%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC110+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 : n019.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 20:49:42 EDT 2023 % Result : Theorem 126.67s 17.50s % Output : Proof 187.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC110+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 18:39:43 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.54/1.46 Prover 1: Preprocessing ... % 4.54/1.48 Prover 4: Preprocessing ... % 4.54/1.49 Prover 2: Preprocessing ... % 4.54/1.49 Prover 5: Preprocessing ... % 4.54/1.49 Prover 6: Preprocessing ... % 4.54/1.49 Prover 0: Preprocessing ... % 4.54/1.49 Prover 3: Preprocessing ... % 15.90/2.98 Prover 2: Proving ... % 17.14/3.07 Prover 5: Constructing countermodel ... % 17.72/3.11 Prover 1: Constructing countermodel ... % 17.72/3.14 Prover 3: Constructing countermodel ... % 17.72/3.16 Prover 6: Proving ... % 24.67/4.04 Prover 4: Constructing countermodel ... % 25.41/4.16 Prover 0: Proving ... % 72.20/10.34 Prover 3: gave up % 72.20/10.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.85/10.37 Prover 2: stopped % 72.85/10.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 74.14/10.69 Prover 7: Preprocessing ... % 74.14/10.70 Prover 8: Preprocessing ... % 76.38/10.91 Prover 7: Constructing countermodel ... % 77.48/11.00 Prover 8: Warning: ignoring some quantifiers % 77.48/11.01 Prover 8: Constructing countermodel ... % 99.61/13.95 Prover 5: stopped % 99.61/13.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 100.70/14.07 Prover 9: Preprocessing ... % 106.46/14.90 Prover 9: Constructing countermodel ... % 114.92/15.96 Prover 1: stopped % 114.92/15.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 115.79/16.09 Prover 10: Preprocessing ... % 116.53/16.19 Prover 10: Constructing countermodel ... % 126.67/17.50 Prover 9: proved (3545ms) % 126.67/17.50 % 126.67/17.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 126.67/17.50 % 126.67/17.51 Prover 6: stopped % 126.67/17.51 Prover 0: stopped % 126.67/17.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 126.67/17.52 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 126.67/17.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 127.48/17.61 Prover 13: Preprocessing ... % 127.48/17.63 Prover 11: Preprocessing ... % 127.48/17.65 Prover 16: Preprocessing ... % 127.48/17.78 Prover 16: Constructing countermodel ... % 128.20/17.81 Prover 13: Constructing countermodel ... % 132.56/18.31 Prover 11: Constructing countermodel ... % 149.30/20.68 Prover 13: stopped % 149.30/20.69 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 150.76/20.82 Prover 19: Preprocessing ... % 154.25/21.34 Prover 19: Warning: ignoring some quantifiers % 154.25/21.39 Prover 19: Constructing countermodel ... % 157.64/21.70 Prover 16: stopped % 172.71/23.83 Prover 19: stopped % 186.84/26.19 Prover 7: Found proof (size 161) % 186.84/26.19 Prover 7: proved (15790ms) % 186.84/26.19 Prover 8: stopped % 186.84/26.19 Prover 4: stopped % 186.84/26.19 Prover 10: stopped % 186.84/26.19 Prover 11: stopped % 186.84/26.19 % 186.84/26.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 186.84/26.19 % 186.84/26.20 % SZS output start Proof for theBenchmark % 186.84/26.21 Assumptions after simplification: % 186.84/26.21 --------------------------------- % 186.84/26.21 % 186.84/26.21 (ax1) % 186.84/26.21 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) | % 186.84/26.21 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) | % 186.84/26.21 ~ ssItem(v0)) % 186.84/26.21 % 186.84/26.21 (ax15) % 186.84/26.22 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 186.84/26.22 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ % 186.84/26.22 neq(v0, v0)) % 186.84/26.22 % 186.84/26.22 (ax17) % 186.84/26.22 $i(nil) & ssList(nil) % 186.84/26.22 % 186.84/26.22 (ax2) % 186.84/26.22 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) & % 186.84/26.22 ssItem(v0)) % 186.84/26.22 % 186.84/26.22 (ax28) % 186.84/26.24 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 186.84/26.24 $i(v0) | ~ ssList(v0)) % 186.84/26.24 % 186.84/26.24 (ax45) % 186.84/26.24 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 186.84/26.24 % 186.84/26.24 (ax46) % 186.84/26.24 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 186.84/26.24 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 186.84/26.24 % 186.84/26.24 (ax5) % 186.84/26.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 186.84/26.24 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 186.84/26.24 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 186.84/26.24 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 186.84/26.24 v2) = v0 & $i(v2) & ssList(v2))) % 186.84/26.24 % 186.84/26.24 (ax51) % 186.84/26.24 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 186.84/26.24 % 186.84/26.24 (ax57) % 186.84/26.25 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil)) % 186.84/26.25 % 186.84/26.25 (ax58) % 186.84/26.25 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 186.84/26.25 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 186.84/26.25 % 186.84/26.25 (ax6) % 186.84/26.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 186.84/26.25 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 186.84/26.25 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 186.84/26.25 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 186.84/26.25 v1) = v0 & $i(v2) & ssList(v2))) % 186.84/26.25 % 186.84/26.25 (ax7) % 186.84/26.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 186.84/26.25 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 186.84/26.25 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 186.84/26.25 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 186.84/26.25 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 186.84/26.25 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 186.84/26.25 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 186.84/26.25 % 186.84/26.25 (ax79) % 186.84/26.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3, % 186.84/26.25 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 186.84/26.25 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 186.84/26.25 % 186.84/26.25 (ax82) % 186.84/26.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 186.84/26.25 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 186.84/26.25 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 186.84/26.25 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! % 186.84/26.25 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (app(v1, v3) = v4) | % 186.84/26.25 ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v3) | % 186.84/26.25 ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : (app(v2, v3) = v5 & app(v0, v4) % 186.84/26.25 = v5 & $i(v5))) % 186.84/26.25 % 186.84/26.25 (ax83) % 186.84/26.26 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 186.84/26.26 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 186.84/26.26 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 186.84/26.26 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 186.84/26.26 v0) | ~ ssList(nil)) % 186.84/26.26 % 186.84/26.26 (ax84) % 186.84/26.26 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 186.84/26.26 $i(v0) | ~ ssList(v0)) % 186.84/26.26 % 186.84/26.26 (co1) % 186.84/26.26 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) % 186.84/26.26 & $i(v1) & $i(v0) & equalelemsP(v0) & ssList(v2) & ssList(v1) & ssList(v0) & % 186.84/26.26 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v3, nil) = % 186.84/26.26 v4) | ~ (app(v6, v4) = v0) | ~ (app(v4, v5) = v2) | ~ $i(v6) | ~ % 186.84/26.26 $i(v5) | ~ $i(v3) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v3)) & ( ~ % 186.84/26.26 (v0 = nil) | v1 = nil) & ((v1 = nil & ~ (v0 = nil)) | (neq(v1, nil) & ( ~ % 186.84/26.26 segmentP(v1, v0) | ~ neq(v0, nil))))) % 186.84/26.26 % 186.84/26.26 (function-axioms) % 186.84/26.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 186.84/26.26 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 186.84/26.26 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 186.84/26.26 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 186.84/26.26 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 186.84/26.26 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 186.84/26.26 % 186.84/26.26 Further assumptions not needed in the proof: % 186.84/26.26 -------------------------------------------- % 186.84/26.26 ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax20, ax21, ax22, ax23, ax24, % 186.84/26.26 ax25, ax26, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, % 186.84/26.26 ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax47, ax48, ax49, ax50, ax52, % 186.84/26.26 ax53, ax54, ax55, ax56, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, % 186.84/26.26 ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax8, ax80, % 186.84/26.26 ax81, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 186.84/26.26 % 186.84/26.26 Those formulas are unsatisfiable: % 186.84/26.26 --------------------------------- % 186.84/26.26 % 186.84/26.26 Begin of proof % 186.84/26.26 | % 186.84/26.26 | ALPHA: (ax1) implies: % 186.84/26.27 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 186.84/26.27 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax5) implies: % 186.84/26.27 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 186.84/26.27 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 186.84/26.27 | v0 & $i(v2) & ssList(v2))) % 186.84/26.27 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ % 186.84/26.27 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ % 186.84/26.27 | ssList(v0) | frontsegP(v0, v1)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax6) implies: % 186.84/26.27 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 186.84/26.27 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 186.84/26.27 | v0 & $i(v2) & ssList(v2))) % 186.84/26.27 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ % 186.84/26.27 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ % 186.84/26.27 | ssList(v0) | rearsegP(v0, v1)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax7) implies: % 186.84/26.27 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, % 186.84/26.27 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] : % 186.84/26.27 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) & % 186.84/26.27 | $i(v2) & ssList(v4) & ssList(v2))) % 186.84/26.27 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 186.84/26.27 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 186.84/26.27 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 186.84/26.27 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax15) implies: % 186.84/26.27 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 186.84/26.27 | ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax17) implies: % 186.84/26.27 | (9) ssList(nil) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax28) implies: % 186.84/26.27 | (10) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 186.84/26.27 | $i(v0) | ~ ssList(v0)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax45) implies: % 186.84/26.27 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax46) implies: % 186.84/26.27 | (12) ~ ssList(nil) | frontsegP(nil, nil) % 186.84/26.27 | (13) ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 186.84/26.27 | ssList(v0)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax51) implies: % 186.84/26.27 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax57) implies: % 186.84/26.27 | (15) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil)) % 186.84/26.27 | % 186.84/26.27 | ALPHA: (ax58) implies: % 186.84/26.27 | (16) ~ ssList(nil) | segmentP(nil, nil) % 186.84/26.28 | % 186.84/26.28 | ALPHA: (ax82) implies: % 186.84/26.28 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 186.84/26.28 | ( ~ (app(v1, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) % 186.84/26.28 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? % 186.84/26.28 | [v5: $i] : (app(v2, v3) = v5 & app(v0, v4) = v5 & $i(v5))) % 186.84/26.28 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 186.84/26.28 | ( ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) % 186.84/26.28 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? % 186.84/26.28 | [v5: $i] : (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 186.84/26.28 | % 186.84/26.28 | ALPHA: (ax83) implies: % 186.84/26.28 | (19) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 186.84/26.28 | (20) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ % 186.84/26.28 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 186.84/26.28 | (21) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 186.84/26.28 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 186.84/26.28 | % 186.84/26.28 | ALPHA: (ax84) implies: % 186.84/26.28 | (22) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 186.84/26.28 | $i(v0) | ~ ssList(v0)) % 186.84/26.28 | % 186.84/26.28 | ALPHA: (co1) implies: % 186.84/26.28 | (23) $i(nil) % 186.84/26.28 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) & % 186.84/26.28 | $i(v1) & $i(v0) & equalelemsP(v0) & ssList(v2) & ssList(v1) & % 186.84/26.28 | ssList(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 186.84/26.28 | ( ~ (cons(v3, nil) = v4) | ~ (app(v6, v4) = v0) | ~ (app(v4, v5) = % 186.84/26.28 | v2) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ ssList(v6) | ~ % 186.84/26.28 | ssList(v5) | ~ ssItem(v3)) & ( ~ (v0 = nil) | v1 = nil) & ((v1 = % 186.84/26.28 | nil & ~ (v0 = nil)) | (neq(v1, nil) & ( ~ segmentP(v1, v0) | ~ % 186.84/26.28 | neq(v0, nil))))) % 186.84/26.28 | % 186.84/26.28 | ALPHA: (function-axioms) implies: % 186.84/26.28 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 186.84/26.28 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 186.84/26.28 | % 186.84/26.28 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives: % 186.84/26.28 | (26) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) & % 186.84/26.28 | ssItem(all_89_0) & ssItem(all_89_1) % 186.84/26.28 | % 186.84/26.28 | ALPHA: (26) implies: % 186.84/26.28 | (27) ~ (all_89_0 = all_89_1) % 186.84/26.28 | (28) ssItem(all_89_1) % 186.84/26.28 | (29) ssItem(all_89_0) % 186.84/26.28 | (30) $i(all_89_1) % 186.84/26.28 | (31) $i(all_89_0) % 186.84/26.28 | % 186.84/26.29 | DELTA: instantiating (24) with fresh symbols all_91_0, all_91_1, all_91_2 % 186.84/26.29 | gives: % 186.84/26.29 | (32) app(all_91_2, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) & % 186.84/26.29 | $i(all_91_2) & equalelemsP(all_91_2) & ssList(all_91_0) & % 186.84/26.29 | ssList(all_91_1) & ssList(all_91_2) & ! [v0: $i] : ! [v1: $i] : ! % 186.84/26.29 | [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v1) = % 186.84/26.29 | all_91_2) | ~ (app(v1, v2) = all_91_0) | ~ $i(v3) | ~ $i(v2) | % 186.84/26.29 | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssItem(v0)) & ( ~ % 186.84/26.29 | (all_91_2 = nil) | all_91_1 = nil) & ((all_91_1 = nil & ~ (all_91_2 % 186.84/26.29 | = nil)) | (neq(all_91_1, nil) & ( ~ segmentP(all_91_1, all_91_2) % 186.84/26.29 | | ~ neq(all_91_2, nil)))) % 186.84/26.29 | % 186.84/26.29 | ALPHA: (32) implies: % 186.84/26.29 | (33) ssList(all_91_2) % 186.84/26.29 | (34) ssList(all_91_1) % 186.84/26.29 | (35) ssList(all_91_0) % 186.84/26.29 | (36) $i(all_91_2) % 186.84/26.29 | (37) $i(all_91_1) % 186.84/26.29 | (38) $i(all_91_0) % 186.84/26.29 | (39) app(all_91_2, all_91_0) = all_91_1 % 186.84/26.29 | (40) (all_91_1 = nil & ~ (all_91_2 = nil)) | (neq(all_91_1, nil) & ( ~ % 186.84/26.29 | segmentP(all_91_1, all_91_2) | ~ neq(all_91_2, nil))) % 186.84/26.29 | (41) ~ (all_91_2 = nil) | all_91_1 = nil % 186.84/26.29 | % 186.84/26.29 | BETA: splitting (12) gives: % 186.84/26.29 | % 186.84/26.29 | Case 1: % 186.84/26.29 | | % 186.84/26.29 | | (42) ~ ssList(nil) % 186.84/26.29 | | % 186.84/26.29 | | PRED_UNIFY: (9), (42) imply: % 186.84/26.29 | | (43) $false % 186.84/26.29 | | % 186.84/26.29 | | CLOSE: (43) is inconsistent. % 186.84/26.29 | | % 186.84/26.29 | Case 2: % 186.84/26.29 | | % 186.84/26.29 | | (44) frontsegP(nil, nil) % 186.84/26.29 | | % 186.84/26.29 | | BETA: splitting (16) gives: % 186.84/26.29 | | % 186.84/26.29 | | Case 1: % 186.84/26.29 | | | % 186.84/26.29 | | | (45) ~ ssList(nil) % 186.84/26.29 | | | % 186.84/26.29 | | | PRED_UNIFY: (9), (45) imply: % 186.84/26.29 | | | (46) $false % 186.84/26.29 | | | % 186.84/26.29 | | | CLOSE: (46) is inconsistent. % 186.84/26.29 | | | % 186.84/26.29 | | Case 2: % 186.84/26.29 | | | % 186.84/26.29 | | | (47) segmentP(nil, nil) % 186.84/26.29 | | | % 186.84/26.29 | | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with % 186.84/26.29 | | | (28), (29), (30), (31) gives: % 186.84/26.29 | | | (48) all_89_0 = all_89_1 | neq(all_89_1, all_89_0) % 186.84/26.29 | | | % 186.84/26.29 | | | GROUND_INST: instantiating (8) with all_91_2, nil, simplifying with (9), % 186.84/26.29 | | | (23), (33), (36) gives: % 186.84/26.29 | | | (49) all_91_2 = nil | neq(all_91_2, nil) % 186.84/26.29 | | | % 186.84/26.29 | | | GROUND_INST: instantiating (14) with all_91_2, simplifying with (33), (36) % 186.84/26.29 | | | gives: % 186.84/26.29 | | | (50) rearsegP(all_91_2, nil) % 186.84/26.29 | | | % 186.84/26.29 | | | GROUND_INST: instantiating (11) with all_91_2, simplifying with (33), (36) % 186.84/26.29 | | | gives: % 186.84/26.29 | | | (51) frontsegP(all_91_2, nil) % 186.84/26.29 | | | % 186.84/26.29 | | | GROUND_INST: instantiating (11) with all_91_1, simplifying with (34), (37) % 186.84/26.29 | | | gives: % 186.84/26.29 | | | (52) frontsegP(all_91_1, nil) % 186.84/26.29 | | | % 186.84/26.30 | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (9), (23), % 186.84/26.30 | | | (44) gives: % 186.84/26.30 | | | (53) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 186.84/26.30 | | | % 186.84/26.30 | | | GROUND_INST: instantiating (6) with nil, nil, simplifying with (9), (23), % 186.84/26.30 | | | (47) gives: % 186.84/26.30 | | | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil & % 186.84/26.30 | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) & % 186.84/26.30 | | | ssList(v0)) % 186.84/26.30 | | | % 186.84/26.30 | | | GROUND_INST: instantiating (3) with all_91_1, all_91_2, all_91_0, % 186.84/26.30 | | | simplifying with (33), (34), (35), (36), (37), (38), (39) % 186.84/26.30 | | | gives: % 186.84/26.30 | | | (55) frontsegP(all_91_1, all_91_2) % 186.84/26.30 | | | % 186.84/26.30 | | | GROUND_INST: instantiating (5) with all_91_1, all_91_0, all_91_2, % 186.84/26.30 | | | simplifying with (33), (34), (35), (36), (37), (38), (39) % 186.84/26.30 | | | gives: % 186.84/26.30 | | | (56) rearsegP(all_91_1, all_91_0) % 186.84/26.30 | | | % 186.84/26.30 | | | DELTA: instantiating (53) with fresh symbol all_114_0 gives: % 186.84/26.30 | | | (57) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0) % 186.84/26.30 | | | % 186.84/26.30 | | | ALPHA: (57) implies: % 186.84/26.30 | | | (58) ssList(all_114_0) % 186.84/26.30 | | | (59) $i(all_114_0) % 186.84/26.30 | | | (60) app(nil, all_114_0) = nil % 186.84/26.30 | | | % 186.84/26.30 | | | DELTA: instantiating (54) with fresh symbols all_116_0, all_116_1, % 186.84/26.30 | | | all_116_2 gives: % 186.84/26.30 | | | (61) app(all_116_1, all_116_0) = nil & app(all_116_2, nil) = all_116_1 % 186.84/26.30 | | | & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) & % 186.84/26.30 | | | ssList(all_116_0) & ssList(all_116_2) % 186.84/26.30 | | | % 186.84/26.30 | | | ALPHA: (61) implies: % 186.84/26.30 | | | (62) ssList(all_116_2) % 186.84/26.30 | | | (63) ssList(all_116_0) % 186.84/26.30 | | | (64) $i(all_116_2) % 186.84/26.30 | | | (65) $i(all_116_0) % 186.84/26.30 | | | (66) app(all_116_2, nil) = all_116_1 % 186.84/26.30 | | | (67) app(all_116_1, all_116_0) = nil % 186.84/26.30 | | | % 186.84/26.30 | | | BETA: splitting (48) gives: % 186.84/26.30 | | | % 186.84/26.30 | | | Case 1: % 186.84/26.30 | | | | % 186.84/26.30 | | | | % 186.84/26.30 | | | | GROUND_INST: instantiating (2) with all_91_2, nil, simplifying with (9), % 186.84/26.30 | | | | (23), (33), (36), (51) gives: % 186.84/26.30 | | | | (68) ? [v0: $i] : (app(nil, v0) = all_91_2 & $i(v0) & ssList(v0)) % 186.84/26.30 | | | | % 186.84/26.30 | | | | GROUND_INST: instantiating (2) with all_91_1, nil, simplifying with (9), % 186.84/26.30 | | | | (23), (34), (37), (52) gives: % 186.84/26.30 | | | | (69) ? [v0: $i] : (app(nil, v0) = all_91_1 & $i(v0) & ssList(v0)) % 186.84/26.30 | | | | % 186.84/26.30 | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_2, simplifying with % 186.84/26.30 | | | | (33), (34), (36), (37), (55) gives: % 186.84/26.30 | | | | (70) ? [v0: $i] : (app(all_91_2, v0) = all_91_1 & $i(v0) & % 186.84/26.30 | | | | ssList(v0)) % 186.84/26.30 | | | | % 186.84/26.30 | | | | GROUND_INST: instantiating (13) with all_91_2, simplifying with (33), % 186.84/26.30 | | | | (36) gives: % 186.84/26.30 | | | | (71) all_91_2 = nil | ~ frontsegP(nil, all_91_2) % 186.84/26.30 | | | | % 186.84/26.30 | | | | GROUND_INST: instantiating (4) with all_91_2, nil, simplifying with (9), % 186.84/26.30 | | | | (23), (33), (36), (50) gives: % 186.84/26.31 | | | | (72) ? [v0: $i] : (app(v0, nil) = all_91_2 & $i(v0) & ssList(v0)) % 186.84/26.31 | | | | % 186.84/26.31 | | | | GROUND_INST: instantiating (4) with all_91_1, all_91_0, simplifying with % 186.84/26.31 | | | | (34), (35), (37), (38), (56) gives: % 186.84/26.31 | | | | (73) ? [v0: $i] : (app(v0, all_91_0) = all_91_1 & $i(v0) & % 186.84/26.31 | | | | ssList(v0)) % 186.84/26.31 | | | | % 186.84/26.31 | | | | GROUND_INST: instantiating (18) with nil, all_114_0, nil, all_114_0, % 186.84/26.31 | | | | nil, simplifying with (9), (23), (58), (59), (60) gives: % 186.84/26.31 | | | | (74) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) = % 186.84/26.31 | | | | nil & $i(v0)) % 186.84/26.31 | | | | % 186.84/26.31 | | | | GROUND_INST: instantiating (10) with all_114_0, nil, simplifying with % 186.84/26.31 | | | | (58), (59), (60) gives: % 186.84/26.31 | | | | (75) all_114_0 = nil % 186.84/26.31 | | | | % 186.84/26.31 | | | | GROUND_INST: instantiating (17) with all_116_2, nil, all_116_1, % 186.84/26.31 | | | | all_114_0, nil, simplifying with (9), (23), (58), (59), % 186.84/26.31 | | | | (60), (62), (64), (66) gives: % 186.84/26.31 | | | | (76) ? [v0: $i] : (app(all_116_1, all_114_0) = v0 & app(all_116_2, % 186.84/26.31 | | | | nil) = v0 & $i(v0)) % 186.84/26.31 | | | | % 186.84/26.31 | | | | GROUND_INST: instantiating (22) with all_116_2, all_116_1, simplifying % 186.84/26.31 | | | | with (62), (64), (66) gives: % 186.84/26.31 | | | | (77) all_116_1 = all_116_2 % 186.84/26.31 | | | | % 186.84/26.31 | | | | GROUND_INST: instantiating (18) with all_116_2, nil, all_116_1, % 186.84/26.31 | | | | all_116_0, nil, simplifying with (9), (23), (62), (63), % 186.84/26.31 | | | | (64), (65), (66), (67) gives: % 186.84/26.31 | | | | (78) ? [v0: $i] : (app(all_116_2, v0) = nil & app(nil, all_116_0) = % 186.84/26.31 | | | | v0 & $i(v0)) % 186.84/26.31 | | | | % 186.84/26.31 | | | | GROUND_INST: instantiating (21) with all_116_2, all_116_0, simplifying % 186.84/26.31 | | | | with (62), (63), (64), (65) gives: % 186.84/26.31 | | | | (79) all_116_0 = nil | ~ (app(all_116_2, all_116_0) = nil) % 186.84/26.31 | | | | % 186.84/26.31 | | | | GROUND_INST: instantiating (20) with all_116_2, all_116_0, simplifying % 186.84/26.31 | | | | with (62), (63), (64), (65) gives: % 186.84/26.31 | | | | (80) all_116_2 = nil | ~ (app(all_116_2, all_116_0) = nil) % 186.84/26.31 | | | | % 186.84/26.31 | | | | DELTA: instantiating (76) with fresh symbol all_132_0 gives: % 186.84/26.31 | | | | (81) app(all_116_1, all_114_0) = all_132_0 & app(all_116_2, nil) = % 186.84/26.31 | | | | all_132_0 & $i(all_132_0) % 186.84/26.31 | | | | % 186.84/26.31 | | | | ALPHA: (81) implies: % 186.84/26.31 | | | | (82) $i(all_132_0) % 186.84/26.31 | | | | (83) app(all_116_1, all_114_0) = all_132_0 % 186.84/26.31 | | | | % 186.84/26.31 | | | | DELTA: instantiating (70) with fresh symbol all_134_0 gives: % 186.84/26.31 | | | | (84) app(all_91_2, all_134_0) = all_91_1 & $i(all_134_0) & % 186.84/26.31 | | | | ssList(all_134_0) % 186.84/26.31 | | | | % 186.84/26.31 | | | | ALPHA: (84) implies: % 186.84/26.31 | | | | (85) ssList(all_134_0) % 186.84/26.31 | | | | (86) $i(all_134_0) % 186.84/26.31 | | | | (87) app(all_91_2, all_134_0) = all_91_1 % 186.84/26.31 | | | | % 186.84/26.31 | | | | DELTA: instantiating (69) with fresh symbol all_136_0 gives: % 186.84/26.31 | | | | (88) app(nil, all_136_0) = all_91_1 & $i(all_136_0) & % 186.84/26.31 | | | | ssList(all_136_0) % 186.84/26.31 | | | | % 186.84/26.31 | | | | ALPHA: (88) implies: % 186.84/26.31 | | | | (89) ssList(all_136_0) % 186.84/26.31 | | | | (90) $i(all_136_0) % 186.84/26.31 | | | | (91) app(nil, all_136_0) = all_91_1 % 186.84/26.31 | | | | % 186.84/26.31 | | | | DELTA: instantiating (78) with fresh symbol all_138_0 gives: % 186.84/26.31 | | | | (92) app(all_116_2, all_138_0) = nil & app(nil, all_116_0) = % 186.84/26.31 | | | | all_138_0 & $i(all_138_0) % 186.84/26.31 | | | | % 186.84/26.31 | | | | ALPHA: (92) implies: % 186.84/26.31 | | | | (93) app(nil, all_116_0) = all_138_0 % 186.84/26.31 | | | | % 186.84/26.31 | | | | DELTA: instantiating (72) with fresh symbol all_146_0 gives: % 186.84/26.31 | | | | (94) app(all_146_0, nil) = all_91_2 & $i(all_146_0) & % 186.84/26.31 | | | | ssList(all_146_0) % 186.84/26.31 | | | | % 186.84/26.31 | | | | ALPHA: (94) implies: % 186.84/26.31 | | | | (95) ssList(all_146_0) % 186.84/26.31 | | | | (96) $i(all_146_0) % 186.84/26.31 | | | | (97) app(all_146_0, nil) = all_91_2 % 186.84/26.31 | | | | % 186.84/26.31 | | | | DELTA: instantiating (74) with fresh symbol all_148_0 gives: % 186.84/26.32 | | | | (98) app(all_114_0, all_114_0) = all_148_0 & app(nil, all_148_0) = % 186.84/26.32 | | | | nil & $i(all_148_0) % 186.84/26.32 | | | | % 186.84/26.32 | | | | ALPHA: (98) implies: % 186.84/26.32 | | | | (99) app(all_114_0, all_114_0) = all_148_0 % 186.84/26.32 | | | | % 186.84/26.32 | | | | DELTA: instantiating (73) with fresh symbol all_154_0 gives: % 186.84/26.32 | | | | (100) app(all_154_0, all_91_0) = all_91_1 & $i(all_154_0) & % 186.84/26.32 | | | | ssList(all_154_0) % 186.84/26.32 | | | | % 186.84/26.32 | | | | ALPHA: (100) implies: % 186.84/26.32 | | | | (101) ssList(all_154_0) % 186.84/26.32 | | | | (102) $i(all_154_0) % 186.84/26.32 | | | | (103) app(all_154_0, all_91_0) = all_91_1 % 186.84/26.32 | | | | % 186.84/26.32 | | | | DELTA: instantiating (68) with fresh symbol all_164_0 gives: % 186.84/26.32 | | | | (104) app(nil, all_164_0) = all_91_2 & $i(all_164_0) & % 186.84/26.32 | | | | ssList(all_164_0) % 186.84/26.32 | | | | % 186.84/26.32 | | | | ALPHA: (104) implies: % 186.84/26.32 | | | | (105) ssList(all_164_0) % 186.84/26.32 | | | | (106) $i(all_164_0) % 186.84/26.32 | | | | (107) app(nil, all_164_0) = all_91_2 % 186.84/26.32 | | | | % 186.84/26.32 | | | | REDUCE: (67), (77) imply: % 186.84/26.32 | | | | (108) app(all_116_2, all_116_0) = nil % 186.84/26.32 | | | | % 186.84/26.32 | | | | REDUCE: (75), (77), (83) imply: % 186.84/26.32 | | | | (109) app(all_116_2, nil) = all_132_0 % 186.84/26.32 | | | | % 186.84/26.32 | | | | REDUCE: (75), (99) imply: % 186.84/26.32 | | | | (110) app(nil, nil) = all_148_0 % 186.84/26.32 | | | | % 186.84/26.32 | | | | BETA: splitting (80) gives: % 186.84/26.32 | | | | % 186.84/26.32 | | | | Case 1: % 186.84/26.32 | | | | | % 186.84/26.32 | | | | | (111) ~ (app(all_116_2, all_116_0) = nil) % 186.84/26.32 | | | | | % 186.84/26.32 | | | | | PRED_UNIFY: (108), (111) imply: % 186.84/26.32 | | | | | (112) $false % 186.84/26.32 | | | | | % 186.84/26.32 | | | | | CLOSE: (112) is inconsistent. % 186.84/26.32 | | | | | % 186.84/26.32 | | | | Case 2: % 186.84/26.32 | | | | | % 186.84/26.32 | | | | | (113) all_116_2 = nil % 186.84/26.32 | | | | | % 186.84/26.32 | | | | | REDUCE: (109), (113) imply: % 186.84/26.32 | | | | | (114) app(nil, nil) = all_132_0 % 186.84/26.32 | | | | | % 186.84/26.32 | | | | | BETA: splitting (79) gives: % 186.84/26.32 | | | | | % 186.84/26.32 | | | | | Case 1: % 186.84/26.32 | | | | | | % 186.84/26.32 | | | | | | (115) ~ (app(all_116_2, all_116_0) = nil) % 186.84/26.32 | | | | | | % 186.84/26.32 | | | | | | PRED_UNIFY: (108), (115) imply: % 186.84/26.32 | | | | | | (116) $false % 186.84/26.32 | | | | | | % 186.84/26.32 | | | | | | CLOSE: (116) is inconsistent. % 186.84/26.32 | | | | | | % 186.84/26.32 | | | | | Case 2: % 186.84/26.32 | | | | | | % 187.41/26.32 | | | | | | (117) all_116_0 = nil % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | REDUCE: (93), (117) imply: % 187.41/26.32 | | | | | | (118) app(nil, nil) = all_138_0 % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (25) with all_132_0, all_138_0, nil, nil, % 187.41/26.32 | | | | | | simplifying with (114), (118) gives: % 187.41/26.32 | | | | | | (119) all_138_0 = all_132_0 % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (25) with all_138_0, all_148_0, nil, nil, % 187.41/26.32 | | | | | | simplifying with (110), (118) gives: % 187.41/26.32 | | | | | | (120) all_148_0 = all_138_0 % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (19) with all_148_0, simplifying with % 187.41/26.32 | | | | | | (9), (110) gives: % 187.41/26.32 | | | | | | (121) all_148_0 = nil % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | COMBINE_EQS: (120), (121) imply: % 187.41/26.32 | | | | | | (122) all_138_0 = nil % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | SIMP: (122) implies: % 187.41/26.32 | | | | | | (123) all_138_0 = nil % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | COMBINE_EQS: (119), (123) imply: % 187.41/26.32 | | | | | | (124) all_132_0 = nil % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (15) with all_136_0, simplifying with % 187.41/26.32 | | | | | | (89), (90) gives: % 187.41/26.32 | | | | | | (125) segmentP(all_136_0, nil) % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (15) with all_146_0, simplifying with % 187.41/26.32 | | | | | | (95), (96) gives: % 187.41/26.32 | | | | | | (126) segmentP(all_146_0, nil) % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (10) with all_136_0, all_91_1, % 187.41/26.32 | | | | | | simplifying with (89), (90), (91) gives: % 187.41/26.32 | | | | | | (127) all_136_0 = all_91_1 % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (10) with all_164_0, all_91_2, % 187.41/26.32 | | | | | | simplifying with (105), (106), (107) gives: % 187.41/26.32 | | | | | | (128) all_164_0 = all_91_2 % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (7) with all_91_1, all_164_0, nil, % 187.41/26.32 | | | | | | all_91_2, all_134_0, simplifying with (9), (23), (34), % 187.41/26.32 | | | | | | (37), (85), (86), (87), (105), (106), (107) gives: % 187.41/26.32 | | | | | | (129) segmentP(all_91_1, all_164_0) % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (22) with all_146_0, all_91_2, % 187.41/26.32 | | | | | | simplifying with (95), (96), (97) gives: % 187.41/26.32 | | | | | | (130) all_146_0 = all_91_2 % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (ax79) with all_154_0, all_91_0, % 187.41/26.32 | | | | | | all_91_1, all_91_2, simplifying with (33), (35), (36), % 187.41/26.32 | | | | | | (38), (39), (101), (102), (103) gives: % 187.41/26.32 | | | | | | (131) all_154_0 = all_91_2 % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | GROUND_INST: instantiating (3) with all_91_1, all_154_0, all_91_0, % 187.41/26.32 | | | | | | simplifying with (34), (35), (37), (38), (101), (102), % 187.41/26.32 | | | | | | (103) gives: % 187.41/26.32 | | | | | | (132) frontsegP(all_91_1, all_154_0) % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | REDUCE: (126), (130) imply: % 187.41/26.32 | | | | | | (133) segmentP(all_91_2, nil) % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | REDUCE: (125), (127) imply: % 187.41/26.32 | | | | | | (134) segmentP(all_91_1, nil) % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | REDUCE: (128), (129) imply: % 187.41/26.32 | | | | | | (135) segmentP(all_91_1, all_91_2) % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | BETA: splitting (41) gives: % 187.41/26.32 | | | | | | % 187.41/26.32 | | | | | | Case 1: % 187.41/26.32 | | | | | | | % 187.41/26.32 | | | | | | | (136) ~ (all_91_2 = nil) % 187.41/26.32 | | | | | | | % 187.41/26.32 | | | | | | | BETA: splitting (49) gives: % 187.41/26.32 | | | | | | | % 187.41/26.32 | | | | | | | Case 1: % 187.41/26.32 | | | | | | | | % 187.41/26.32 | | | | | | | | (137) neq(all_91_2, nil) % 187.41/26.32 | | | | | | | | % 187.41/26.32 | | | | | | | | BETA: splitting (40) gives: % 187.41/26.32 | | | | | | | | % 187.41/26.32 | | | | | | | | Case 1: % 187.41/26.32 | | | | | | | | | % 187.41/26.32 | | | | | | | | | (138) all_91_1 = nil & ~ (all_91_2 = nil) % 187.41/26.32 | | | | | | | | | % 187.41/26.32 | | | | | | | | | ALPHA: (138) implies: % 187.41/26.32 | | | | | | | | | (139) all_91_1 = nil % 187.41/26.32 | | | | | | | | | % 187.41/26.32 | | | | | | | | | REDUCE: (55), (139) imply: % 187.41/26.32 | | | | | | | | | (140) frontsegP(nil, all_91_2) % 187.41/26.32 | | | | | | | | | % 187.41/26.32 | | | | | | | | | BETA: splitting (71) gives: % 187.41/26.32 | | | | | | | | | % 187.41/26.32 | | | | | | | | | Case 1: % 187.41/26.32 | | | | | | | | | | % 187.41/26.32 | | | | | | | | | | (141) ~ frontsegP(nil, all_91_2) % 187.41/26.32 | | | | | | | | | | % 187.41/26.32 | | | | | | | | | | PRED_UNIFY: (140), (141) imply: % 187.41/26.32 | | | | | | | | | | (142) $false % 187.41/26.32 | | | | | | | | | | % 187.41/26.32 | | | | | | | | | | CLOSE: (142) is inconsistent. % 187.41/26.32 | | | | | | | | | | % 187.41/26.32 | | | | | | | | | Case 2: % 187.41/26.32 | | | | | | | | | | % 187.41/26.32 | | | | | | | | | | (143) all_91_2 = nil % 187.41/26.32 | | | | | | | | | | % 187.41/26.32 | | | | | | | | | | REF_CLOSE: (40), (47), (139), (143) are inconsistent by % 187.41/26.33 | | | | | | | | | | sub-proof #1. % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | End of split % 187.41/26.33 | | | | | | | | | % 187.41/26.33 | | | | | | | | Case 2: % 187.41/26.33 | | | | | | | | | % 187.41/26.33 | | | | | | | | | (144) neq(all_91_1, nil) & ( ~ segmentP(all_91_1, all_91_2) % 187.41/26.33 | | | | | | | | | | ~ neq(all_91_2, nil)) % 187.41/26.33 | | | | | | | | | % 187.41/26.33 | | | | | | | | | ALPHA: (144) implies: % 187.41/26.33 | | | | | | | | | (145) ~ segmentP(all_91_1, all_91_2) | ~ neq(all_91_2, % 187.41/26.33 | | | | | | | | | nil) % 187.41/26.33 | | | | | | | | | % 187.41/26.33 | | | | | | | | | BETA: splitting (145) gives: % 187.41/26.33 | | | | | | | | | % 187.41/26.33 | | | | | | | | | Case 1: % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | | (146) ~ neq(all_91_2, nil) % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | | PRED_UNIFY: (137), (146) imply: % 187.41/26.33 | | | | | | | | | | (147) $false % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | | CLOSE: (147) is inconsistent. % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | Case 2: % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | | (148) ~ segmentP(all_91_1, all_91_2) % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | | PRED_UNIFY: (135), (148) imply: % 187.41/26.33 | | | | | | | | | | (149) $false % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | | CLOSE: (149) is inconsistent. % 187.41/26.33 | | | | | | | | | | % 187.41/26.33 | | | | | | | | | End of split % 187.41/26.33 | | | | | | | | | % 187.41/26.33 | | | | | | | | End of split % 187.41/26.33 | | | | | | | | % 187.41/26.33 | | | | | | | Case 2: % 187.41/26.33 | | | | | | | | % 187.41/26.33 | | | | | | | | (150) all_91_2 = nil % 187.41/26.33 | | | | | | | | % 187.41/26.33 | | | | | | | | REDUCE: (136), (150) imply: % 187.41/26.33 | | | | | | | | (151) $false % 187.41/26.33 | | | | | | | | % 187.41/26.33 | | | | | | | | CLOSE: (151) is inconsistent. % 187.41/26.33 | | | | | | | | % 187.41/26.33 | | | | | | | End of split % 187.41/26.33 | | | | | | | % 187.41/26.33 | | | | | | Case 2: % 187.41/26.33 | | | | | | | % 187.41/26.33 | | | | | | | (152) all_91_2 = nil % 187.41/26.33 | | | | | | | (153) all_91_1 = nil % 187.41/26.33 | | | | | | | % 187.41/26.33 | | | | | | | REF_CLOSE: (40), (47), (152), (153) are inconsistent by sub-proof % 187.41/26.33 | | | | | | | #1. % 187.41/26.33 | | | | | | | % 187.41/26.33 | | | | | | End of split % 187.41/26.33 | | | | | | % 187.41/26.33 | | | | | End of split % 187.41/26.33 | | | | | % 187.41/26.33 | | | | End of split % 187.41/26.33 | | | | % 187.41/26.33 | | | Case 2: % 187.41/26.33 | | | | % 187.41/26.33 | | | | (154) all_89_0 = all_89_1 % 187.41/26.33 | | | | % 187.41/26.33 | | | | REDUCE: (27), (154) imply: % 187.41/26.33 | | | | (155) $false % 187.41/26.33 | | | | % 187.41/26.33 | | | | CLOSE: (155) is inconsistent. % 187.41/26.33 | | | | % 187.41/26.33 | | | End of split % 187.41/26.33 | | | % 187.41/26.33 | | End of split % 187.41/26.33 | | % 187.41/26.33 | End of split % 187.41/26.33 | % 187.41/26.33 End of proof % 187.41/26.33 % 187.41/26.33 Sub-proof #1 shows that the following formulas are inconsistent: % 187.41/26.33 ---------------------------------------------------------------- % 187.41/26.33 (1) (all_91_1 = nil & ~ (all_91_2 = nil)) | (neq(all_91_1, nil) & ( ~ % 187.41/26.33 segmentP(all_91_1, all_91_2) | ~ neq(all_91_2, nil))) % 187.41/26.33 (2) all_91_2 = nil % 187.41/26.33 (3) all_91_1 = nil % 187.41/26.33 (4) segmentP(nil, nil) % 187.41/26.33 % 187.41/26.33 Begin of proof % 187.41/26.33 | % 187.41/26.33 | BETA: splitting (1) gives: % 187.41/26.33 | % 187.41/26.33 | Case 1: % 187.41/26.33 | | % 187.41/26.33 | | (5) all_91_1 = nil & ~ (all_91_2 = nil) % 187.41/26.33 | | % 187.41/26.33 | | ALPHA: (5) implies: % 187.41/26.33 | | (6) ~ (all_91_2 = nil) % 187.41/26.33 | | % 187.41/26.33 | | REDUCE: (2), (6) imply: % 187.41/26.33 | | (7) $false % 187.41/26.33 | | % 187.41/26.33 | | CLOSE: (7) is inconsistent. % 187.41/26.33 | | % 187.41/26.33 | Case 2: % 187.41/26.33 | | % 187.41/26.33 | | (8) neq(all_91_1, nil) & ( ~ segmentP(all_91_1, all_91_2) | ~ % 187.41/26.33 | | neq(all_91_2, nil)) % 187.41/26.33 | | % 187.41/26.33 | | ALPHA: (8) implies: % 187.41/26.33 | | (9) neq(all_91_1, nil) % 187.41/26.33 | | (10) ~ segmentP(all_91_1, all_91_2) | ~ neq(all_91_2, nil) % 187.41/26.33 | | % 187.41/26.33 | | REDUCE: (3), (9) imply: % 187.41/26.33 | | (11) neq(nil, nil) % 187.41/26.33 | | % 187.41/26.33 | | BETA: splitting (10) gives: % 187.41/26.33 | | % 187.41/26.33 | | Case 1: % 187.41/26.33 | | | % 187.41/26.33 | | | (12) ~ neq(all_91_2, nil) % 187.41/26.33 | | | % 187.41/26.33 | | | REDUCE: (2), (12) imply: % 187.41/26.33 | | | (13) ~ neq(nil, nil) % 187.41/26.33 | | | % 187.41/26.33 | | | PRED_UNIFY: (11), (13) imply: % 187.41/26.33 | | | (14) $false % 187.41/26.33 | | | % 187.41/26.33 | | | CLOSE: (14) is inconsistent. % 187.41/26.33 | | | % 187.41/26.33 | | Case 2: % 187.41/26.33 | | | % 187.41/26.33 | | | (15) ~ segmentP(all_91_1, all_91_2) % 187.41/26.33 | | | % 187.41/26.33 | | | REDUCE: (2), (3), (15) imply: % 187.41/26.33 | | | (16) ~ segmentP(nil, nil) % 187.41/26.33 | | | % 187.41/26.33 | | | PRED_UNIFY: (4), (16) imply: % 187.41/26.33 | | | (17) $false % 187.41/26.33 | | | % 187.41/26.33 | | | CLOSE: (17) is inconsistent. % 187.41/26.33 | | | % 187.41/26.33 | | End of split % 187.41/26.33 | | % 187.41/26.33 | End of split % 187.41/26.33 | % 187.41/26.33 End of proof % 187.41/26.33 % SZS output end Proof for theBenchmark % 187.41/26.33 % 187.41/26.33 25729ms %------------------------------------------------------------------------------