v0: $i] : % 79.28/11.54 | (memberP(all_97_0, v0) = 0 & cons(v0, nil) = all_93_0 & ssItem(v0) = % 79.28/11.54 | 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~ (memberP(all_97_0, v1) = % 79.28/11.55 | 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (leq(v0, v1) = % 79.28/11.55 | v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) | % 79.28/11.55 | (all_97_0 = nil & all_93_0 = nil)) & ((all_97_0 = nil & ~ (all_93_0 % 79.28/11.55 | = nil)) | (all_93_0 = nil & ~ (all_97_0 = nil))) % 79.28/11.55 | % 79.28/11.55 | ALPHA: (18) implies: % 79.28/11.55 | (19) (all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ % 79.28/11.55 | (all_97_0 = nil)) % 79.28/11.55 | (20) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) = all_93_0 & % 79.28/11.55 | ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~ % 79.28/11.55 | (memberP(all_97_0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: % 79.28/11.55 | any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ % 79.28/11.55 | (v2 = 0))))) | (all_97_0 = nil & all_93_0 = nil) % 79.28/11.55 | % 79.28/11.55 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (11) gives: % 79.28/11.55 | (21) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.28/11.55 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 79.28/11.55 | ( ~ (v2 = 0) | v3 = nil))) % 79.28/11.55 | % 79.68/11.55 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (11) gives: % 79.68/11.55 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? % 79.68/11.55 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) & % 79.68/11.55 | ( ~ (v2 = 0) | v3 = v0))) % 79.68/11.55 | % 79.68/11.55 | GROUND_INST: instantiating (ax18) with nil, simplifying with (1), (11) gives: % 79.68/11.55 | (23) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : ( % 79.68/11.55 | ~ (v1 = 0) & ssItem(v0) = v1)) % 79.68/11.55 | % 79.68/11.55 | GROUND_INST: instantiating (2) with all_93_0, simplifying with (15), (16) % 79.68/11.55 | gives: % 79.68/11.55 | (24) all_93_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 79.68/11.55 | : (cons(v1, v0) = all_93_0 & ssItem(v1) = 0 & $i(v1))) % 79.68/11.55 | % 79.68/11.55 | BETA: splitting (20) gives: % 79.68/11.55 | % 79.68/11.55 | Case 1: % 79.68/11.55 | | % 79.68/11.56 | | (25) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) = all_93_0 % 79.68/11.56 | | & ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~ % 79.68/11.56 | | (memberP(all_97_0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: % 79.68/11.56 | | any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ % 79.68/11.56 | | (v2 = 0))))) % 79.68/11.56 | | % 79.68/11.56 | | DELTA: instantiating (25) with fresh symbol all_294_0 gives: % 79.68/11.56 | | (26) memberP(all_97_0, all_294_0) = 0 & cons(all_294_0, nil) = all_93_0 & % 79.68/11.56 | | ssItem(all_294_0) = 0 & $i(all_294_0) & ! [v0: any] : (v0 = % 79.68/11.56 | | all_294_0 | ~ (memberP(all_97_0, v0) = 0) | ~ $i(v0) | ? [v1: % 79.68/11.56 | | any] : ? [v2: any] : (leq(all_294_0, v0) = v2 & ssItem(v0) = v1 % 79.68/11.56 | | & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 79.68/11.56 | | % 79.68/11.56 | | ALPHA: (26) implies: % 79.68/11.56 | | (27) $i(all_294_0) % 79.68/11.56 | | (28) ssItem(all_294_0) = 0 % 79.68/11.56 | | (29) cons(all_294_0, nil) = all_93_0 % 79.68/11.56 | | (30) memberP(all_97_0, all_294_0) = 0 % 79.68/11.56 | | % 79.68/11.56 | | BETA: splitting (19) gives: % 79.68/11.56 | | % 79.68/11.56 | | Case 1: % 79.68/11.56 | | | % 79.68/11.56 | | | (31) all_97_0 = nil & ~ (all_93_0 = nil) % 79.68/11.56 | | | % 79.68/11.56 | | | ALPHA: (31) implies: % 79.68/11.56 | | | (32) all_97_0 = nil % 79.68/11.56 | | | % 79.68/11.56 | | | REDUCE: (30), (32) imply: % 79.68/11.56 | | | (33) memberP(nil, all_294_0) = 0 % 79.68/11.56 | | | % 79.68/11.56 | | | BETA: splitting (24) gives: % 79.68/11.56 | | | % 79.68/11.56 | | | Case 1: % 79.68/11.56 | | | | % 79.68/11.56 | | | | (34) all_93_0 = nil % 79.68/11.56 | | | | % 79.68/11.56 | | | | REF_CLOSE: (19), (32), (34) are inconsistent by sub-proof #1. % 79.68/11.56 | | | | % 79.68/11.56 | | | Case 2: % 79.68/11.56 | | | | % 79.68/11.56 | | | | % 79.68/11.56 | | | | GROUND_INST: instantiating (21) with all_294_0, all_93_0, simplifying % 79.68/11.56 | | | | with (27), (29) gives: % 79.68/11.56 | | | | (35) ? [v0: any] : ? [v1: $i] : (tl(all_93_0) = v1 & % 79.68/11.56 | | | | ssItem(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 79.68/11.56 | | | | % 79.68/11.56 | | | | GROUND_INST: instantiating (22) with all_294_0, all_93_0, simplifying % 79.68/11.56 | | | | with (27), (29) gives: % 79.68/11.56 | | | | (36) ? [v0: any] : ? [v1: $i] : (hd(all_93_0) = v1 & % 79.68/11.57 | | | | ssItem(all_294_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 79.68/11.57 | | | | all_294_0)) % 79.68/11.57 | | | | % 79.68/11.57 | | | | GROUND_INST: instantiating (10) with all_294_0, all_93_0, simplifying % 79.68/11.57 | | | | with (27), (29) gives: % 79.68/11.57 | | | | (37) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_0) = v1 & % 79.68/11.57 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 79.68/11.57 | | | | % 79.68/11.57 | | | | GROUND_INST: instantiating (9) with all_294_0, all_93_0, simplifying % 79.68/11.57 | | | | with (27), (29) gives: % 79.68/11.57 | | | | (38) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_0) = v1 & % 79.68/11.57 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 79.68/11.57 | | | | % 79.68/11.57 | | | | GROUND_INST: instantiating (8) with all_294_0, all_93_0, simplifying % 79.68/11.57 | | | | with (27), (29) gives: % 79.68/11.57 | | | | (39) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_0) = v1 & % 79.68/11.57 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 79.68/11.57 | | | | % 79.68/11.57 | | | | GROUND_INST: instantiating (7) with all_294_0, all_93_0, simplifying % 79.68/11.57 | | | | with (27), (29) gives: % 79.68/11.57 | | | | (40) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_0) = v1 & % 79.68/11.57 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 79.68/11.57 | | | | % 79.68/11.57 | | | | GROUND_INST: instantiating (6) with all_294_0, all_93_0, simplifying % 79.68/11.57 | | | | with (27), (29) gives: % 79.68/11.57 | | | | (41) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_0) = v1 & % 79.68/11.57 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 79.68/11.57 | | | | % 79.68/11.57 | | | | GROUND_INST: instantiating (5) with all_294_0, all_93_0, simplifying % 79.68/11.57 | | | | with (27), (29) gives: % 79.68/11.57 | | | | (42) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_0) = v1 & % 79.68/11.57 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 79.68/11.57 | | | | % 79.68/11.57 | | | | GROUND_INST: instantiating (4) with all_294_0, all_93_0, simplifying % 79.68/11.57 | | | | with (27), (29) gives: % 79.68/11.57 | | | | (43) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_0) = v1 & % 79.68/11.57 | | | | ssItem(all_294_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 79.68/11.57 | | | | % 79.68/11.57 | | | | GROUND_INST: instantiating (3) with all_294_0, simplifying with (27), % 79.68/11.57 | | | | (33) gives: % 79.68/11.57 | | | | (44) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_294_0) = v0) % 79.68/11.57 | | | | % 79.68/11.57 | | | | DELTA: instantiating (44) with fresh symbol all_517_0 gives: % 79.68/11.57 | | | | (45) ~ (all_517_0 = 0) & ssItem(all_294_0) = all_517_0 % 79.68/11.57 | | | | % 79.68/11.57 | | | | ALPHA: (45) implies: % 79.68/11.57 | | | | (46) ~ (all_517_0 = 0) % 79.68/11.57 | | | | (47) ssItem(all_294_0) = all_517_0 % 79.68/11.57 | | | | % 79.68/11.57 | | | | DELTA: instantiating (38) with fresh symbols all_519_0, all_519_1 gives: % 79.68/11.58 | | | | (48) duplicatefreeP(all_93_0) = all_519_0 & ssItem(all_294_0) = % 79.68/11.58 | | | | all_519_1 & ( ~ (all_519_1 = 0) | all_519_0 = 0) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (48) implies: % 79.68/11.58 | | | | (49) ssItem(all_294_0) = all_519_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | DELTA: instantiating (43) with fresh symbols all_521_0, all_521_1 gives: % 79.68/11.58 | | | | (50) cyclefreeP(all_93_0) = all_521_0 & ssItem(all_294_0) = all_521_1 % 79.68/11.58 | | | | & ( ~ (all_521_1 = 0) | all_521_0 = 0) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (50) implies: % 79.68/11.58 | | | | (51) ssItem(all_294_0) = all_521_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | DELTA: instantiating (42) with fresh symbols all_523_0, all_523_1 gives: % 79.68/11.58 | | | | (52) totalorderP(all_93_0) = all_523_0 & ssItem(all_294_0) = % 79.68/11.58 | | | | all_523_1 & ( ~ (all_523_1 = 0) | all_523_0 = 0) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (52) implies: % 79.68/11.58 | | | | (53) ssItem(all_294_0) = all_523_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | DELTA: instantiating (41) with fresh symbols all_525_0, all_525_1 gives: % 79.68/11.58 | | | | (54) strictorderP(all_93_0) = all_525_0 & ssItem(all_294_0) = % 79.68/11.58 | | | | all_525_1 & ( ~ (all_525_1 = 0) | all_525_0 = 0) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (54) implies: % 79.68/11.58 | | | | (55) ssItem(all_294_0) = all_525_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | DELTA: instantiating (37) with fresh symbols all_527_0, all_527_1 gives: % 79.68/11.58 | | | | (56) equalelemsP(all_93_0) = all_527_0 & ssItem(all_294_0) = % 79.68/11.58 | | | | all_527_1 & ( ~ (all_527_1 = 0) | all_527_0 = 0) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (56) implies: % 79.68/11.58 | | | | (57) ssItem(all_294_0) = all_527_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | DELTA: instantiating (40) with fresh symbols all_529_0, all_529_1 gives: % 79.68/11.58 | | | | (58) totalorderedP(all_93_0) = all_529_0 & ssItem(all_294_0) = % 79.68/11.58 | | | | all_529_1 & ( ~ (all_529_1 = 0) | all_529_0 = 0) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (58) implies: % 79.68/11.58 | | | | (59) ssItem(all_294_0) = all_529_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | DELTA: instantiating (39) with fresh symbols all_531_0, all_531_1 gives: % 79.68/11.58 | | | | (60) strictorderedP(all_93_0) = all_531_0 & ssItem(all_294_0) = % 79.68/11.58 | | | | all_531_1 & ( ~ (all_531_1 = 0) | all_531_0 = 0) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (60) implies: % 79.68/11.58 | | | | (61) ssItem(all_294_0) = all_531_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | DELTA: instantiating (36) with fresh symbols all_533_0, all_533_1 gives: % 79.68/11.58 | | | | (62) hd(all_93_0) = all_533_0 & ssItem(all_294_0) = all_533_1 & % 79.68/11.58 | | | | $i(all_533_0) & ( ~ (all_533_1 = 0) | all_533_0 = all_294_0) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (62) implies: % 79.68/11.58 | | | | (63) ssItem(all_294_0) = all_533_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | DELTA: instantiating (35) with fresh symbols all_535_0, all_535_1 gives: % 79.68/11.58 | | | | (64) tl(all_93_0) = all_535_0 & ssItem(all_294_0) = all_535_1 & % 79.68/11.58 | | | | $i(all_535_0) & ( ~ (all_535_1 = 0) | all_535_0 = nil) % 79.68/11.58 | | | | % 79.68/11.58 | | | | ALPHA: (64) implies: % 79.68/11.58 | | | | (65) ssItem(all_294_0) = all_535_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | GROUND_INST: instantiating (13) with all_521_1, all_523_1, all_294_0, % 79.68/11.58 | | | | simplifying with (51), (53) gives: % 79.68/11.58 | | | | (66) all_523_1 = all_521_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | GROUND_INST: instantiating (13) with 0, all_529_1, all_294_0, % 79.68/11.58 | | | | simplifying with (28), (59) gives: % 79.68/11.58 | | | | (67) all_529_1 = 0 % 79.68/11.58 | | | | % 79.68/11.58 | | | | GROUND_INST: instantiating (13) with all_521_1, all_529_1, all_294_0, % 79.68/11.58 | | | | simplifying with (51), (59) gives: % 79.68/11.58 | | | | (68) all_529_1 = all_521_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | GROUND_INST: instantiating (13) with all_519_1, all_529_1, all_294_0, % 79.68/11.58 | | | | simplifying with (49), (59) gives: % 79.68/11.58 | | | | (69) all_529_1 = all_519_1 % 79.68/11.58 | | | | % 79.68/11.58 | | | | GROUND_INST: instantiating (13) with all_529_1, all_531_1, all_294_0, % 79.68/11.58 | | | | simplifying with (59), (61) gives: % 79.68/11.58 | | | | (70) all_531_1 = all_529_1 % 79.68/11.58 | | | | % 79.68/11.59 | | | | GROUND_INST: instantiating (13) with all_525_1, all_531_1, all_294_0, % 79.68/11.59 | | | | simplifying with (55), (61) gives: % 79.68/11.59 | | | | (71) all_531_1 = all_525_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | GROUND_INST: instantiating (13) with all_527_1, all_533_1, all_294_0, % 79.68/11.59 | | | | simplifying with (57), (63) gives: % 79.68/11.59 | | | | (72) all_533_1 = all_527_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | GROUND_INST: instantiating (13) with all_523_1, all_533_1, all_294_0, % 79.68/11.59 | | | | simplifying with (53), (63) gives: % 79.68/11.59 | | | | (73) all_533_1 = all_523_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | GROUND_INST: instantiating (13) with all_533_1, all_535_1, all_294_0, % 79.68/11.59 | | | | simplifying with (63), (65) gives: % 79.68/11.59 | | | | (74) all_535_1 = all_533_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | GROUND_INST: instantiating (13) with all_517_0, all_535_1, all_294_0, % 79.68/11.59 | | | | simplifying with (47), (65) gives: % 79.68/11.59 | | | | (75) all_535_1 = all_517_0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (74), (75) imply: % 79.68/11.59 | | | | (76) all_533_1 = all_517_0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | SIMP: (76) implies: % 79.68/11.59 | | | | (77) all_533_1 = all_517_0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (72), (77) imply: % 79.68/11.59 | | | | (78) all_527_1 = all_517_0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (72), (73) imply: % 79.68/11.59 | | | | (79) all_527_1 = all_523_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (70), (71) imply: % 79.68/11.59 | | | | (80) all_529_1 = all_525_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | SIMP: (80) implies: % 79.68/11.59 | | | | (81) all_529_1 = all_525_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (67), (81) imply: % 79.68/11.59 | | | | (82) all_525_1 = 0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (68), (81) imply: % 79.68/11.59 | | | | (83) all_525_1 = all_521_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (69), (81) imply: % 79.68/11.59 | | | | (84) all_525_1 = all_519_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (78), (79) imply: % 79.68/11.59 | | | | (85) all_523_1 = all_517_0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | SIMP: (85) implies: % 79.68/11.59 | | | | (86) all_523_1 = all_517_0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (82), (84) imply: % 79.68/11.59 | | | | (87) all_519_1 = 0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (83), (84) imply: % 79.68/11.59 | | | | (88) all_521_1 = all_519_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | SIMP: (88) implies: % 79.68/11.59 | | | | (89) all_521_1 = all_519_1 % 79.68/11.59 | | | | % 79.68/11.59 | | | | COMBINE_EQS: (66), (86) imply: % 79.68/11.59 | | | | (90) all_521_1 = all_517_0 % 79.68/11.59 | | | | % 79.68/11.59 | | | | SIMP: (90) implies: % 79.68/11.59 | | | | (91) all_521_1 = all_517_0 % 79.68/11.59 | | | | % 79.68/11.60 | | | | COMBINE_EQS: (89), (91) imply: % 79.68/11.60 | | | | (92) all_519_1 = all_517_0 % 79.68/11.60 | | | | % 79.68/11.60 | | | | SIMP: (92) implies: % 79.68/11.60 | | | | (93) all_519_1 = all_517_0 % 79.68/11.60 | | | | % 79.68/11.60 | | | | COMBINE_EQS: (87), (93) imply: % 79.68/11.60 | | | | (94) all_517_0 = 0 % 79.68/11.60 | | | | % 79.68/11.60 | | | | SIMP: (94) implies: % 79.68/11.60 | | | | (95) all_517_0 = 0 % 79.68/11.60 | | | | % 79.68/11.60 | | | | REDUCE: (46), (95) imply: % 79.68/11.60 | | | | (96) $false % 79.68/11.60 | | | | % 79.68/11.60 | | | | CLOSE: (96) is inconsistent. % 79.68/11.60 | | | | % 79.68/11.60 | | | End of split % 79.68/11.60 | | | % 79.68/11.60 | | Case 2: % 79.68/11.60 | | | % 79.68/11.60 | | | (97) all_93_0 = nil & ~ (all_97_0 = nil) % 79.68/11.60 | | | % 79.68/11.60 | | | ALPHA: (97) implies: % 79.68/11.60 | | | (98) all_93_0 = nil % 79.68/11.60 | | | % 79.68/11.60 | | | REDUCE: (29), (98) imply: % 79.68/11.60 | | | (99) cons(all_294_0, nil) = nil % 79.68/11.60 | | | % 79.68/11.60 | | | GROUND_INST: instantiating (23) with all_294_0, simplifying with (27), % 79.68/11.60 | | | (99) gives: % 79.68/11.60 | | | (100) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_294_0) = v0) % 79.68/11.60 | | | % 79.68/11.60 | | | GROUND_INST: instantiating (21) with all_294_0, nil, simplifying with % 79.68/11.60 | | | (27), (99) gives: % 79.68/11.60 | | | (101) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 & ssItem(all_294_0) = % 79.68/11.60 | | | v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil)) % 79.68/11.60 | | | % 79.68/11.60 | | | GROUND_INST: instantiating (22) with all_294_0, nil, simplifying with % 79.68/11.60 | | | (27), (99) gives: % 80.01/11.60 | | | (102) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 & ssItem(all_294_0) = % 80.01/11.60 | | | v0 & $i(v1) & ( ~ (v0 = 0) | v1 = all_294_0)) % 80.01/11.60 | | | % 80.01/11.60 | | | DELTA: instantiating (100) with fresh symbol all_517_0 gives: % 80.01/11.60 | | | (103) ~ (all_517_0 = 0) & ssItem(all_294_0) = all_517_0 % 80.01/11.60 | | | % 80.01/11.60 | | | ALPHA: (103) implies: % 80.01/11.60 | | | (104) ~ (all_517_0 = 0) % 80.01/11.60 | | | (105) ssItem(all_294_0) = all_517_0 % 80.01/11.60 | | | % 80.01/11.60 | | | DELTA: instantiating (101) with fresh symbols all_519_0, all_519_1 gives: % 80.01/11.60 | | | (106) tl(nil) = all_519_0 & ssItem(all_294_0) = all_519_1 & % 80.01/11.60 | | | $i(all_519_0) & ( ~ (all_519_1 = 0) | all_519_0 = nil) % 80.01/11.60 | | | % 80.01/11.60 | | | ALPHA: (106) implies: % 80.01/11.60 | | | (107) ssItem(all_294_0) = all_519_1 % 80.01/11.60 | | | % 80.01/11.60 | | | DELTA: instantiating (102) with fresh symbols all_521_0, all_521_1 gives: % 80.01/11.60 | | | (108) hd(nil) = all_521_0 & ssItem(all_294_0) = all_521_1 & % 80.01/11.60 | | | $i(all_521_0) & ( ~ (all_521_1 = 0) | all_521_0 = all_294_0) % 80.01/11.60 | | | % 80.01/11.60 | | | ALPHA: (108) implies: % 80.01/11.60 | | | (109) ssItem(all_294_0) = all_521_1 % 80.01/11.60 | | | % 80.01/11.60 | | | GROUND_INST: instantiating (13) with all_517_0, all_519_1, all_294_0, % 80.01/11.60 | | | simplifying with (105), (107) gives: % 80.01/11.60 | | | (110) all_519_1 = all_517_0 % 80.01/11.60 | | | % 80.01/11.60 | | | GROUND_INST: instantiating (13) with 0, all_521_1, all_294_0, simplifying % 80.01/11.60 | | | with (28), (109) gives: % 80.01/11.60 | | | (111) all_521_1 = 0 % 80.01/11.60 | | | % 80.01/11.60 | | | GROUND_INST: instantiating (13) with all_519_1, all_521_1, all_294_0, % 80.01/11.60 | | | simplifying with (107), (109) gives: % 80.01/11.60 | | | (112) all_521_1 = all_519_1 % 80.01/11.60 | | | % 80.01/11.60 | | | COMBINE_EQS: (111), (112) imply: % 80.01/11.60 | | | (113) all_519_1 = 0 % 80.01/11.60 | | | % 80.01/11.60 | | | SIMP: (113) implies: % 80.01/11.60 | | | (114) all_519_1 = 0 % 80.01/11.60 | | | % 80.01/11.60 | | | COMBINE_EQS: (110), (114) imply: % 80.01/11.61 | | | (115) all_517_0 = 0 % 80.01/11.61 | | | % 80.01/11.61 | | | REDUCE: (104), (115) imply: % 80.01/11.61 | | | (116) $false % 80.01/11.61 | | | % 80.01/11.61 | | | CLOSE: (116) is inconsistent. % 80.01/11.61 | | | % 80.01/11.61 | | End of split % 80.01/11.61 | | % 80.01/11.61 | Case 2: % 80.01/11.61 | | % 80.01/11.61 | | (117) all_97_0 = nil & all_93_0 = nil % 80.01/11.61 | | % 80.01/11.61 | | ALPHA: (117) implies: % 80.01/11.61 | | (118) all_93_0 = nil % 80.01/11.61 | | (119) all_97_0 = nil % 80.01/11.61 | | % 80.01/11.61 | | REF_CLOSE: (19), (118), (119) are inconsistent by sub-proof #1. % 80.01/11.61 | | % 80.01/11.61 | End of split % 80.01/11.61 | % 80.01/11.61 End of proof % 80.01/11.61 % 80.01/11.61 Sub-proof #1 shows that the following formulas are inconsistent: % 80.01/11.61 ---------------------------------------------------------------- % 80.01/11.61 (1) (all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ (all_97_0 = % 80.01/11.61 nil)) % 80.01/11.61 (2) all_93_0 = nil % 80.01/11.61 (3) all_97_0 = nil % 80.01/11.61 % 80.01/11.61 Begin of proof % 80.01/11.61 | % 80.01/11.61 | BETA: splitting (1) gives: % 80.01/11.61 | % 80.01/11.61 | Case 1: % 80.01/11.61 | | % 80.01/11.61 | | (4) all_97_0 = nil & ~ (all_93_0 = nil) % 80.01/11.61 | | % 80.01/11.61 | | ALPHA: (4) implies: % 80.01/11.61 | | (5) ~ (all_93_0 = nil) % 80.01/11.61 | | % 80.01/11.61 | | REDUCE: (2), (5) imply: % 80.01/11.61 | | (6) $false % 80.01/11.61 | | % 80.01/11.61 | | CLOSE: (6) is inconsistent. % 80.01/11.61 | | % 80.01/11.61 | Case 2: % 80.01/11.61 | | % 80.01/11.61 | | (7) all_93_0 = nil & ~ (all_97_0 = nil) % 80.01/11.61 | | % 80.01/11.61 | | ALPHA: (7) implies: % 80.01/11.61 | | (8) ~ (all_97_0 = nil) % 80.01/11.61 | | % 80.01/11.61 | | REDUCE: (3), (8) imply: % 80.01/11.61 | | (9) $false % 80.01/11.61 | | % 80.01/11.61 | | CLOSE: (9) is inconsistent. % 80.01/11.61 | | % 80.01/11.61 | End of split % 80.01/11.61 | % 80.01/11.61 End of proof % 80.01/11.61 % SZS output end Proof for theBenchmark % 80.01/11.61 % 80.01/11.61 10988ms %------------------------------------------------------------------------------