%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC355+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 : n020.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 20:51:00 EDT 2023 % Result : Theorem 118.68s 16.06s % Output : Proof 125.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC355+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n020.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 16:11:44 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.53/0.62 Running up to 7 provers in parallel. % 0.53/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.53/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.53/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.53/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.53/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.53/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.53/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.14/1.38 Prover 1: Preprocessing ... % 5.14/1.40 Prover 4: Preprocessing ... % 5.43/1.42 Prover 6: Preprocessing ... % 5.43/1.42 Prover 5: Preprocessing ... % 5.43/1.42 Prover 0: Preprocessing ... % 5.43/1.42 Prover 3: Preprocessing ... % 5.43/1.42 Prover 2: Preprocessing ... % 15.47/2.77 Prover 2: Proving ... % 15.47/2.78 Prover 5: Constructing countermodel ... % 16.28/2.86 Prover 1: Constructing countermodel ... % 16.28/2.86 Prover 6: Proving ... % 16.28/2.88 Prover 3: Constructing countermodel ... % 22.79/3.74 Prover 4: Constructing countermodel ... % 24.67/3.98 Prover 0: Proving ... % 73.97/10.34 Prover 2: stopped % 73.97/10.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 75.21/10.50 Prover 7: Preprocessing ... % 77.03/10.70 Prover 7: Constructing countermodel ... % 97.37/13.34 Prover 3: gave up % 97.37/13.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 97.78/13.44 Prover 8: Preprocessing ... % 100.12/13.66 Prover 8: Warning: ignoring some quantifiers % 100.12/13.67 Prover 8: Constructing countermodel ... % 102.44/13.96 Prover 5: stopped % 102.44/13.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 103.18/14.11 Prover 9: Preprocessing ... % 108.59/14.75 Prover 9: Constructing countermodel ... % 117.81/15.97 Prover 1: stopped % 117.81/15.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 118.68/16.06 Prover 9: proved (2076ms) % 118.68/16.06 % 118.68/16.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 118.68/16.06 % 118.68/16.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 118.68/16.07 Prover 6: stopped % 118.68/16.08 Prover 0: stopped % 118.68/16.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 119.04/16.10 Prover 10: Preprocessing ... % 119.04/16.10 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 119.04/16.19 Prover 11: Preprocessing ... % 119.50/16.20 Prover 13: Preprocessing ... % 119.50/16.20 Prover 16: Preprocessing ... % 119.50/16.22 Prover 10: Constructing countermodel ... % 120.52/16.32 Prover 16: Constructing countermodel ... % 120.95/16.37 Prover 13: Constructing countermodel ... % 124.18/16.83 Prover 11: Constructing countermodel ... % 124.18/16.86 Prover 10: Found proof (size 50) % 124.18/16.86 Prover 10: proved (891ms) % 124.18/16.86 Prover 16: stopped % 124.18/16.86 Prover 8: stopped % 124.18/16.87 Prover 7: stopped % 124.18/16.87 Prover 13: stopped % 124.18/16.87 Prover 11: stopped % 124.18/16.90 Prover 4: stopped % 124.18/16.90 % 124.18/16.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 124.18/16.90 % 125.12/16.90 % SZS output start Proof for theBenchmark % 125.12/16.91 Assumptions after simplification: % 125.12/16.91 --------------------------------- % 125.12/16.91 % 125.12/16.91 (ax1) % 125.12/16.91 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) | % 125.12/16.91 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) | % 125.12/16.91 ~ ssItem(v0)) % 125.12/16.91 % 125.12/16.91 (ax16) % 125.12/16.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1) % 125.12/16.93 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) % 125.12/16.93 % 125.12/16.93 (ax17) % 125.12/16.93 $i(nil) & ssList(nil) % 125.12/16.93 % 125.12/16.93 (ax2) % 125.12/16.94 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) & % 125.12/16.94 ssItem(v0)) % 125.12/16.94 % 125.12/16.94 (ax23) % 125.12/16.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1) % 125.12/16.94 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) % 125.12/16.94 % 125.12/16.94 (ax25) % 125.12/16.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1) % 125.12/16.94 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) % 125.12/16.94 % 125.12/16.94 (ax44) % 125.12/16.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 125.12/16.94 $i] : (v1 = v0 | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ $i(v4) % 125.12/16.94 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v3, v5) | ~ ssList(v4) | % 125.12/16.94 ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0: $i] : ! [v1: $i] : % 125.12/16.94 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v1, v4) = % 125.12/16.94 v5) | ~ (cons(v0, v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ % 125.12/16.94 $i(v0) | ~ frontsegP(v3, v5) | ~ ssList(v4) | ~ ssList(v2) | ~ % 125.12/16.94 ssItem(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) & ! [v0: $i] : ! [v1: $i] % 125.12/16.94 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v0, v3) = v4) | ~ % 125.12/16.94 (cons(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v1, % 125.12/16.94 v3) | ~ ssList(v3) | ~ ssList(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) % 125.12/16.94 % 125.12/16.94 (ax46) % 125.12/16.94 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 125.12/16.94 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 125.12/16.94 % 125.12/16.94 (ax49) % 125.12/16.94 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0)) % 125.12/16.94 % 125.12/16.94 (ax5) % 125.12/16.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 125.12/16.95 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 125.12/16.95 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 125.12/16.95 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 125.12/16.95 v2) = v0 & $i(v2) & ssList(v2))) % 125.12/16.95 % 125.12/16.95 (ax58) % 125.12/16.95 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 125.12/16.95 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 125.12/16.95 % 125.12/16.95 (ax6) % 125.12/16.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 125.12/16.95 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 125.12/16.95 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 125.12/16.95 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 125.12/16.95 v1) = v0 & $i(v2) & ssList(v2))) % 125.12/16.95 % 125.12/16.95 (ax7) % 125.12/16.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 125.12/16.95 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 125.12/16.95 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 125.12/16.95 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 125.12/16.95 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 125.12/16.95 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 125.12/16.95 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 125.12/16.95 % 125.12/16.95 (ax77) % 125.12/16.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~ % 125.12/16.95 ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3 = v0 | % 125.12/16.95 v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~ ssList(v3) | ? % 125.12/16.95 [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 & $i(v4))))) % 125.12/16.95 % 125.12/16.95 (ax81) % 125.12/16.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 125.12/16.95 (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 125.12/16.95 ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3))) % 125.12/16.95 % 125.12/16.95 (co1) % 125.35/16.95 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2, % 125.35/16.95 nil) = v3 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 125.35/16.95 ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ~ segmentP(v1, v0)) % 125.35/16.95 % 125.35/16.95 (function-axioms) % 125.35/16.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 125.35/16.96 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 125.35/16.96 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 125.35/16.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 125.35/16.96 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 125.35/16.96 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 125.35/16.96 % 125.35/16.96 Further assumptions not needed in the proof: % 125.35/16.96 -------------------------------------------- % 125.35/16.96 ax10, ax11, ax12, ax13, ax14, ax15, ax18, ax19, ax20, ax21, ax22, ax24, ax26, % 125.35/16.96 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, % 125.35/16.96 ax39, ax4, ax40, ax41, ax42, ax43, ax45, ax47, ax48, ax50, ax51, ax52, ax53, % 125.35/16.96 ax54, ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, % 125.35/16.96 ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax78, ax79, ax8, ax80, % 125.35/16.96 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 125.35/16.96 ax94, ax95 % 125.35/16.96 % 125.35/16.96 Those formulas are unsatisfiable: % 125.35/16.96 --------------------------------- % 125.35/16.96 % 125.35/16.96 Begin of proof % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax1) implies: % 125.35/16.96 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 125.35/16.96 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax5) implies: % 125.35/16.96 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 125.35/16.96 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 125.35/16.96 | v0 & $i(v2) & ssList(v2))) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax6) implies: % 125.35/16.96 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 125.35/16.96 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 125.35/16.96 | v0 & $i(v2) & ssList(v2))) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax7) implies: % 125.35/16.96 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 125.35/16.96 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 125.35/16.96 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 125.35/16.96 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax17) implies: % 125.35/16.96 | (5) ssList(nil) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax44) implies: % 125.35/16.96 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 125.35/16.96 | ~ (cons(v0, v3) = v4) | ~ (cons(v0, v1) = v2) | ~ $i(v3) | ~ % 125.35/16.96 | $i(v1) | ~ $i(v0) | ~ frontsegP(v1, v3) | ~ ssList(v3) | ~ % 125.35/16.96 | ssList(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax46) implies: % 125.35/16.96 | (7) ~ ssList(nil) | frontsegP(nil, nil) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax58) implies: % 125.35/16.96 | (8) ~ ssList(nil) | segmentP(nil, nil) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax77) implies: % 125.35/16.96 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~ % 125.35/16.96 | ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3 % 125.35/16.96 | = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~ % 125.35/16.96 | ssList(v3) | ? [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 & % 125.35/16.96 | $i(v4))))) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (ax81) implies: % 125.35/16.96 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, % 125.35/16.96 | nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 125.35/16.96 | ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3))) % 125.35/16.96 | % 125.35/16.96 | ALPHA: (co1) implies: % 125.35/16.97 | (11) $i(nil) % 125.35/16.97 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) % 125.35/16.97 | = v3 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 125.35/16.97 | ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ~ % 125.35/16.97 | segmentP(v1, v0)) % 125.35/16.97 | % 125.35/16.97 | ALPHA: (function-axioms) implies: % 125.35/16.97 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (hd(v2) = v1) % 125.35/16.97 | | ~ (hd(v2) = v0)) % 125.35/16.97 | % 125.35/16.97 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives: % 125.35/16.97 | (14) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) & % 125.35/16.97 | ssItem(all_89_0) & ssItem(all_89_1) % 125.35/16.97 | % 125.35/16.97 | ALPHA: (14) implies: % 125.35/16.97 | (15) ~ (all_89_0 = all_89_1) % 125.35/16.97 | (16) ssItem(all_89_1) % 125.35/16.97 | (17) ssItem(all_89_0) % 125.35/16.97 | (18) $i(all_89_1) % 125.35/16.97 | (19) $i(all_89_0) % 125.35/16.97 | % 125.35/16.97 | DELTA: instantiating (12) with fresh symbols all_91_0, all_91_1, all_91_2, % 125.35/16.97 | all_91_3 gives: % 125.35/16.97 | (20) cons(all_91_1, nil) = all_91_0 & app(all_91_3, all_91_0) = all_91_2 & % 125.35/16.97 | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & % 125.35/16.97 | ssList(all_91_2) & ssList(all_91_3) & neq(all_91_2, nil) & % 125.35/16.97 | ssItem(all_91_1) & ~ segmentP(all_91_2, all_91_3) % 125.35/16.97 | % 125.35/16.97 | ALPHA: (20) implies: % 125.35/16.97 | (21) ~ segmentP(all_91_2, all_91_3) % 125.35/16.97 | (22) ssItem(all_91_1) % 125.35/16.97 | (23) ssList(all_91_3) % 125.35/16.97 | (24) ssList(all_91_2) % 125.35/16.97 | (25) $i(all_91_3) % 125.35/16.97 | (26) $i(all_91_2) % 125.35/16.97 | (27) $i(all_91_1) % 125.35/16.97 | (28) $i(all_91_0) % 125.35/16.97 | (29) app(all_91_3, all_91_0) = all_91_2 % 125.35/16.97 | (30) cons(all_91_1, nil) = all_91_0 % 125.35/16.97 | % 125.35/16.97 | BETA: splitting (7) gives: % 125.35/16.97 | % 125.35/16.97 | Case 1: % 125.35/16.97 | | % 125.35/16.97 | | (31) ~ ssList(nil) % 125.35/16.97 | | % 125.35/16.97 | | PRED_UNIFY: (5), (31) imply: % 125.35/16.97 | | (32) $false % 125.35/16.97 | | % 125.35/16.97 | | CLOSE: (32) is inconsistent. % 125.35/16.97 | | % 125.35/16.97 | Case 2: % 125.35/16.97 | | % 125.35/16.97 | | (33) frontsegP(nil, nil) % 125.35/16.97 | | % 125.35/16.97 | | BETA: splitting (8) gives: % 125.35/16.97 | | % 125.35/16.97 | | Case 1: % 125.35/16.97 | | | % 125.35/16.97 | | | (34) ~ ssList(nil) % 125.35/16.97 | | | % 125.35/16.97 | | | PRED_UNIFY: (5), (34) imply: % 125.35/16.97 | | | (35) $false % 125.35/16.97 | | | % 125.35/16.97 | | | CLOSE: (35) is inconsistent. % 125.35/16.97 | | | % 125.35/16.97 | | Case 2: % 125.35/16.97 | | | % 125.35/16.97 | | | % 125.35/16.97 | | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with % 125.35/16.97 | | | (16), (17), (18), (19) gives: % 125.35/16.97 | | | (36) all_89_0 = all_89_1 | neq(all_89_1, all_89_0) % 125.35/16.97 | | | % 125.35/16.97 | | | GROUND_INST: instantiating (ax49) with all_91_3, simplifying with (23), % 125.35/16.97 | | | (25) gives: % 125.35/16.97 | | | (37) rearsegP(all_91_3, all_91_3) % 125.35/16.97 | | | % 125.35/16.98 | | | GROUND_INST: instantiating (6) with all_91_1, nil, all_91_0, nil, % 125.35/16.98 | | | all_91_0, simplifying with (5), (11), (22), (27), (30), (33) % 125.35/16.98 | | | gives: % 125.35/16.98 | | | (38) frontsegP(all_91_0, all_91_0) % 125.35/16.98 | | | % 125.35/16.98 | | | GROUND_INST: instantiating (ax25) with nil, all_91_1, all_91_0, % 125.35/16.98 | | | simplifying with (5), (11), (22), (27), (30) gives: % 125.35/16.98 | | | (39) tl(all_91_0) = nil % 125.35/16.98 | | | % 125.35/16.98 | | | GROUND_INST: instantiating (ax23) with nil, all_91_1, all_91_0, % 125.35/16.98 | | | simplifying with (5), (11), (22), (27), (30) gives: % 125.35/16.98 | | | (40) hd(all_91_0) = all_91_1 % 125.35/16.98 | | | % 125.35/16.98 | | | GROUND_INST: instantiating (ax16) with nil, all_91_1, all_91_0, % 125.35/16.98 | | | simplifying with (5), (11), (22), (27), (30) gives: % 125.35/16.98 | | | (41) ssList(all_91_0) % 125.35/16.98 | | | % 125.35/16.98 | | | BETA: splitting (36) gives: % 125.35/16.98 | | | % 125.35/16.98 | | | Case 1: % 125.35/16.98 | | | | % 125.35/16.98 | | | | % 125.35/16.98 | | | | GROUND_INST: instantiating (2) with all_91_0, all_91_0, simplifying with % 125.35/16.98 | | | | (28), (38), (41) gives: % 125.35/16.98 | | | | (42) ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) & % 125.35/16.98 | | | | ssList(v0)) % 125.35/16.98 | | | | % 125.35/16.98 | | | | GROUND_INST: instantiating (3) with all_91_3, all_91_3, simplifying with % 125.35/16.98 | | | | (23), (25), (37) gives: % 125.35/16.98 | | | | (43) ? [v0: $i] : (app(v0, all_91_3) = all_91_3 & $i(v0) & % 125.35/16.98 | | | | ssList(v0)) % 125.35/16.98 | | | | % 125.35/16.98 | | | | GROUND_INST: instantiating (9) with all_91_0, nil, simplifying with % 125.35/16.98 | | | | (28), (39), (41) gives: % 125.35/16.98 | | | | (44) ? [v0: $i] : (hd(all_91_0) = v0 & $i(v0) & ! [v1: any] : (v1 = % 125.35/16.98 | | | | all_91_0 | v1 = nil | all_91_0 = nil | ~ (tl(v1) = nil) | % 125.35/16.98 | | | | ~ $i(v1) | ~ ssList(v1) | ? [v2: $i] : ( ~ (v2 = v0) & % 125.35/16.98 | | | | hd(v1) = v2 & $i(v2)))) % 125.35/16.98 | | | | % 125.35/16.98 | | | | DELTA: instantiating (43) with fresh symbol all_145_0 gives: % 125.35/16.98 | | | | (45) app(all_145_0, all_91_3) = all_91_3 & $i(all_145_0) & % 125.35/16.98 | | | | ssList(all_145_0) % 125.35/16.98 | | | | % 125.35/16.98 | | | | ALPHA: (45) implies: % 125.35/16.98 | | | | (46) ssList(all_145_0) % 125.35/16.98 | | | | (47) $i(all_145_0) % 125.35/16.98 | | | | (48) app(all_145_0, all_91_3) = all_91_3 % 125.35/16.98 | | | | % 125.35/16.98 | | | | DELTA: instantiating (42) with fresh symbol all_149_0 gives: % 125.35/16.98 | | | | (49) app(all_91_0, all_149_0) = all_91_0 & $i(all_149_0) & % 125.35/16.98 | | | | ssList(all_149_0) % 125.35/16.98 | | | | % 125.35/16.98 | | | | ALPHA: (49) implies: % 125.35/16.98 | | | | (50) ssList(all_149_0) % 125.35/16.98 | | | | (51) $i(all_149_0) % 125.35/16.98 | | | | (52) app(all_91_0, all_149_0) = all_91_0 % 125.35/16.98 | | | | % 125.35/16.98 | | | | DELTA: instantiating (44) with fresh symbol all_165_0 gives: % 125.35/16.98 | | | | (53) hd(all_91_0) = all_165_0 & $i(all_165_0) & ! [v0: any] : (v0 = % 125.35/16.98 | | | | all_91_0 | v0 = nil | all_91_0 = nil | ~ (tl(v0) = nil) | ~ % 125.35/16.98 | | | | $i(v0) | ~ ssList(v0) | ? [v1: any] : ( ~ (v1 = all_165_0) & % 125.35/16.98 | | | | hd(v0) = v1 & $i(v1))) % 125.35/16.98 | | | | % 125.35/16.98 | | | | ALPHA: (53) implies: % 125.35/16.98 | | | | (54) $i(all_165_0) % 125.35/16.98 | | | | (55) hd(all_91_0) = all_165_0 % 125.35/16.98 | | | | % 125.35/16.98 | | | | GROUND_INST: instantiating (13) with all_91_1, all_165_0, all_91_0, % 125.35/16.98 | | | | simplifying with (40), (55) gives: % 125.35/16.98 | | | | (56) all_165_0 = all_91_1 % 125.35/16.98 | | | | % 125.35/16.98 | | | | GROUND_INST: instantiating (10) with all_149_0, all_91_1, all_91_0, % 125.35/16.98 | | | | all_91_0, simplifying with (22), (27), (30), (50), (51), % 125.35/16.98 | | | | (52) gives: % 125.35/16.98 | | | | (57) cons(all_91_1, all_149_0) = all_91_0 & $i(all_91_0) % 125.35/16.98 | | | | % 125.35/16.99 | | | | GROUND_INST: instantiating (4) with all_91_2, all_91_3, all_145_0, % 125.35/16.99 | | | | all_91_3, all_91_0, simplifying with (21), (23), (24), % 125.35/16.99 | | | | (25), (26), (28), (29), (41), (46), (47), (48) gives: % 125.35/16.99 | | | | (58) $false % 125.35/16.99 | | | | % 125.35/16.99 | | | | CLOSE: (58) is inconsistent. % 125.35/16.99 | | | | % 125.35/16.99 | | | Case 2: % 125.35/16.99 | | | | % 125.35/16.99 | | | | (59) all_89_0 = all_89_1 % 125.35/16.99 | | | | % 125.35/16.99 | | | | REDUCE: (15), (59) imply: % 125.35/16.99 | | | | (60) $false % 125.35/16.99 | | | | % 125.35/16.99 | | | | CLOSE: (60) is inconsistent. % 125.35/16.99 | | | | % 125.35/16.99 | | | End of split % 125.35/16.99 | | | % 125.35/16.99 | | End of split % 125.35/16.99 | | % 125.35/16.99 | End of split % 125.35/16.99 | % 125.35/16.99 End of proof % 125.35/16.99 % SZS output end Proof for theBenchmark % 125.35/16.99 % 125.35/16.99 16376ms %------------------------------------------------------------------------------