%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC092+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 : n001.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 20:49:36 EDT 2023 % Result : Theorem 134.47s 18.77s % Output : Proof 155.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC092+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 : n001.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 19:07:50 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.82/1.56 Prover 1: Preprocessing ... % 5.82/1.57 Prover 4: Preprocessing ... % 5.82/1.59 Prover 3: Preprocessing ... % 5.82/1.59 Prover 5: Preprocessing ... % 5.82/1.59 Prover 6: Preprocessing ... % 5.82/1.60 Prover 2: Preprocessing ... % 5.82/1.60 Prover 0: Preprocessing ... % 15.94/2.98 Prover 2: Proving ... % 16.54/3.07 Prover 1: Constructing countermodel ... % 16.82/3.09 Prover 5: Constructing countermodel ... % 16.82/3.12 Prover 6: Proving ... % 17.20/3.13 Prover 3: Constructing countermodel ... % 22.52/3.87 Prover 4: Constructing countermodel ... % 23.95/4.05 Prover 0: Proving ... % 71.02/10.36 Prover 2: stopped % 71.50/10.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.52/10.54 Prover 7: Preprocessing ... % 74.39/10.80 Prover 7: Constructing countermodel ... % 98.13/14.01 Prover 5: stopped % 98.13/14.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 100.38/14.19 Prover 8: Preprocessing ... % 102.63/14.48 Prover 8: Warning: ignoring some quantifiers % 102.63/14.49 Prover 8: Constructing countermodel ... % 113.76/15.98 Prover 1: stopped % 113.76/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 114.20/16.04 Prover 9: Preprocessing ... % 119.34/16.72 Prover 9: Constructing countermodel ... % 127.96/17.90 Prover 6: stopped % 127.96/17.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 129.11/18.03 Prover 10: Preprocessing ... % 130.24/18.19 Prover 10: Constructing countermodel ... % 134.47/18.76 Prover 9: proved (2771ms) % 134.47/18.76 % 134.47/18.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 134.47/18.77 % 134.91/18.79 Prover 3: stopped % 134.91/18.80 Prover 0: stopped % 134.91/18.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 134.91/18.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 134.91/18.82 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 135.47/18.87 Prover 11: Preprocessing ... % 135.47/18.89 Prover 13: Preprocessing ... % 135.47/18.93 Prover 16: Preprocessing ... % 136.24/19.09 Prover 16: Constructing countermodel ... % 136.95/19.15 Prover 13: Constructing countermodel ... % 140.97/19.72 Prover 11: Constructing countermodel ... % 155.57/21.65 Prover 7: Found proof (size 127) % 155.57/21.65 Prover 7: proved (11193ms) % 155.57/21.65 Prover 13: stopped % 155.57/21.65 Prover 8: stopped % 155.57/21.65 Prover 16: stopped % 155.57/21.65 Prover 11: stopped % 155.57/21.65 Prover 10: stopped % 155.57/21.65 Prover 4: stopped % 155.57/21.65 % 155.57/21.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 155.57/21.65 % 155.57/21.66 % SZS output start Proof for theBenchmark % 155.57/21.67 Assumptions after simplification: % 155.57/21.67 --------------------------------- % 155.57/21.67 % 155.57/21.67 (ax15) % 155.57/21.68 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 155.57/21.68 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ % 155.57/21.68 neq(v0, v0)) % 155.57/21.68 % 155.57/21.68 (ax17) % 155.57/21.68 $i(nil) & ssList(nil) % 155.57/21.68 % 155.57/21.68 (ax26) % 155.57/21.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | % 155.57/21.70 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 155.57/21.70 % 155.57/21.70 (ax28) % 155.57/21.70 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 155.57/21.70 $i(v0) | ~ ssList(v0)) % 155.57/21.70 % 155.57/21.70 (ax45) % 155.57/21.70 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 155.57/21.70 % 155.57/21.70 (ax46) % 155.57/21.70 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 155.57/21.70 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 155.57/21.70 % 155.57/21.70 (ax5) % 155.57/21.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 155.57/21.71 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 155.57/21.71 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 155.57/21.71 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 155.57/21.71 v2) = v0 & $i(v2) & ssList(v2))) % 155.57/21.71 % 155.57/21.71 (ax51) % 155.57/21.71 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 155.57/21.71 % 155.57/21.71 (ax55) % 155.57/21.71 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, v0)) % 155.57/21.71 % 155.57/21.71 (ax58) % 155.57/21.71 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 155.57/21.71 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 155.57/21.71 % 155.57/21.71 (ax6) % 155.57/21.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 155.57/21.71 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 155.57/21.71 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 155.57/21.71 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 155.57/21.71 v1) = v0 & $i(v2) & ssList(v2))) % 155.57/21.71 % 155.57/21.71 (ax7) % 155.57/21.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 155.57/21.71 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 155.57/21.71 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 155.57/21.71 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 155.57/21.71 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 155.57/21.71 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 155.57/21.71 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 155.57/21.71 % 155.57/21.71 (ax82) % 155.57/21.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 155.57/21.72 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 155.57/21.72 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 155.57/21.72 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! % 155.57/21.72 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (app(v1, v3) = v4) | % 155.57/21.72 ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v3) | % 155.57/21.72 ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : (app(v2, v3) = v5 & app(v0, v4) % 155.57/21.72 = v5 & $i(v5))) % 155.57/21.72 % 155.57/21.72 (ax83) % 155.57/21.72 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 155.57/21.72 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 155.57/21.72 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 155.57/21.72 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 155.57/21.72 v0) | ~ ssList(nil)) % 155.57/21.72 % 155.57/21.72 (ax84) % 155.57/21.72 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 155.57/21.72 $i(v0) | ~ ssList(v0)) % 155.57/21.72 % 155.57/21.72 (co1) % 155.57/21.73 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) % 155.57/21.73 & $i(v1) & $i(v0) & strictorderedP(v0) & ssList(v2) & ssList(v1) & % 155.57/21.73 ssList(v0) & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 155.57/21.73 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v6, nil) = v7) | ~ % 155.57/21.73 (cons(v3, nil) = v4) | ~ (app(v8, v7) = v0) | ~ (app(v4, v5) = v2) | ~ % 155.57/21.73 $i(v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ lt(v6, v3) | ~ ssList(v8) % 155.57/21.73 | ~ ssList(v5) | ~ ssItem(v6) | ~ ssItem(v3)) & ! [v3: $i] : ( ~ % 155.57/21.73 $i(v3) | ~ segmentP(v1, v3) | ~ segmentP(v0, v3) | ~ ssList(v3) | ~ % 155.57/21.73 neq(v3, nil)) & ( ~ (v0 = nil) | v1 = nil)) % 155.57/21.73 % 155.57/21.73 (function-axioms) % 155.57/21.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.57/21.73 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 155.57/21.73 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 155.57/21.73 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 155.57/21.73 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 155.57/21.73 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 155.57/21.73 % 155.57/21.73 Further assumptions not needed in the proof: % 155.57/21.73 -------------------------------------------- % 155.57/21.73 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 155.57/21.73 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 155.57/21.73 ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax47, ax48, ax49, ax50, % 155.57/21.73 ax52, ax53, ax54, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, % 155.57/21.73 ax67, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, % 155.57/21.73 ax8, ax80, ax81, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 155.57/21.73 ax94, ax95 % 155.57/21.73 % 155.57/21.73 Those formulas are unsatisfiable: % 155.57/21.73 --------------------------------- % 155.57/21.73 % 155.57/21.73 Begin of proof % 155.57/21.73 | % 155.57/21.73 | ALPHA: (ax5) implies: % 155.57/21.73 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 155.57/21.73 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 155.57/21.73 | v0 & $i(v2) & ssList(v2))) % 155.57/21.73 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ % 155.57/21.73 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ % 155.57/21.73 | ssList(v0) | frontsegP(v0, v1)) % 155.57/21.73 | % 155.57/21.74 | ALPHA: (ax6) implies: % 155.57/21.74 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 155.57/21.74 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 155.57/21.74 | v0 & $i(v2) & ssList(v2))) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax7) implies: % 155.57/21.74 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, % 155.57/21.74 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] : % 155.57/21.74 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) & % 155.57/21.74 | $i(v2) & ssList(v4) & ssList(v2))) % 155.57/21.74 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 155.57/21.74 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 155.57/21.74 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 155.57/21.74 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax15) implies: % 155.57/21.74 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 155.57/21.74 | ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax17) implies: % 155.57/21.74 | (7) ssList(nil) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax28) implies: % 155.57/21.74 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 155.57/21.74 | $i(v0) | ~ ssList(v0)) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax45) implies: % 155.57/21.74 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax46) implies: % 155.57/21.74 | (10) ~ ssList(nil) | frontsegP(nil, nil) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax51) implies: % 155.57/21.74 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax58) implies: % 155.57/21.74 | (12) ~ ssList(nil) | segmentP(nil, nil) % 155.57/21.74 | % 155.57/21.74 | ALPHA: (ax82) implies: % 155.57/21.74 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 155.57/21.74 | ( ~ (app(v1, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) % 155.57/21.74 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? % 155.57/21.74 | [v5: $i] : (app(v2, v3) = v5 & app(v0, v4) = v5 & $i(v5))) % 155.57/21.75 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 155.57/21.75 | ( ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) % 155.57/21.75 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? % 155.57/21.75 | [v5: $i] : (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 155.57/21.75 | % 155.57/21.75 | ALPHA: (ax83) implies: % 155.57/21.75 | (15) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 155.57/21.75 | (16) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ % 155.57/21.75 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 155.57/21.75 | (17) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 155.57/21.75 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 155.57/21.75 | % 155.57/21.75 | ALPHA: (ax84) implies: % 155.57/21.75 | (18) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 155.57/21.75 | $i(v0) | ~ ssList(v0)) % 155.57/21.75 | % 155.57/21.75 | ALPHA: (co1) implies: % 155.57/21.75 | (19) $i(nil) % 155.57/21.75 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) & % 155.57/21.75 | $i(v1) & $i(v0) & strictorderedP(v0) & ssList(v2) & ssList(v1) & % 155.57/21.75 | ssList(v0) & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 155.57/21.75 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v6, nil) = v7) % 155.57/21.75 | | ~ (cons(v3, nil) = v4) | ~ (app(v8, v7) = v0) | ~ (app(v4, % 155.57/21.75 | v5) = v2) | ~ $i(v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ % 155.57/21.75 | lt(v6, v3) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v6) | ~ % 155.57/21.75 | ssItem(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ segmentP(v1, v3) | ~ % 155.57/21.75 | segmentP(v0, v3) | ~ ssList(v3) | ~ neq(v3, nil)) & ( ~ (v0 = % 155.57/21.75 | nil) | v1 = nil)) % 155.57/21.75 | % 155.57/21.75 | ALPHA: (function-axioms) implies: % 155.57/21.75 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.57/21.75 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 155.57/21.75 | % 155.57/21.75 | DELTA: instantiating (20) with fresh symbols all_91_0, all_91_1, all_91_2 % 155.57/21.75 | gives: % 155.57/21.75 | (22) app(all_91_2, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) & % 155.57/21.75 | $i(all_91_2) & strictorderedP(all_91_2) & ssList(all_91_0) & % 155.57/21.75 | ssList(all_91_1) & ssList(all_91_2) & neq(all_91_1, nil) & ! [v0: $i] % 155.57/21.75 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 155.57/21.75 | : ( ~ (cons(v3, nil) = v4) | ~ (cons(v0, nil) = v1) | ~ (app(v5, v4) % 155.57/21.75 | = all_91_2) | ~ (app(v1, v2) = all_91_0) | ~ $i(v5) | ~ $i(v3) % 155.57/21.75 | | ~ $i(v2) | ~ $i(v0) | ~ lt(v3, v0) | ~ ssList(v5) | ~ % 155.57/21.75 | ssList(v2) | ~ ssItem(v3) | ~ ssItem(v0)) & ! [v0: $i] : ( ~ % 155.57/21.75 | $i(v0) | ~ segmentP(all_91_1, v0) | ~ segmentP(all_91_2, v0) | ~ % 155.57/21.75 | ssList(v0) | ~ neq(v0, nil)) & ( ~ (all_91_2 = nil) | all_91_1 = % 155.57/21.75 | nil) % 155.57/21.75 | % 155.57/21.75 | ALPHA: (22) implies: % 155.57/21.76 | (23) neq(all_91_1, nil) % 155.57/21.76 | (24) ssList(all_91_2) % 155.57/21.76 | (25) ssList(all_91_1) % 155.57/21.76 | (26) ssList(all_91_0) % 155.57/21.76 | (27) $i(all_91_2) % 155.57/21.76 | (28) $i(all_91_1) % 155.57/21.76 | (29) $i(all_91_0) % 155.57/21.76 | (30) app(all_91_2, all_91_0) = all_91_1 % 155.57/21.76 | (31) ~ (all_91_2 = nil) | all_91_1 = nil % 155.57/21.76 | (32) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_1, v0) | ~ % 155.57/21.76 | segmentP(all_91_2, v0) | ~ ssList(v0) | ~ neq(v0, nil)) % 155.57/21.76 | % 155.57/21.76 | BETA: splitting (10) gives: % 155.57/21.76 | % 155.57/21.76 | Case 1: % 155.57/21.76 | | % 155.57/21.76 | | (33) ~ ssList(nil) % 155.57/21.76 | | % 155.57/21.76 | | PRED_UNIFY: (7), (33) imply: % 155.57/21.76 | | (34) $false % 155.57/21.76 | | % 155.57/21.76 | | CLOSE: (34) is inconsistent. % 155.57/21.76 | | % 155.57/21.76 | Case 2: % 155.57/21.76 | | % 155.57/21.76 | | (35) frontsegP(nil, nil) % 155.57/21.76 | | % 155.57/21.76 | | BETA: splitting (12) gives: % 155.57/21.76 | | % 155.57/21.76 | | Case 1: % 155.57/21.76 | | | % 155.57/21.76 | | | (36) ~ ssList(nil) % 155.57/21.76 | | | % 155.57/21.76 | | | PRED_UNIFY: (7), (36) imply: % 155.57/21.76 | | | (37) $false % 155.57/21.76 | | | % 155.57/21.76 | | | CLOSE: (37) is inconsistent. % 155.57/21.76 | | | % 155.57/21.76 | | Case 2: % 155.57/21.76 | | | % 155.57/21.76 | | | (38) segmentP(nil, nil) % 155.57/21.76 | | | % 155.57/21.76 | | | GROUND_INST: instantiating (ax55) with all_91_2, simplifying with (24), % 155.57/21.76 | | | (27) gives: % 155.57/21.76 | | | (39) segmentP(all_91_2, all_91_2) % 155.57/21.76 | | | % 155.57/21.76 | | | GROUND_INST: instantiating (11) with all_91_2, simplifying with (24), (27) % 155.57/21.76 | | | gives: % 155.57/21.76 | | | (40) rearsegP(all_91_2, nil) % 155.57/21.76 | | | % 155.57/21.76 | | | GROUND_INST: instantiating (9) with all_91_2, simplifying with (24), (27) % 155.57/21.76 | | | gives: % 155.57/21.76 | | | (41) frontsegP(all_91_2, nil) % 155.57/21.76 | | | % 155.57/21.76 | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (7), (19), % 155.57/21.76 | | | (35) gives: % 155.57/21.76 | | | (42) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 155.57/21.76 | | | % 155.57/21.76 | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (7), (19), % 155.57/21.76 | | | (38) gives: % 155.57/21.76 | | | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil & % 155.57/21.76 | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) & % 155.57/21.76 | | | ssList(v0)) % 155.57/21.76 | | | % 155.57/21.76 | | | GROUND_INST: instantiating (2) with all_91_1, all_91_2, all_91_0, % 155.57/21.76 | | | simplifying with (24), (25), (26), (27), (28), (29), (30) % 155.57/21.76 | | | gives: % 155.57/21.76 | | | (44) frontsegP(all_91_1, all_91_2) % 155.57/21.76 | | | % 155.57/21.76 | | | DELTA: instantiating (42) with fresh symbol all_114_0 gives: % 155.57/21.76 | | | (45) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0) % 155.57/21.77 | | | % 155.57/21.77 | | | ALPHA: (45) implies: % 155.57/21.77 | | | (46) ssList(all_114_0) % 155.57/21.77 | | | (47) $i(all_114_0) % 155.57/21.77 | | | (48) app(nil, all_114_0) = nil % 155.57/21.77 | | | % 155.57/21.77 | | | DELTA: instantiating (43) with fresh symbols all_116_0, all_116_1, % 155.57/21.77 | | | all_116_2 gives: % 155.57/21.77 | | | (49) app(all_116_1, all_116_0) = nil & app(all_116_2, nil) = all_116_1 % 155.57/21.77 | | | & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) & % 155.57/21.77 | | | ssList(all_116_0) & ssList(all_116_2) % 155.57/21.77 | | | % 155.57/21.77 | | | ALPHA: (49) implies: % 155.57/21.77 | | | (50) ssList(all_116_2) % 155.57/21.77 | | | (51) ssList(all_116_0) % 155.57/21.77 | | | (52) $i(all_116_2) % 155.57/21.77 | | | (53) $i(all_116_0) % 155.57/21.77 | | | (54) app(all_116_2, nil) = all_116_1 % 155.57/21.77 | | | (55) app(all_116_1, all_116_0) = nil % 155.57/21.77 | | | % 155.57/21.77 | | | GROUND_INST: instantiating (1) with all_91_2, nil, simplifying with (7), % 155.57/21.77 | | | (19), (24), (27), (41) gives: % 155.57/21.77 | | | (56) ? [v0: $i] : (app(nil, v0) = all_91_2 & $i(v0) & ssList(v0)) % 155.57/21.77 | | | % 155.57/21.77 | | | GROUND_INST: instantiating (1) with all_91_1, all_91_2, simplifying with % 155.57/21.77 | | | (24), (25), (27), (28), (44) gives: % 155.57/21.77 | | | (57) ? [v0: $i] : (app(all_91_2, v0) = all_91_1 & $i(v0) & ssList(v0)) % 155.57/21.77 | | | % 155.57/21.77 | | | GROUND_INST: instantiating (3) with all_91_2, nil, simplifying with (7), % 155.57/21.77 | | | (19), (24), (27), (40) gives: % 155.57/21.77 | | | (58) ? [v0: $i] : (app(v0, nil) = all_91_2 & $i(v0) & ssList(v0)) % 155.57/21.77 | | | % 155.57/21.77 | | | GROUND_INST: instantiating (32) with all_91_2, simplifying with (24), % 155.57/21.77 | | | (27), (39) gives: % 155.57/21.77 | | | (59) ~ segmentP(all_91_1, all_91_2) | ~ neq(all_91_2, nil) % 155.57/21.77 | | | % 155.57/21.77 | | | GROUND_INST: instantiating (14) with nil, nil, nil, nil, nil, simplifying % 155.57/21.77 | | | with (7), (19) gives: % 155.57/21.77 | | | (60) ~ (app(nil, nil) = nil) | ? [v0: $i] : (app(nil, v0) = nil & % 155.57/21.77 | | | app(nil, nil) = v0 & $i(v0)) % 155.57/21.77 | | | % 155.57/21.77 | | | GROUND_INST: instantiating (14) with nil, all_114_0, nil, all_114_0, nil, % 155.57/21.77 | | | simplifying with (7), (19), (46), (47), (48) gives: % 155.57/21.77 | | | (61) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) = nil % 155.57/21.77 | | | & $i(v0)) % 155.57/21.77 | | | % 155.57/21.77 | | | GROUND_INST: instantiating (8) with all_114_0, nil, simplifying with (46), % 155.57/21.77 | | | (47), (48) gives: % 155.57/21.77 | | | (62) all_114_0 = nil % 155.57/21.77 | | | % 155.57/21.77 | | | GROUND_INST: instantiating (14) with all_116_2, nil, all_116_2, nil, % 155.57/21.77 | | | all_116_2, simplifying with (7), (19), (50), (52) gives: % 155.57/21.77 | | | (63) ~ (app(all_116_2, nil) = all_116_2) | ? [v0: $i] : % 155.57/21.77 | | | (app(all_116_2, v0) = all_116_2 & app(nil, nil) = v0 & $i(v0)) % 155.57/21.77 | | | % 155.57/21.78 | | | GROUND_INST: instantiating (13) with all_116_2, nil, all_116_1, all_114_0, % 155.57/21.78 | | | nil, simplifying with (7), (19), (46), (47), (48), (50), % 155.57/21.78 | | | (52), (54) gives: % 155.57/21.78 | | | (64) ? [v0: $i] : (app(all_116_1, all_114_0) = v0 & app(all_116_2, % 155.57/21.78 | | | nil) = v0 & $i(v0)) % 155.57/21.78 | | | % 155.57/21.78 | | | GROUND_INST: instantiating (ax26) with all_116_2, nil, all_116_1, % 155.57/21.78 | | | simplifying with (7), (19), (50), (52), (54) gives: % 155.57/21.78 | | | (65) ssList(all_116_1) % 155.57/21.78 | | | % 155.57/21.78 | | | GROUND_INST: instantiating (18) with all_116_2, all_116_1, simplifying % 155.57/21.78 | | | with (50), (52), (54) gives: % 155.57/21.78 | | | (66) all_116_1 = all_116_2 % 155.57/21.78 | | | % 155.57/21.78 | | | GROUND_INST: instantiating (14) with all_116_2, nil, all_116_1, all_116_0, % 155.57/21.78 | | | nil, simplifying with (7), (19), (50), (51), (52), (53), % 155.57/21.78 | | | (54), (55) gives: % 155.57/21.78 | | | (67) ? [v0: $i] : (app(all_116_2, v0) = nil & app(nil, all_116_0) = v0 % 155.57/21.78 | | | & $i(v0)) % 155.57/21.78 | | | % 155.57/21.78 | | | GROUND_INST: instantiating (17) with all_116_2, all_116_0, simplifying % 155.57/21.78 | | | with (50), (51), (52), (53) gives: % 155.57/21.78 | | | (68) all_116_0 = nil | ~ (app(all_116_2, all_116_0) = nil) % 155.57/21.78 | | | % 155.57/21.78 | | | GROUND_INST: instantiating (16) with all_116_2, all_116_0, simplifying % 155.57/21.78 | | | with (50), (51), (52), (53) gives: % 155.57/21.78 | | | (69) all_116_2 = nil | ~ (app(all_116_2, all_116_0) = nil) % 155.57/21.78 | | | % 155.57/21.78 | | | DELTA: instantiating (64) with fresh symbol all_132_0 gives: % 155.57/21.78 | | | (70) app(all_116_1, all_114_0) = all_132_0 & app(all_116_2, nil) = % 155.57/21.78 | | | all_132_0 & $i(all_132_0) % 155.57/21.78 | | | % 155.57/21.78 | | | ALPHA: (70) implies: % 155.57/21.78 | | | (71) $i(all_132_0) % 155.57/21.78 | | | (72) app(all_116_1, all_114_0) = all_132_0 % 155.57/21.78 | | | % 155.57/21.78 | | | DELTA: instantiating (61) with fresh symbol all_134_0 gives: % 155.57/21.78 | | | (73) app(all_114_0, all_114_0) = all_134_0 & app(nil, all_134_0) = nil % 155.57/21.78 | | | & $i(all_134_0) % 155.57/21.78 | | | % 155.57/21.78 | | | ALPHA: (73) implies: % 155.57/21.78 | | | (74) app(all_114_0, all_114_0) = all_134_0 % 155.57/21.78 | | | % 155.57/21.78 | | | DELTA: instantiating (57) with fresh symbol all_140_0 gives: % 155.57/21.78 | | | (75) app(all_91_2, all_140_0) = all_91_1 & $i(all_140_0) & % 155.57/21.78 | | | ssList(all_140_0) % 155.57/21.78 | | | % 155.57/21.78 | | | ALPHA: (75) implies: % 155.57/21.78 | | | (76) ssList(all_140_0) % 155.57/21.78 | | | (77) $i(all_140_0) % 155.57/21.78 | | | (78) app(all_91_2, all_140_0) = all_91_1 % 155.57/21.78 | | | % 155.57/21.78 | | | DELTA: instantiating (56) with fresh symbol all_146_0 gives: % 155.57/21.78 | | | (79) app(nil, all_146_0) = all_91_2 & $i(all_146_0) & ssList(all_146_0) % 155.57/21.78 | | | % 155.57/21.78 | | | ALPHA: (79) implies: % 155.57/21.78 | | | (80) ssList(all_146_0) % 155.57/21.78 | | | (81) $i(all_146_0) % 155.57/21.78 | | | (82) app(nil, all_146_0) = all_91_2 % 155.57/21.78 | | | % 155.57/21.78 | | | DELTA: instantiating (67) with fresh symbol all_150_0 gives: % 155.57/21.78 | | | (83) app(all_116_2, all_150_0) = nil & app(nil, all_116_0) = all_150_0 % 155.57/21.78 | | | & $i(all_150_0) % 155.57/21.78 | | | % 155.57/21.78 | | | ALPHA: (83) implies: % 155.57/21.78 | | | (84) app(nil, all_116_0) = all_150_0 % 155.57/21.78 | | | % 155.57/21.78 | | | DELTA: instantiating (58) with fresh symbol all_154_0 gives: % 155.57/21.78 | | | (85) app(all_154_0, nil) = all_91_2 & $i(all_154_0) & ssList(all_154_0) % 155.57/21.78 | | | % 155.57/21.78 | | | ALPHA: (85) implies: % 155.57/21.78 | | | (86) ssList(all_154_0) % 155.57/21.78 | | | (87) $i(all_154_0) % 155.57/21.78 | | | (88) app(all_154_0, nil) = all_91_2 % 155.57/21.78 | | | % 155.57/21.78 | | | REDUCE: (55), (66) imply: % 155.57/21.78 | | | (89) app(all_116_2, all_116_0) = nil % 155.57/21.78 | | | % 155.57/21.78 | | | REDUCE: (62), (66), (72) imply: % 155.57/21.78 | | | (90) app(all_116_2, nil) = all_132_0 % 155.57/21.78 | | | % 155.57/21.79 | | | REDUCE: (54), (66) imply: % 155.57/21.79 | | | (91) app(all_116_2, nil) = all_116_2 % 155.57/21.79 | | | % 155.57/21.79 | | | REDUCE: (62), (74) imply: % 155.57/21.79 | | | (92) app(nil, nil) = all_134_0 % 155.57/21.79 | | | % 155.57/21.79 | | | REDUCE: (48), (62) imply: % 155.57/21.79 | | | (93) app(nil, nil) = nil % 155.57/21.79 | | | % 155.57/21.79 | | | BETA: splitting (63) gives: % 155.57/21.79 | | | % 155.57/21.79 | | | Case 1: % 155.57/21.79 | | | | % 155.57/21.79 | | | | (94) ~ (app(all_116_2, nil) = all_116_2) % 155.57/21.79 | | | | % 155.57/21.79 | | | | PRED_UNIFY: (91), (94) imply: % 155.57/21.79 | | | | (95) $false % 155.57/21.79 | | | | % 155.57/21.79 | | | | CLOSE: (95) is inconsistent. % 155.57/21.79 | | | | % 155.57/21.79 | | | Case 2: % 155.57/21.79 | | | | % 155.57/21.79 | | | | (96) ? [v0: $i] : (app(all_116_2, v0) = all_116_2 & app(nil, nil) = % 155.57/21.79 | | | | v0 & $i(v0)) % 155.57/21.79 | | | | % 155.57/21.79 | | | | DELTA: instantiating (96) with fresh symbol all_182_0 gives: % 155.57/21.79 | | | | (97) app(all_116_2, all_182_0) = all_116_2 & app(nil, nil) = % 155.57/21.79 | | | | all_182_0 & $i(all_182_0) % 155.57/21.79 | | | | % 155.57/21.79 | | | | ALPHA: (97) implies: % 155.57/21.79 | | | | (98) app(nil, nil) = all_182_0 % 155.57/21.79 | | | | % 155.57/21.79 | | | | BETA: splitting (60) gives: % 155.57/21.79 | | | | % 155.57/21.79 | | | | Case 1: % 155.57/21.79 | | | | | % 155.57/21.79 | | | | | (99) ~ (app(nil, nil) = nil) % 155.57/21.79 | | | | | % 155.57/21.79 | | | | | PRED_UNIFY: (93), (99) imply: % 155.57/21.79 | | | | | (100) $false % 155.57/21.79 | | | | | % 155.57/21.79 | | | | | CLOSE: (100) is inconsistent. % 155.57/21.79 | | | | | % 155.57/21.79 | | | | Case 2: % 155.57/21.79 | | | | | % 155.57/21.79 | | | | | (101) ? [v0: $i] : (app(nil, v0) = nil & app(nil, nil) = v0 & % 155.57/21.79 | | | | | $i(v0)) % 155.57/21.79 | | | | | % 155.57/21.79 | | | | | DELTA: instantiating (101) with fresh symbol all_188_0 gives: % 155.57/21.79 | | | | | (102) app(nil, all_188_0) = nil & app(nil, nil) = all_188_0 & % 155.57/21.79 | | | | | $i(all_188_0) % 155.57/21.79 | | | | | % 155.57/21.79 | | | | | ALPHA: (102) implies: % 155.57/21.79 | | | | | (103) app(nil, nil) = all_188_0 % 155.57/21.79 | | | | | % 155.57/21.79 | | | | | BETA: splitting (68) gives: % 155.57/21.79 | | | | | % 155.57/21.79 | | | | | Case 1: % 155.57/21.79 | | | | | | % 155.57/21.79 | | | | | | (104) ~ (app(all_116_2, all_116_0) = nil) % 155.57/21.79 | | | | | | % 155.57/21.79 | | | | | | PRED_UNIFY: (89), (104) imply: % 155.57/21.79 | | | | | | (105) $false % 155.57/21.79 | | | | | | % 155.57/21.79 | | | | | | CLOSE: (105) is inconsistent. % 155.57/21.79 | | | | | | % 155.57/21.79 | | | | | Case 2: % 155.57/21.79 | | | | | | % 155.57/21.79 | | | | | | (106) all_116_0 = nil % 155.57/21.79 | | | | | | % 155.57/21.79 | | | | | | REDUCE: (84), (106) imply: % 155.57/21.79 | | | | | | (107) app(nil, nil) = all_150_0 % 155.57/21.79 | | | | | | % 155.57/21.79 | | | | | | BETA: splitting (69) gives: % 155.57/21.79 | | | | | | % 155.57/21.79 | | | | | | Case 1: % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | (108) ~ (app(all_116_2, all_116_0) = nil) % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | PRED_UNIFY: (89), (108) imply: % 155.57/21.79 | | | | | | | (109) $false % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | CLOSE: (109) is inconsistent. % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | Case 2: % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | (110) all_116_2 = nil % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | REDUCE: (90), (110) imply: % 155.57/21.79 | | | | | | | (111) app(nil, nil) = all_132_0 % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | GROUND_INST: instantiating (21) with all_150_0, all_182_0, nil, % 155.57/21.79 | | | | | | | nil, simplifying with (98), (107) gives: % 155.57/21.79 | | | | | | | (112) all_182_0 = all_150_0 % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | GROUND_INST: instantiating (21) with all_134_0, all_182_0, nil, % 155.57/21.79 | | | | | | | nil, simplifying with (92), (98) gives: % 155.57/21.79 | | | | | | | (113) all_182_0 = all_134_0 % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | GROUND_INST: instantiating (21) with all_132_0, all_182_0, nil, % 155.57/21.79 | | | | | | | nil, simplifying with (98), (111) gives: % 155.57/21.79 | | | | | | | (114) all_182_0 = all_132_0 % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | GROUND_INST: instantiating (21) with all_150_0, all_188_0, nil, % 155.57/21.79 | | | | | | | nil, simplifying with (103), (107) gives: % 155.57/21.79 | | | | | | | (115) all_188_0 = all_150_0 % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | GROUND_INST: instantiating (15) with all_188_0, simplifying with % 155.57/21.79 | | | | | | | (7), (103) gives: % 155.57/21.79 | | | | | | | (116) all_188_0 = nil % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | COMBINE_EQS: (115), (116) imply: % 155.57/21.79 | | | | | | | (117) all_150_0 = nil % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | SIMP: (117) implies: % 155.57/21.79 | | | | | | | (118) all_150_0 = nil % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | COMBINE_EQS: (112), (113) imply: % 155.57/21.79 | | | | | | | (119) all_150_0 = all_134_0 % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | SIMP: (119) implies: % 155.57/21.79 | | | | | | | (120) all_150_0 = all_134_0 % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | COMBINE_EQS: (113), (114) imply: % 155.57/21.79 | | | | | | | (121) all_134_0 = all_132_0 % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | COMBINE_EQS: (118), (120) imply: % 155.57/21.79 | | | | | | | (122) all_134_0 = nil % 155.57/21.79 | | | | | | | % 155.57/21.79 | | | | | | | SIMP: (122) implies: % 155.57/21.79 | | | | | | | (123) all_134_0 = nil % 155.57/21.79 | | | | | | | % 155.57/21.80 | | | | | | | COMBINE_EQS: (121), (123) imply: % 155.57/21.80 | | | | | | | (124) all_132_0 = nil % 155.57/21.80 | | | | | | | % 155.57/21.80 | | | | | | | SIMP: (124) implies: % 155.57/21.80 | | | | | | | (125) all_132_0 = nil % 155.57/21.80 | | | | | | | % 155.57/21.80 | | | | | | | GROUND_INST: instantiating (6) with all_154_0, nil, simplifying % 155.57/21.80 | | | | | | | with (7), (19), (86), (87) gives: % 155.57/21.80 | | | | | | | (126) all_154_0 = nil | neq(all_154_0, nil) % 155.57/21.80 | | | | | | | % 155.57/21.80 | | | | | | | GROUND_INST: instantiating (8) with all_146_0, all_91_2, % 155.57/21.80 | | | | | | | simplifying with (80), (81), (82) gives: % 155.57/21.80 | | | | | | | (127) all_146_0 = all_91_2 % 155.57/21.80 | | | | | | | % 155.57/21.80 | | | | | | | GROUND_INST: instantiating (5) with all_91_1, all_146_0, nil, % 155.57/21.80 | | | | | | | all_91_2, all_140_0, simplifying with (7), (19), % 155.57/21.80 | | | | | | | (25), (28), (76), (77), (78), (80), (81), (82) gives: % 155.57/21.80 | | | | | | | (128) segmentP(all_91_1, all_146_0) % 155.57/21.80 | | | | | | | % 155.57/21.80 | | | | | | | GROUND_INST: instantiating (18) with all_154_0, all_91_2, % 155.57/21.80 | | | | | | | simplifying with (86), (87), (88) gives: % 155.57/21.80 | | | | | | | (129) all_154_0 = all_91_2 % 155.57/21.80 | | | | | | | % 155.57/21.80 | | | | | | | REDUCE: (127), (128) imply: % 155.57/21.80 | | | | | | | (130) segmentP(all_91_1, all_91_2) % 155.57/21.80 | | | | | | | % 155.57/21.80 | | | | | | | BETA: splitting (59) gives: % 155.57/21.80 | | | | | | | % 155.57/21.80 | | | | | | | Case 1: % 155.57/21.80 | | | | | | | | % 155.57/21.80 | | | | | | | | (131) ~ neq(all_91_2, nil) % 155.57/21.80 | | | | | | | | % 155.57/21.80 | | | | | | | | BETA: splitting (126) gives: % 155.57/21.80 | | | | | | | | % 155.57/21.80 | | | | | | | | Case 1: % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | (132) neq(all_154_0, nil) % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | REDUCE: (129), (132) imply: % 155.57/21.80 | | | | | | | | | (133) neq(all_91_2, nil) % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | PRED_UNIFY: (131), (133) imply: % 155.57/21.80 | | | | | | | | | (134) $false % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | CLOSE: (134) is inconsistent. % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | Case 2: % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | (135) all_154_0 = nil % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | COMBINE_EQS: (129), (135) imply: % 155.57/21.80 | | | | | | | | | (136) all_91_2 = nil % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | REDUCE: (131), (136) imply: % 155.57/21.80 | | | | | | | | | (137) ~ neq(nil, nil) % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | BETA: splitting (31) gives: % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | | Case 1: % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | | (138) ~ (all_91_2 = nil) % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | | REDUCE: (136), (138) imply: % 155.57/21.80 | | | | | | | | | | (139) $false % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | | CLOSE: (139) is inconsistent. % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | Case 2: % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | | (140) all_91_1 = nil % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | | REDUCE: (23), (140) imply: % 155.57/21.80 | | | | | | | | | | (141) neq(nil, nil) % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | | PRED_UNIFY: (137), (141) imply: % 155.57/21.80 | | | | | | | | | | (142) $false % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | | CLOSE: (142) is inconsistent. % 155.57/21.80 | | | | | | | | | | % 155.57/21.80 | | | | | | | | | End of split % 155.57/21.80 | | | | | | | | | % 155.57/21.80 | | | | | | | | End of split % 155.57/21.80 | | | | | | | | % 155.57/21.80 | | | | | | | Case 2: % 155.57/21.80 | | | | | | | | % 155.57/21.80 | | | | | | | | (143) ~ segmentP(all_91_1, all_91_2) % 155.57/21.80 | | | | | | | | % 155.57/21.80 | | | | | | | | PRED_UNIFY: (130), (143) imply: % 155.57/21.80 | | | | | | | | (144) $false % 155.57/21.80 | | | | | | | | % 155.57/21.80 | | | | | | | | CLOSE: (144) is inconsistent. % 155.57/21.80 | | | | | | | | % 155.57/21.80 | | | | | | | End of split % 155.57/21.80 | | | | | | | % 155.57/21.81 | | | | | | End of split % 155.57/21.81 | | | | | | % 155.57/21.81 | | | | | End of split % 155.57/21.81 | | | | | % 155.57/21.81 | | | | End of split % 155.57/21.81 | | | | % 155.57/21.81 | | | End of split % 155.57/21.81 | | | % 155.57/21.81 | | End of split % 155.57/21.81 | | % 155.57/21.81 | End of split % 155.57/21.81 | % 155.57/21.81 End of proof % 155.57/21.81 % SZS output end Proof for theBenchmark % 155.57/21.81 % 155.57/21.81 21190ms %------------------------------------------------------------------------------