%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC076+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 : n025.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 20:49:31 EDT 2023 % Result : Theorem 137.90s 19.07s % Output : Proof 165.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC076+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 16:00:24 EDT 2023 % 0.12/0.35 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.66/1.68 Prover 4: Preprocessing ... % 6.66/1.69 Prover 1: Preprocessing ... % 7.30/1.71 Prover 0: Preprocessing ... % 7.30/1.71 Prover 5: Preprocessing ... % 7.30/1.71 Prover 6: Preprocessing ... % 7.30/1.71 Prover 2: Preprocessing ... % 7.30/1.71 Prover 3: Preprocessing ... % 16.48/2.98 Prover 2: Proving ... % 16.76/3.01 Prover 1: Constructing countermodel ... % 16.76/3.02 Prover 5: Constructing countermodel ... % 16.76/3.03 Prover 3: Constructing countermodel ... % 16.76/3.04 Prover 6: Proving ... % 21.85/3.72 Prover 4: Constructing countermodel ... % 22.72/3.83 Prover 0: Proving ... % 71.91/10.32 Prover 2: stopped % 72.47/10.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.82/10.44 Prover 7: Preprocessing ... % 74.18/10.63 Prover 7: Constructing countermodel ... % 99.76/13.97 Prover 5: stopped % 99.76/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 101.28/14.12 Prover 8: Preprocessing ... % 103.38/14.42 Prover 8: Warning: ignoring some quantifiers % 104.00/14.46 Prover 8: Constructing countermodel ... % 115.39/15.97 Prover 1: stopped % 115.39/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.79/16.12 Prover 9: Preprocessing ... % 122.15/16.93 Prover 9: Constructing countermodel ... % 129.63/17.89 Prover 6: stopped % 129.63/17.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 130.92/18.06 Prover 10: Preprocessing ... % 131.90/18.21 Prover 10: Constructing countermodel ... % 137.90/19.07 Prover 9: proved (3092ms) % 137.90/19.07 % 137.90/19.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 137.90/19.07 % 137.90/19.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 137.90/19.08 Prover 3: stopped % 137.90/19.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 138.81/19.08 Prover 0: stopped % 138.81/19.09 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 139.34/19.15 Prover 11: Preprocessing ... % 139.50/19.18 Prover 13: Preprocessing ... % 139.50/19.19 Prover 16: Preprocessing ... % 140.22/19.30 Prover 16: Constructing countermodel ... % 141.19/19.38 Prover 13: Constructing countermodel ... % 144.30/19.82 Prover 11: Constructing countermodel ... % 162.63/22.23 Prover 13: stopped % 162.63/22.25 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 163.42/22.29 Prover 10: Found proof (size 122) % 163.42/22.30 Prover 10: proved (4383ms) % 163.42/22.30 Prover 7: stopped % 163.42/22.30 Prover 8: stopped % 163.42/22.30 Prover 11: stopped % 163.42/22.30 Prover 4: stopped % 163.42/22.32 Prover 16: stopped % 163.42/22.34 Prover 19: Preprocessing ... % 164.38/22.58 Prover 19: Warning: ignoring some quantifiers % 164.70/22.60 Prover 19: Constructing countermodel ... % 164.70/22.61 Prover 19: stopped % 164.70/22.61 % 164.70/22.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 164.70/22.61 % 164.70/22.64 % SZS output start Proof for theBenchmark % 164.70/22.65 Assumptions after simplification: % 164.70/22.65 --------------------------------- % 164.70/22.65 % 164.70/22.65 (ax15) % 164.70/22.66 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 164.70/22.66 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ % 164.70/22.66 neq(v0, v0)) % 164.70/22.66 % 164.70/22.66 (ax17) % 164.70/22.66 $i(nil) & ssList(nil) % 164.70/22.66 % 164.70/22.66 (ax26) % 165.13/22.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | % 165.13/22.69 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 165.13/22.69 % 165.13/22.69 (ax28) % 165.13/22.69 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 165.13/22.69 $i(v0) | ~ ssList(v0)) % 165.13/22.69 % 165.13/22.69 (ax42) % 165.13/22.69 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0)) % 165.13/22.69 % 165.13/22.69 (ax45) % 165.13/22.69 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 165.13/22.69 % 165.13/22.69 (ax46) % 165.13/22.70 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 165.13/22.70 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 165.13/22.70 % 165.13/22.70 (ax5) % 165.13/22.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 165.13/22.70 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 165.13/22.70 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 165.13/22.70 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 165.13/22.70 v2) = v0 & $i(v2) & ssList(v2))) % 165.13/22.70 % 165.13/22.70 (ax51) % 165.13/22.70 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 165.13/22.70 % 165.13/22.70 (ax52) % 165.13/22.70 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~ % 165.13/22.70 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil)) % 165.13/22.70 % 165.13/22.70 (ax58) % 165.13/22.70 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 165.13/22.70 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 165.13/22.70 % 165.13/22.70 (ax6) % 165.13/22.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 165.13/22.70 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 165.13/22.70 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 165.13/22.70 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 165.13/22.70 v1) = v0 & $i(v2) & ssList(v2))) % 165.13/22.70 % 165.13/22.70 (ax7) % 165.13/22.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 165.13/22.71 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 165.13/22.71 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 165.13/22.71 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 165.13/22.71 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 165.13/22.71 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 165.13/22.71 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 165.13/22.71 % 165.24/22.71 (ax82) % 165.24/22.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 165.24/22.71 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 165.24/22.71 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 165.24/22.71 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 165.24/22.71 % 165.24/22.71 (ax83) % 165.24/22.71 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 165.24/22.71 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 165.24/22.71 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 165.24/22.71 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 165.24/22.71 v0) | ~ ssList(nil)) % 165.24/22.71 % 165.24/22.71 (ax84) % 165.24/22.71 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 165.24/22.71 $i(v0) | ~ ssList(v0)) % 165.24/22.71 % 165.24/22.71 (co1) % 165.24/22.72 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 165.29/22.72 : (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 165.29/22.72 $i(v0) & equalelemsP(v0) & ssList(v4) & ssList(v2) & ssList(v1) & ssList(v0) % 165.29/22.72 & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v5, nil) % 165.29/22.72 = v6) | ~ (app(v8, v6) = v0) | ~ (app(v6, v7) = v4) | ~ $i(v8) | ~ % 165.29/22.72 $i(v7) | ~ $i(v5) | ~ ssList(v8) | ~ ssList(v7) | ~ ssItem(v5)) & ! % 165.29/22.72 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v5, nil) = % 165.29/22.72 v6) | ~ (app(v7, v6) = v2) | ~ (app(v6, v8) = v0) | ~ $i(v8) | ~ % 165.29/22.72 $i(v7) | ~ $i(v5) | ~ ssList(v8) | ~ ssList(v7) | ~ ssItem(v5)) & ! % 165.29/22.72 [v5: $i] : ( ~ $i(v5) | ~ segmentP(v1, v5) | ~ segmentP(v0, v5) | ~ % 165.29/22.72 ssList(v5) | ~ neq(v5, nil)) & ( ~ (v1 = nil) | ~ (v0 = nil)) & ( ~ (v0 % 165.29/22.72 = nil) | v1 = nil)) % 165.29/22.72 % 165.29/22.72 (function-axioms) % 165.29/22.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 165.29/22.72 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 165.29/22.72 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 165.29/22.72 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 165.29/22.72 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 165.29/22.72 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 165.29/22.72 % 165.29/22.72 Further assumptions not needed in the proof: % 165.29/22.72 -------------------------------------------- % 165.29/22.72 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 165.29/22.72 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 165.29/22.72 ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax49, ax50, ax53, % 165.29/22.72 ax54, ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, % 165.29/22.72 ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, % 165.29/22.72 ax80, ax81, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, % 165.29/22.72 ax95 % 165.29/22.72 % 165.29/22.72 Those formulas are unsatisfiable: % 165.29/22.72 --------------------------------- % 165.29/22.72 % 165.29/22.72 Begin of proof % 165.29/22.72 | % 165.29/22.72 | ALPHA: (ax5) implies: % 165.29/22.72 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 165.29/22.72 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 165.29/22.72 | v0 & $i(v2) & ssList(v2))) % 165.29/22.72 | % 165.29/22.72 | ALPHA: (ax6) implies: % 165.29/22.72 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 165.29/22.73 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 165.29/22.73 | v0 & $i(v2) & ssList(v2))) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax7) implies: % 165.29/22.73 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, % 165.29/22.73 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] : % 165.29/22.73 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) & % 165.29/22.73 | $i(v2) & ssList(v4) & ssList(v2))) % 165.29/22.73 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 165.29/22.73 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 165.29/22.73 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 165.29/22.73 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax15) implies: % 165.29/22.73 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 165.29/22.73 | ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax17) implies: % 165.29/22.73 | (6) ssList(nil) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax28) implies: % 165.29/22.73 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 165.29/22.73 | $i(v0) | ~ ssList(v0)) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax45) implies: % 165.29/22.73 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax46) implies: % 165.29/22.73 | (9) ~ ssList(nil) | frontsegP(nil, nil) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax51) implies: % 165.29/22.73 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax52) implies: % 165.29/22.73 | (11) ~ ssList(nil) | rearsegP(nil, nil) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax58) implies: % 165.29/22.73 | (12) ~ ssList(nil) | segmentP(nil, nil) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax83) implies: % 165.29/22.73 | (13) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 165.29/22.73 | (14) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ % 165.29/22.73 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 165.29/22.73 | (15) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 165.29/22.73 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (ax84) implies: % 165.29/22.73 | (16) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 165.29/22.73 | $i(v0) | ~ ssList(v0)) % 165.29/22.73 | % 165.29/22.73 | ALPHA: (co1) implies: % 165.29/22.73 | (17) $i(nil) % 165.29/22.74 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 165.29/22.74 | (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) & % 165.29/22.74 | $i(v1) & $i(v0) & equalelemsP(v0) & ssList(v4) & ssList(v2) & % 165.29/22.74 | ssList(v1) & ssList(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 165.29/22.74 | ! [v8: $i] : ( ~ (cons(v5, nil) = v6) | ~ (app(v8, v6) = v0) | ~ % 165.29/22.74 | (app(v6, v7) = v4) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ % 165.29/22.74 | ssList(v8) | ~ ssList(v7) | ~ ssItem(v5)) & ! [v5: $i] : ! % 165.29/22.74 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v5, nil) = v6) | ~ % 165.29/22.74 | (app(v7, v6) = v2) | ~ (app(v6, v8) = v0) | ~ $i(v8) | ~ $i(v7) % 165.29/22.74 | | ~ $i(v5) | ~ ssList(v8) | ~ ssList(v7) | ~ ssItem(v5)) & ! % 165.29/22.74 | [v5: $i] : ( ~ $i(v5) | ~ segmentP(v1, v5) | ~ segmentP(v0, v5) | % 165.29/22.74 | ~ ssList(v5) | ~ neq(v5, nil)) & ( ~ (v1 = nil) | ~ (v0 = nil)) % 165.29/22.74 | & ( ~ (v0 = nil) | v1 = nil)) % 165.29/22.74 | % 165.29/22.74 | ALPHA: (function-axioms) implies: % 165.29/22.74 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 165.29/22.74 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 165.29/22.74 | % 165.29/22.74 | DELTA: instantiating (18) with fresh symbols all_91_0, all_91_1, all_91_2, % 165.29/22.74 | all_91_3, all_91_4 gives: % 165.29/22.74 | (20) app(all_91_1, all_91_0) = all_91_3 & app(all_91_2, all_91_4) = % 165.29/22.74 | all_91_1 & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & % 165.29/22.74 | $i(all_91_4) & equalelemsP(all_91_4) & ssList(all_91_0) & % 165.29/22.74 | ssList(all_91_2) & ssList(all_91_3) & ssList(all_91_4) & ! [v0: $i] : % 165.29/22.74 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, nil) = v1) | % 165.29/22.74 | ~ (app(v3, v1) = all_91_4) | ~ (app(v1, v2) = all_91_0) | ~ $i(v3) % 165.29/22.74 | | ~ $i(v2) | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v2) | ~ % 165.29/22.74 | ssItem(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 165.29/22.74 | : ( ~ (cons(v0, nil) = v1) | ~ (app(v2, v1) = all_91_2) | ~ (app(v1, % 165.29/22.74 | v3) = all_91_4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ % 165.29/22.74 | ssList(v3) | ~ ssList(v2) | ~ ssItem(v0)) & ! [v0: $i] : ( ~ % 165.29/22.74 | $i(v0) | ~ segmentP(all_91_3, v0) | ~ segmentP(all_91_4, v0) | ~ % 165.29/22.74 | ssList(v0) | ~ neq(v0, nil)) & ( ~ (all_91_3 = nil) | ~ (all_91_4 % 165.29/22.74 | = nil)) & ( ~ (all_91_4 = nil) | all_91_3 = nil) % 165.29/22.74 | % 165.29/22.74 | ALPHA: (20) implies: % 165.29/22.74 | (21) ssList(all_91_4) % 165.29/22.74 | (22) ssList(all_91_3) % 165.29/22.74 | (23) ssList(all_91_2) % 165.29/22.74 | (24) ssList(all_91_0) % 165.29/22.74 | (25) $i(all_91_4) % 165.29/22.74 | (26) $i(all_91_3) % 165.29/22.74 | (27) $i(all_91_2) % 165.29/22.74 | (28) $i(all_91_0) % 165.29/22.74 | (29) app(all_91_2, all_91_4) = all_91_1 % 165.29/22.74 | (30) app(all_91_1, all_91_0) = all_91_3 % 165.29/22.74 | (31) ~ (all_91_4 = nil) | all_91_3 = nil % 165.29/22.74 | (32) ~ (all_91_3 = nil) | ~ (all_91_4 = nil) % 165.29/22.74 | (33) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_3, v0) | ~ % 165.29/22.74 | segmentP(all_91_4, v0) | ~ ssList(v0) | ~ neq(v0, nil)) % 165.29/22.74 | % 165.29/22.74 | BETA: splitting (11) gives: % 165.29/22.74 | % 165.29/22.74 | Case 1: % 165.29/22.74 | | % 165.29/22.74 | | (34) ~ ssList(nil) % 165.29/22.74 | | % 165.29/22.75 | | PRED_UNIFY: (6), (34) imply: % 165.29/22.75 | | (35) $false % 165.29/22.75 | | % 165.29/22.75 | | CLOSE: (35) is inconsistent. % 165.29/22.75 | | % 165.29/22.75 | Case 2: % 165.29/22.75 | | % 165.29/22.75 | | (36) rearsegP(nil, nil) % 165.29/22.75 | | % 165.29/22.75 | | BETA: splitting (9) gives: % 165.29/22.75 | | % 165.29/22.75 | | Case 1: % 165.29/22.75 | | | % 165.29/22.75 | | | (37) ~ ssList(nil) % 165.29/22.75 | | | % 165.29/22.75 | | | PRED_UNIFY: (6), (37) imply: % 165.29/22.75 | | | (38) $false % 165.29/22.75 | | | % 165.29/22.75 | | | CLOSE: (38) is inconsistent. % 165.29/22.75 | | | % 165.29/22.75 | | Case 2: % 165.29/22.75 | | | % 165.29/22.75 | | | (39) frontsegP(nil, nil) % 165.29/22.75 | | | % 165.29/22.75 | | | BETA: splitting (12) gives: % 165.29/22.75 | | | % 165.29/22.75 | | | Case 1: % 165.29/22.75 | | | | % 165.29/22.75 | | | | (40) ~ ssList(nil) % 165.29/22.75 | | | | % 165.29/22.75 | | | | PRED_UNIFY: (6), (40) imply: % 165.29/22.75 | | | | (41) $false % 165.29/22.75 | | | | % 165.29/22.75 | | | | CLOSE: (41) is inconsistent. % 165.29/22.75 | | | | % 165.29/22.75 | | | Case 2: % 165.29/22.75 | | | | % 165.29/22.75 | | | | (42) segmentP(nil, nil) % 165.29/22.75 | | | | % 165.29/22.75 | | | | GROUND_INST: instantiating (10) with all_91_4, simplifying with (21), % 165.29/22.75 | | | | (25) gives: % 165.29/22.75 | | | | (43) rearsegP(all_91_4, nil) % 165.29/22.75 | | | | % 165.29/22.75 | | | | GROUND_INST: instantiating (ax42) with all_91_4, simplifying with (21), % 165.29/22.75 | | | | (25) gives: % 165.29/22.75 | | | | (44) frontsegP(all_91_4, all_91_4) % 165.29/22.75 | | | | % 165.29/22.75 | | | | GROUND_INST: instantiating (8) with all_91_4, simplifying with (21), % 165.29/22.75 | | | | (25) gives: % 165.29/22.75 | | | | (45) frontsegP(all_91_4, nil) % 165.29/22.75 | | | | % 165.29/22.75 | | | | GROUND_INST: instantiating (10) with all_91_2, simplifying with (23), % 165.29/22.75 | | | | (27) gives: % 165.29/22.75 | | | | (46) rearsegP(all_91_2, nil) % 165.29/22.75 | | | | % 165.29/22.75 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (6), % 165.29/22.75 | | | | (17), (39) gives: % 165.29/22.75 | | | | (47) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 165.29/22.75 | | | | % 165.29/22.75 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (6), % 165.29/22.75 | | | | (17), (36) gives: % 165.29/22.75 | | | | (48) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0)) % 165.29/22.75 | | | | % 165.29/22.75 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (6), % 165.29/22.75 | | | | (17), (42) gives: % 165.29/22.75 | | | | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil & % 165.29/22.75 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) & % 165.29/22.75 | | | | ssList(v0)) % 165.29/22.75 | | | | % 165.29/22.75 | | | | GROUND_INST: instantiating (4) with all_91_3, all_91_4, all_91_2, % 165.29/22.75 | | | | all_91_1, all_91_0, simplifying with (21), (22), (23), % 165.29/22.75 | | | | (24), (25), (26), (27), (28), (29), (30) gives: % 165.29/22.75 | | | | (50) segmentP(all_91_3, all_91_4) % 165.29/22.75 | | | | % 165.29/22.75 | | | | DELTA: instantiating (48) with fresh symbol all_112_0 gives: % 165.29/22.75 | | | | (51) app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0) % 165.29/22.75 | | | | % 165.29/22.75 | | | | ALPHA: (51) implies: % 165.29/22.75 | | | | (52) ssList(all_112_0) % 165.29/22.75 | | | | (53) $i(all_112_0) % 165.29/22.75 | | | | (54) app(all_112_0, nil) = nil % 165.29/22.75 | | | | % 165.29/22.75 | | | | DELTA: instantiating (47) with fresh symbol all_114_0 gives: % 165.29/22.75 | | | | (55) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0) % 165.29/22.75 | | | | % 165.29/22.75 | | | | ALPHA: (55) implies: % 165.29/22.75 | | | | (56) ssList(all_114_0) % 165.29/22.75 | | | | (57) $i(all_114_0) % 165.29/22.75 | | | | (58) app(nil, all_114_0) = nil % 165.29/22.75 | | | | % 165.29/22.75 | | | | DELTA: instantiating (49) with fresh symbols all_118_0, all_118_1, % 165.29/22.75 | | | | all_118_2 gives: % 165.29/22.75 | | | | (59) app(all_118_1, all_118_0) = nil & app(all_118_2, nil) = % 165.29/22.76 | | | | all_118_1 & $i(all_118_0) & $i(all_118_1) & $i(all_118_2) & % 165.29/22.76 | | | | ssList(all_118_0) & ssList(all_118_2) % 165.29/22.76 | | | | % 165.29/22.76 | | | | ALPHA: (59) implies: % 165.29/22.76 | | | | (60) ssList(all_118_2) % 165.29/22.76 | | | | (61) ssList(all_118_0) % 165.29/22.76 | | | | (62) $i(all_118_2) % 165.29/22.76 | | | | (63) $i(all_118_1) % 165.29/22.76 | | | | (64) $i(all_118_0) % 165.29/22.76 | | | | (65) app(all_118_2, nil) = all_118_1 % 165.29/22.76 | | | | (66) app(all_118_1, all_118_0) = nil % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (5) with all_91_4, all_118_2, simplifying % 165.29/22.76 | | | | with (21), (25), (60), (62) gives: % 165.29/22.76 | | | | (67) all_118_2 = all_91_4 | neq(all_91_4, all_118_2) % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (1) with all_91_4, nil, simplifying with (6), % 165.29/22.76 | | | | (17), (21), (25), (45) gives: % 165.29/22.76 | | | | (68) ? [v0: $i] : (app(nil, v0) = all_91_4 & $i(v0) & ssList(v0)) % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (1) with all_91_4, all_91_4, simplifying with % 165.29/22.76 | | | | (21), (25), (44) gives: % 165.29/22.76 | | | | (69) ? [v0: $i] : (app(all_91_4, v0) = all_91_4 & $i(v0) & % 165.29/22.76 | | | | ssList(v0)) % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (2) with all_91_4, nil, simplifying with (6), % 165.29/22.76 | | | | (17), (21), (25), (43) gives: % 165.29/22.76 | | | | (70) ? [v0: $i] : (app(v0, nil) = all_91_4 & $i(v0) & ssList(v0)) % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (2) with all_91_2, nil, simplifying with (6), % 165.29/22.76 | | | | (17), (23), (27), (46) gives: % 165.29/22.76 | | | | (71) ? [v0: $i] : (app(v0, nil) = all_91_2 & $i(v0) & ssList(v0)) % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (ax82) with nil, all_114_0, nil, all_114_0, % 165.29/22.76 | | | | nil, simplifying with (6), (17), (56), (57), (58) gives: % 165.29/22.76 | | | | (72) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) = % 165.29/22.76 | | | | nil & $i(v0)) % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (7) with all_114_0, nil, simplifying with % 165.29/22.76 | | | | (56), (57), (58) gives: % 165.29/22.76 | | | | (73) all_114_0 = nil % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (16) with all_112_0, nil, simplifying with % 165.29/22.76 | | | | (52), (53), (54) gives: % 165.29/22.76 | | | | (74) all_112_0 = nil % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (ax26) with all_118_2, nil, all_118_1, % 165.29/22.76 | | | | simplifying with (6), (17), (60), (62), (65) gives: % 165.29/22.76 | | | | (75) ssList(all_118_1) % 165.29/22.76 | | | | % 165.29/22.76 | | | | GROUND_INST: instantiating (16) with all_118_2, all_118_1, simplifying % 165.29/22.76 | | | | with (60), (62), (65) gives: % 165.29/22.76 | | | | (76) all_118_1 = all_118_2 % 165.29/22.76 | | | | % 165.29/22.76 | | | | DELTA: instantiating (71) with fresh symbol all_140_0 gives: % 165.29/22.76 | | | | (77) app(all_140_0, nil) = all_91_2 & $i(all_140_0) & % 165.29/22.76 | | | | ssList(all_140_0) % 165.29/22.76 | | | | % 165.29/22.76 | | | | ALPHA: (77) implies: % 165.29/22.76 | | | | (78) ssList(all_140_0) % 165.29/22.76 | | | | (79) $i(all_140_0) % 165.29/22.76 | | | | (80) app(all_140_0, nil) = all_91_2 % 165.29/22.76 | | | | % 165.29/22.76 | | | | DELTA: instantiating (72) with fresh symbol all_142_0 gives: % 165.29/22.76 | | | | (81) app(all_114_0, all_114_0) = all_142_0 & app(nil, all_142_0) = % 165.29/22.76 | | | | nil & $i(all_142_0) % 165.29/22.76 | | | | % 165.29/22.76 | | | | ALPHA: (81) implies: % 165.29/22.76 | | | | (82) $i(all_142_0) % 165.29/22.76 | | | | (83) app(all_114_0, all_114_0) = all_142_0 % 165.29/22.76 | | | | % 165.29/22.76 | | | | DELTA: instantiating (70) with fresh symbol all_164_0 gives: % 165.29/22.76 | | | | (84) app(all_164_0, nil) = all_91_4 & $i(all_164_0) & % 165.29/22.76 | | | | ssList(all_164_0) % 165.29/22.76 | | | | % 165.29/22.76 | | | | ALPHA: (84) implies: % 165.29/22.77 | | | | (85) ssList(all_164_0) % 165.29/22.77 | | | | (86) $i(all_164_0) % 165.29/22.77 | | | | (87) app(all_164_0, nil) = all_91_4 % 165.29/22.77 | | | | % 165.29/22.77 | | | | DELTA: instantiating (69) with fresh symbol all_166_0 gives: % 165.29/22.77 | | | | (88) app(all_91_4, all_166_0) = all_91_4 & $i(all_166_0) & % 165.29/22.77 | | | | ssList(all_166_0) % 165.29/22.77 | | | | % 165.29/22.77 | | | | ALPHA: (88) implies: % 165.29/22.77 | | | | (89) ssList(all_166_0) % 165.29/22.77 | | | | (90) $i(all_166_0) % 165.29/22.77 | | | | (91) app(all_91_4, all_166_0) = all_91_4 % 165.29/22.77 | | | | % 165.29/22.77 | | | | DELTA: instantiating (68) with fresh symbol all_168_0 gives: % 165.29/22.77 | | | | (92) app(nil, all_168_0) = all_91_4 & $i(all_168_0) & % 165.29/22.77 | | | | ssList(all_168_0) % 165.29/22.77 | | | | % 165.29/22.77 | | | | ALPHA: (92) implies: % 165.29/22.77 | | | | (93) ssList(all_168_0) % 165.29/22.77 | | | | (94) $i(all_168_0) % 165.29/22.77 | | | | (95) app(nil, all_168_0) = all_91_4 % 165.29/22.77 | | | | % 165.29/22.77 | | | | REDUCE: (66), (76) imply: % 165.29/22.77 | | | | (96) app(all_118_2, all_118_0) = nil % 165.29/22.77 | | | | % 165.29/22.77 | | | | REDUCE: (73), (83) imply: % 165.29/22.77 | | | | (97) app(nil, nil) = all_142_0 % 165.29/22.77 | | | | % 165.29/22.77 | | | | GROUND_INST: instantiating (13) with all_142_0, simplifying with (6), % 165.29/22.77 | | | | (97) gives: % 165.29/22.77 | | | | (98) all_142_0 = nil % 165.29/22.77 | | | | % 165.29/22.77 | | | | REDUCE: (97), (98) imply: % 165.29/22.77 | | | | (99) app(nil, nil) = nil % 165.29/22.77 | | | | % 165.29/22.77 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_168_0, % 165.29/22.77 | | | | all_91_4, simplifying with (6), (17), (93), (94), (95), % 165.29/22.77 | | | | (99) gives: % 165.29/22.77 | | | | (100) ? [v0: $i] : (app(nil, v0) = all_91_4 & app(nil, all_168_0) = % 165.29/22.77 | | | | v0 & $i(v0) & $i(all_91_4)) % 165.29/22.77 | | | | % 165.29/22.77 | | | | GROUND_INST: instantiating (7) with all_168_0, all_91_4, simplifying % 165.29/22.77 | | | | with (93), (94), (95) gives: % 165.29/22.77 | | | | (101) all_168_0 = all_91_4 % 165.29/22.77 | | | | % 165.29/22.77 | | | | GROUND_INST: instantiating (4) with all_91_4, all_168_0, nil, all_91_4, % 165.29/22.77 | | | | all_166_0, simplifying with (6), (17), (21), (25), (89), % 165.29/22.77 | | | | (90), (91), (93), (94), (95) gives: % 165.29/22.77 | | | | (102) segmentP(all_91_4, all_168_0) % 165.29/22.77 | | | | % 165.29/22.77 | | | | GROUND_INST: instantiating (ax82) with all_118_2, all_118_0, nil, % 165.29/22.77 | | | | all_168_0, all_91_4, simplifying with (60), (61), (62), % 165.29/22.77 | | | | (64), (93), (94), (95), (96) gives: % 165.29/22.77 | | | | (103) ? [v0: $i] : (app(all_118_0, all_168_0) = v0 & app(all_118_2, % 165.29/22.77 | | | | v0) = all_91_4 & $i(v0) & $i(all_91_4)) % 165.29/22.77 | | | | % 165.29/22.77 | | | | GROUND_INST: instantiating (15) with all_118_2, all_118_0, simplifying % 165.29/22.77 | | | | with (60), (61), (62), (64), (96) gives: % 165.29/22.77 | | | | (104) all_118_0 = nil % 165.29/22.77 | | | | % 165.29/22.77 | | | | GROUND_INST: instantiating (14) with all_118_2, all_118_0, simplifying % 165.29/22.77 | | | | with (60), (61), (62), (64), (96) gives: % 165.29/22.77 | | | | (105) all_118_2 = nil % 165.29/22.77 | | | | % 165.29/22.77 | | | | GROUND_INST: instantiating (ax82) with all_140_0, nil, all_91_2, % 165.29/22.77 | | | | all_91_4, all_91_1, simplifying with (6), (17), (21), (25), % 165.29/22.77 | | | | (29), (78), (79), (80) gives: % 165.29/22.78 | | | | (106) ? [v0: $i] : (app(all_140_0, v0) = all_91_1 & app(nil, % 165.29/22.78 | | | | all_91_4) = v0 & $i(v0) & $i(all_91_1)) % 165.29/22.78 | | | | % 165.29/22.78 | | | | GROUND_INST: instantiating (16) with all_164_0, all_91_4, simplifying % 165.29/22.78 | | | | with (85), (86), (87) gives: % 165.29/22.78 | | | | (107) all_164_0 = all_91_4 % 165.29/22.78 | | | | % 165.29/22.78 | | | | DELTA: instantiating (103) with fresh symbol all_264_0 gives: % 165.29/22.78 | | | | (108) app(all_118_0, all_168_0) = all_264_0 & app(all_118_2, % 165.29/22.78 | | | | all_264_0) = all_91_4 & $i(all_264_0) & $i(all_91_4) % 165.29/22.78 | | | | % 165.29/22.78 | | | | ALPHA: (108) implies: % 165.29/22.78 | | | | (109) $i(all_264_0) % 165.29/22.78 | | | | (110) app(all_118_0, all_168_0) = all_264_0 % 165.29/22.78 | | | | % 165.29/22.78 | | | | DELTA: instantiating (106) with fresh symbol all_282_0 gives: % 165.29/22.78 | | | | (111) app(all_140_0, all_282_0) = all_91_1 & app(nil, all_91_4) = % 165.29/22.78 | | | | all_282_0 & $i(all_282_0) & $i(all_91_1) % 165.29/22.78 | | | | % 165.29/22.78 | | | | ALPHA: (111) implies: % 165.29/22.78 | | | | (112) app(nil, all_91_4) = all_282_0 % 165.29/22.78 | | | | % 165.29/22.78 | | | | DELTA: instantiating (100) with fresh symbol all_306_0 gives: % 165.29/22.78 | | | | (113) app(nil, all_306_0) = all_91_4 & app(nil, all_168_0) = % 165.29/22.78 | | | | all_306_0 & $i(all_306_0) & $i(all_91_4) % 165.29/22.78 | | | | % 165.29/22.78 | | | | ALPHA: (113) implies: % 165.29/22.78 | | | | (114) app(nil, all_168_0) = all_306_0 % 165.29/22.78 | | | | % 165.29/22.78 | | | | REDUCE: (101), (104), (110) imply: % 165.29/22.78 | | | | (115) app(nil, all_91_4) = all_264_0 % 165.29/22.78 | | | | % 165.29/22.78 | | | | REDUCE: (101), (114) imply: % 165.29/22.78 | | | | (116) app(nil, all_91_4) = all_306_0 % 165.29/22.78 | | | | % 165.29/22.78 | | | | REDUCE: (95), (101) imply: % 165.29/22.78 | | | | (117) app(nil, all_91_4) = all_91_4 % 165.29/22.78 | | | | % 165.29/22.78 | | | | REDUCE: (101), (102) imply: % 165.29/22.78 | | | | (118) segmentP(all_91_4, all_91_4) % 165.29/22.78 | | | | % 165.29/22.78 | | | | GROUND_INST: instantiating (19) with all_264_0, all_282_0, all_91_4, % 165.29/22.78 | | | | nil, simplifying with (112), (115) gives: % 165.29/22.78 | | | | (119) all_282_0 = all_264_0 % 165.29/22.78 | | | | % 165.29/22.78 | | | | GROUND_INST: instantiating (19) with all_282_0, all_306_0, all_91_4, % 165.29/22.78 | | | | nil, simplifying with (112), (116) gives: % 165.29/22.78 | | | | (120) all_306_0 = all_282_0 % 165.29/22.78 | | | | % 165.29/22.78 | | | | GROUND_INST: instantiating (19) with all_91_4, all_306_0, all_91_4, nil, % 165.29/22.78 | | | | simplifying with (116), (117) gives: % 165.29/22.78 | | | | (121) all_306_0 = all_91_4 % 165.29/22.78 | | | | % 165.29/22.78 | | | | COMBINE_EQS: (120), (121) imply: % 165.29/22.78 | | | | (122) all_282_0 = all_91_4 % 165.29/22.78 | | | | % 165.29/22.78 | | | | SIMP: (122) implies: % 165.29/22.78 | | | | (123) all_282_0 = all_91_4 % 165.29/22.78 | | | | % 165.29/22.78 | | | | COMBINE_EQS: (119), (123) imply: % 165.29/22.78 | | | | (124) all_264_0 = all_91_4 % 165.29/22.78 | | | | % 165.29/22.78 | | | | SIMP: (124) implies: % 165.29/22.78 | | | | (125) all_264_0 = all_91_4 % 165.29/22.78 | | | | % 165.29/22.78 | | | | BETA: splitting (31) gives: % 165.29/22.78 | | | | % 165.29/22.78 | | | | Case 1: % 165.29/22.78 | | | | | % 165.29/22.78 | | | | | (126) ~ (all_91_4 = nil) % 165.29/22.78 | | | | | % 165.29/22.78 | | | | | REF_CLOSE: (21), (25), (33), (50), (67), (105), (118), (126) are % 165.29/22.78 | | | | | inconsistent by sub-proof #1. % 165.29/22.78 | | | | | % 165.29/22.78 | | | | Case 2: % 165.29/22.78 | | | | | % 165.29/22.78 | | | | | (127) all_91_3 = nil % 165.29/22.78 | | | | | % 165.29/22.78 | | | | | BETA: splitting (32) gives: % 165.29/22.78 | | | | | % 165.29/22.78 | | | | | Case 1: % 165.29/22.78 | | | | | | % 165.29/22.78 | | | | | | (128) ~ (all_91_3 = nil) % 165.29/22.78 | | | | | | % 165.29/22.78 | | | | | | REDUCE: (127), (128) imply: % 165.29/22.78 | | | | | | (129) $false % 165.29/22.78 | | | | | | % 165.29/22.78 | | | | | | CLOSE: (129) is inconsistent. % 165.29/22.78 | | | | | | % 165.29/22.78 | | | | | Case 2: % 165.29/22.78 | | | | | | % 165.29/22.78 | | | | | | (130) ~ (all_91_4 = nil) % 165.29/22.78 | | | | | | % 165.29/22.78 | | | | | | REF_CLOSE: (21), (25), (33), (50), (67), (105), (118), (130) are % 165.29/22.78 | | | | | | inconsistent by sub-proof #1. % 165.29/22.78 | | | | | | % 165.29/22.78 | | | | | End of split % 165.29/22.78 | | | | | % 165.29/22.78 | | | | End of split % 165.29/22.78 | | | | % 165.29/22.78 | | | End of split % 165.29/22.78 | | | % 165.29/22.78 | | End of split % 165.29/22.78 | | % 165.29/22.78 | End of split % 165.29/22.78 | % 165.29/22.78 End of proof % 165.29/22.78 % 165.29/22.78 Sub-proof #1 shows that the following formulas are inconsistent: % 165.29/22.78 ---------------------------------------------------------------- % 165.29/22.78 (1) $i(all_91_4) % 165.29/22.78 (2) all_118_2 = nil % 165.29/22.78 (3) all_118_2 = all_91_4 | neq(all_91_4, all_118_2) % 165.29/22.78 (4) ~ (all_91_4 = nil) % 165.29/22.78 (5) segmentP(all_91_3, all_91_4) % 165.29/22.78 (6) ssList(all_91_4) % 165.29/22.78 (7) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_3, v0) | ~ % 165.29/22.78 segmentP(all_91_4, v0) | ~ ssList(v0) | ~ neq(v0, nil)) % 165.29/22.78 (8) segmentP(all_91_4, all_91_4) % 165.29/22.78 % 165.29/22.78 Begin of proof % 165.29/22.78 | % 165.29/22.78 | BETA: splitting (3) gives: % 165.29/22.78 | % 165.29/22.78 | Case 1: % 165.29/22.78 | | % 165.29/22.78 | | (9) neq(all_91_4, all_118_2) % 165.29/22.78 | | % 165.29/22.78 | | REDUCE: (2), (9) imply: % 165.29/22.79 | | (10) neq(all_91_4, nil) % 165.29/22.79 | | % 165.29/22.79 | | GROUND_INST: instantiating (7) with all_91_4, simplifying with (1), (5), % 165.29/22.79 | | (6), (8), (10) gives: % 165.29/22.79 | | (11) $false % 165.29/22.79 | | % 165.29/22.79 | | CLOSE: (11) is inconsistent. % 165.29/22.79 | | % 165.29/22.79 | Case 2: % 165.29/22.79 | | % 165.29/22.79 | | (12) all_118_2 = all_91_4 % 165.29/22.79 | | % 165.29/22.79 | | COMBINE_EQS: (2), (12) imply: % 165.29/22.79 | | (13) all_91_4 = nil % 165.29/22.79 | | % 165.29/22.79 | | SIMP: (13) implies: % 165.29/22.79 | | (14) all_91_4 = nil % 165.29/22.79 | | % 165.29/22.79 | | REDUCE: (4), (14) imply: % 165.29/22.79 | | (15) $false % 165.29/22.79 | | % 165.29/22.79 | | CLOSE: (15) is inconsistent. % 165.29/22.79 | | % 165.29/22.79 | End of split % 165.29/22.79 | % 165.29/22.79 End of proof % 165.29/22.79 % SZS output end Proof for theBenchmark % 165.29/22.79 % 165.29/22.79 22174ms %------------------------------------------------------------------------------