%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC182+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 : n005.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 20:50:07 EDT 2023 % Result : Theorem 33.11s 7.03s % Output : Proof 52.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SWC182+1 : TPTP v8.1.2. Released v2.4.0. % 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n005.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 16:12:08 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.63 ________ _____ % 0.19/0.63 ___ __ \_________(_)________________________________ % 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.63 % 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.63 (2023-06-19) % 0.19/0.63 % 0.19/0.63 (c) Philipp Rümmer, 2009-2023 % 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.63 Amanda Stjerna. % 0.19/0.63 Free software under BSD-3-Clause. % 0.19/0.63 % 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.63 % 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.64 Running up to 7 provers in parallel. % 0.19/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.56/1.68 Prover 4: Preprocessing ... % 4.56/1.68 Prover 1: Preprocessing ... % 4.96/1.73 Prover 3: Preprocessing ... % 4.96/1.73 Prover 6: Preprocessing ... % 4.96/1.73 Prover 2: Preprocessing ... % 4.96/1.73 Prover 5: Preprocessing ... % 4.96/1.73 Prover 0: Preprocessing ... % 13.82/3.45 Prover 2: Proving ... % 14.10/3.51 Prover 5: Constructing countermodel ... % 14.10/3.53 Prover 6: Proving ... % 14.10/3.54 Prover 1: Constructing countermodel ... % 14.67/3.60 Prover 3: Constructing countermodel ... % 19.00/4.45 Prover 4: Constructing countermodel ... % 20.43/4.73 Prover 0: Proving ... % 33.11/7.02 Prover 3: proved (6353ms) % 33.11/7.03 % 33.11/7.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 33.11/7.03 % 33.11/7.04 Prover 5: stopped % 33.11/7.04 Prover 2: stopped % 33.11/7.04 Prover 6: stopped % 33.11/7.06 Prover 0: stopped % 33.11/7.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 33.11/7.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 33.11/7.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 33.11/7.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 33.11/7.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 34.74/7.41 Prover 11: Preprocessing ... % 34.74/7.45 Prover 8: Preprocessing ... % 34.74/7.47 Prover 10: Preprocessing ... % 34.74/7.48 Prover 7: Preprocessing ... % 34.74/7.48 Prover 13: Preprocessing ... % 36.92/7.74 Prover 10: Constructing countermodel ... % 37.41/7.81 Prover 7: Constructing countermodel ... % 37.78/7.89 Prover 13: Constructing countermodel ... % 38.61/8.00 Prover 8: Warning: ignoring some quantifiers % 38.61/8.03 Prover 8: Constructing countermodel ... % 43.44/8.90 Prover 11: Constructing countermodel ... % 51.51/10.42 Prover 10: Found proof (size 70) % 51.51/10.42 Prover 10: proved (3374ms) % 51.51/10.42 Prover 11: stopped % 51.51/10.42 Prover 7: stopped % 51.51/10.42 Prover 13: stopped % 51.51/10.42 Prover 8: stopped % 52.05/10.43 Prover 1: stopped % 52.05/10.44 Prover 4: stopped % 52.05/10.44 % 52.05/10.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 52.05/10.44 % 52.05/10.44 % SZS output start Proof for theBenchmark % 52.05/10.45 Assumptions after simplification: % 52.05/10.45 --------------------------------- % 52.05/10.45 % 52.05/10.45 (ax1) % 52.05/10.46 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) | % 52.05/10.46 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) | % 52.05/10.46 ~ ssItem(v0)) % 52.05/10.46 % 52.05/10.46 (ax16) % 52.30/10.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1) % 52.30/10.50 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) % 52.30/10.50 % 52.30/10.50 (ax2) % 52.30/10.50 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) & % 52.30/10.50 ssItem(v0)) % 52.30/10.50 % 52.30/10.50 (ax27) % 52.30/10.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 52.30/10.50 (cons(v3, v2) = v4) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 52.30/10.50 $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | ? [v5: $i] : % 52.30/10.50 (cons(v3, v1) = v5 & app(v5, v0) = v4 & $i(v5) & $i(v4))) % 52.30/10.50 % 52.30/10.50 (ax28) % 52.30/10.50 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 52.30/10.50 $i(v0) | ~ ssList(v0)) % 52.30/10.50 % 52.30/10.50 (ax39) % 52.30/10.50 $i(nil) & ~ singletonP(nil) % 52.30/10.50 % 52.30/10.50 (ax4) % 52.30/10.51 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | % 52.30/10.51 ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0: $i] : ( % 52.30/10.51 ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1: $i] : (cons(v1, nil) % 52.30/10.51 = v0 & $i(v1) & ssItem(v1))) % 52.30/10.51 % 52.30/10.51 (ax46) % 52.30/10.51 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 52.30/10.51 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 52.30/10.51 % 52.30/10.51 (ax5) % 52.30/10.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 52.30/10.51 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 52.30/10.51 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 52.30/10.51 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 52.30/10.51 v2) = v0 & $i(v2) & ssList(v2))) % 52.30/10.51 % 52.30/10.51 (ax52) % 52.30/10.51 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~ % 52.30/10.51 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil)) % 52.30/10.51 % 52.30/10.51 (ax54) % 52.30/10.51 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ segmentP(v1, % 52.30/10.51 v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 52.30/10.51 % 52.30/10.51 (ax57) % 52.30/10.51 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil)) % 52.30/10.51 % 52.30/10.51 (ax58) % 52.30/10.52 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 52.30/10.52 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 52.30/10.52 % 52.30/10.52 (ax6) % 52.30/10.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 52.30/10.52 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 52.30/10.52 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 52.30/10.52 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 52.30/10.52 v1) = v0 & $i(v2) & ssList(v2))) % 52.30/10.52 % 52.30/10.52 (ax7) % 52.30/10.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 52.30/10.52 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 52.30/10.52 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 52.30/10.52 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 52.30/10.52 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 52.30/10.52 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 52.30/10.52 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 52.30/10.52 % 52.30/10.52 (ax82) % 52.30/10.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 52.30/10.52 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 52.30/10.52 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 52.30/10.52 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 52.30/10.52 % 52.30/10.52 (ax83) % 52.30/10.52 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 52.30/10.52 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 52.30/10.52 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 52.30/10.52 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 52.30/10.52 v0) | ~ ssList(nil)) % 52.30/10.52 % 52.30/10.53 (ax84) % 52.30/10.53 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 52.30/10.53 $i(v0) | ~ ssList(v0)) % 52.30/10.53 % 52.30/10.53 (co1) % 52.30/10.53 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 52.30/10.53 : ? [v5: $i] : (cons(v1, nil) = v2 & app(v4, v5) = nil & app(v3, v2) = v4 & % 52.30/10.53 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v5) & % 52.30/10.53 ssList(v3) & ssList(v0) & ssList(nil) & ssItem(v1) & (memberP(v5, v1) | % 52.30/10.53 memberP(v3, v1))) % 52.30/10.53 % 52.30/10.53 (function-axioms) % 52.30/10.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.30/10.53 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 52.30/10.53 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 52.30/10.53 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 52.30/10.53 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 52.30/10.53 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 52.30/10.53 % 52.30/10.53 Further assumptions not needed in the proof: % 52.30/10.53 -------------------------------------------- % 52.30/10.53 ax10, ax11, ax12, ax13, ax14, ax15, ax17, ax18, ax19, ax20, ax21, ax22, ax23, % 52.30/10.53 ax24, ax25, ax26, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, % 52.30/10.53 ax38, ax40, ax41, ax42, ax43, ax44, ax45, ax47, ax48, ax49, ax50, ax51, ax53, % 52.30/10.53 ax55, ax56, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, % 52.30/10.53 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 52.30/10.53 ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 52.30/10.53 % 52.30/10.53 Those formulas are unsatisfiable: % 52.30/10.53 --------------------------------- % 52.30/10.53 % 52.30/10.53 Begin of proof % 52.30/10.53 | % 52.30/10.53 | ALPHA: (ax1) implies: % 52.30/10.53 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 52.30/10.53 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 52.30/10.53 | % 52.30/10.53 | ALPHA: (ax4) implies: % 52.30/10.53 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | ~ % 52.30/10.53 | $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) % 52.30/10.53 | % 52.30/10.53 | ALPHA: (ax5) implies: % 52.30/10.53 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 52.30/10.53 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 52.30/10.53 | v0 & $i(v2) & ssList(v2))) % 52.30/10.53 | % 52.30/10.53 | ALPHA: (ax6) implies: % 52.30/10.54 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 52.30/10.54 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 52.30/10.54 | v0 & $i(v2) & ssList(v2))) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax7) implies: % 52.30/10.54 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 52.30/10.54 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 52.30/10.54 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 52.30/10.54 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax28) implies: % 52.30/10.54 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 52.30/10.54 | $i(v0) | ~ ssList(v0)) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax39) implies: % 52.30/10.54 | (7) ~ singletonP(nil) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax46) implies: % 52.30/10.54 | (8) ~ ssList(nil) | frontsegP(nil, nil) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax52) implies: % 52.30/10.54 | (9) ~ ssList(nil) | rearsegP(nil, nil) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax57) implies: % 52.30/10.54 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil)) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax58) implies: % 52.30/10.54 | (11) ~ ssList(nil) | segmentP(nil, nil) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax83) implies: % 52.30/10.54 | (12) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (ax84) implies: % 52.30/10.54 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 52.30/10.54 | $i(v0) | ~ ssList(v0)) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (co1) implies: % 52.30/10.54 | (14) $i(nil) % 52.30/10.54 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 52.30/10.54 | ? [v5: $i] : (cons(v1, nil) = v2 & app(v4, v5) = nil & app(v3, v2) = % 52.30/10.54 | v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 52.30/10.54 | ssList(v5) & ssList(v3) & ssList(v0) & ssList(nil) & ssItem(v1) & % 52.30/10.54 | (memberP(v5, v1) | memberP(v3, v1))) % 52.30/10.54 | % 52.30/10.54 | ALPHA: (function-axioms) implies: % 52.30/10.54 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.30/10.54 | (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 52.30/10.54 | % 52.30/10.54 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives: % 52.30/10.55 | (17) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) & % 52.30/10.55 | ssItem(all_89_0) & ssItem(all_89_1) % 52.30/10.55 | % 52.30/10.55 | ALPHA: (17) implies: % 52.30/10.55 | (18) ~ (all_89_0 = all_89_1) % 52.30/10.55 | (19) ssItem(all_89_1) % 52.30/10.55 | (20) ssItem(all_89_0) % 52.30/10.55 | (21) $i(all_89_1) % 52.30/10.55 | (22) $i(all_89_0) % 52.30/10.55 | % 52.30/10.55 | DELTA: instantiating (15) with fresh symbols all_91_0, all_91_1, all_91_2, % 52.30/10.55 | all_91_3, all_91_4, all_91_5 gives: % 52.30/10.55 | (23) cons(all_91_4, nil) = all_91_3 & app(all_91_1, all_91_0) = nil & % 52.30/10.55 | app(all_91_2, all_91_3) = all_91_1 & $i(all_91_0) & $i(all_91_1) & % 52.30/10.55 | $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & $i(all_91_5) & % 52.30/10.55 | ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_5) & ssList(nil) & % 52.30/10.55 | ssItem(all_91_4) & (memberP(all_91_0, all_91_4) | memberP(all_91_2, % 52.30/10.55 | all_91_4)) % 52.30/10.55 | % 52.30/10.55 | ALPHA: (23) implies: % 52.30/10.55 | (24) ssItem(all_91_4) % 52.30/10.55 | (25) ssList(nil) % 52.30/10.55 | (26) ssList(all_91_2) % 52.30/10.55 | (27) ssList(all_91_0) % 52.30/10.55 | (28) $i(all_91_4) % 52.30/10.55 | (29) $i(all_91_3) % 52.30/10.55 | (30) $i(all_91_2) % 52.30/10.55 | (31) $i(all_91_0) % 52.30/10.55 | (32) app(all_91_2, all_91_3) = all_91_1 % 52.30/10.55 | (33) app(all_91_1, all_91_0) = nil % 52.30/10.55 | (34) cons(all_91_4, nil) = all_91_3 % 52.30/10.55 | % 52.30/10.55 | BETA: splitting (9) gives: % 52.30/10.55 | % 52.30/10.55 | Case 1: % 52.30/10.55 | | % 52.30/10.55 | | (35) ~ ssList(nil) % 52.30/10.55 | | % 52.30/10.55 | | PRED_UNIFY: (25), (35) imply: % 52.30/10.55 | | (36) $false % 52.30/10.55 | | % 52.30/10.55 | | CLOSE: (36) is inconsistent. % 52.30/10.55 | | % 52.30/10.55 | Case 2: % 52.30/10.55 | | % 52.30/10.55 | | (37) rearsegP(nil, nil) % 52.30/10.55 | | % 52.30/10.55 | | BETA: splitting (8) gives: % 52.30/10.55 | | % 52.30/10.55 | | Case 1: % 52.30/10.55 | | | % 52.30/10.55 | | | (38) ~ ssList(nil) % 52.30/10.55 | | | % 52.30/10.55 | | | PRED_UNIFY: (25), (38) imply: % 52.30/10.55 | | | (39) $false % 52.30/10.55 | | | % 52.30/10.55 | | | CLOSE: (39) is inconsistent. % 52.30/10.55 | | | % 52.30/10.55 | | Case 2: % 52.30/10.55 | | | % 52.30/10.55 | | | (40) frontsegP(nil, nil) % 52.30/10.55 | | | % 52.30/10.55 | | | BETA: splitting (11) gives: % 52.30/10.55 | | | % 52.30/10.55 | | | Case 1: % 52.30/10.55 | | | | % 52.30/10.55 | | | | (41) ~ ssList(nil) % 52.30/10.55 | | | | % 52.30/10.55 | | | | PRED_UNIFY: (25), (41) imply: % 52.30/10.55 | | | | (42) $false % 52.30/10.55 | | | | % 52.30/10.55 | | | | CLOSE: (42) is inconsistent. % 52.30/10.55 | | | | % 52.30/10.55 | | | Case 2: % 52.30/10.55 | | | | % 52.30/10.55 | | | | % 52.30/10.56 | | | | GROUND_INST: instantiating (1) with all_89_0, all_89_1, simplifying with % 52.30/10.56 | | | | (19), (20), (21), (22) gives: % 52.30/10.56 | | | | (43) all_89_0 = all_89_1 | neq(all_89_0, all_89_1) % 52.30/10.56 | | | | % 52.30/10.56 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (14), % 52.30/10.56 | | | | (25), (40) gives: % 52.30/10.56 | | | | (44) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 52.30/10.56 | | | | % 52.30/10.56 | | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (14), % 52.30/10.56 | | | | (25), (37) gives: % 52.30/10.56 | | | | (45) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0)) % 52.30/10.56 | | | | % 52.30/10.56 | | | | GROUND_INST: instantiating (ax16) with nil, all_91_4, all_91_3, % 52.30/10.56 | | | | simplifying with (14), (24), (25), (28), (34) gives: % 52.30/10.56 | | | | (46) ssList(all_91_3) % 52.30/10.56 | | | | % 52.30/10.56 | | | | DELTA: instantiating (45) with fresh symbol all_111_0 gives: % 52.30/10.56 | | | | (47) app(all_111_0, nil) = nil & $i(all_111_0) & ssList(all_111_0) % 52.30/10.56 | | | | % 52.30/10.56 | | | | ALPHA: (47) implies: % 52.30/10.56 | | | | (48) ssList(all_111_0) % 52.30/10.56 | | | | (49) $i(all_111_0) % 52.30/10.56 | | | | (50) app(all_111_0, nil) = nil % 52.30/10.56 | | | | % 52.30/10.56 | | | | DELTA: instantiating (44) with fresh symbol all_113_0 gives: % 52.30/10.56 | | | | (51) app(nil, all_113_0) = nil & $i(all_113_0) & ssList(all_113_0) % 52.30/10.56 | | | | % 52.30/10.56 | | | | ALPHA: (51) implies: % 52.30/10.56 | | | | (52) ssList(all_113_0) % 52.30/10.56 | | | | (53) $i(all_113_0) % 52.30/10.56 | | | | (54) app(nil, all_113_0) = nil % 52.30/10.56 | | | | % 52.30/10.56 | | | | BETA: splitting (43) gives: % 52.30/10.56 | | | | % 52.30/10.56 | | | | Case 1: % 52.30/10.56 | | | | | % 52.30/10.56 | | | | | % 52.30/10.56 | | | | | GROUND_INST: instantiating (2) with all_91_3, all_91_4, simplifying % 52.30/10.56 | | | | | with (24), (28), (29), (34), (46) gives: % 52.30/10.56 | | | | | (55) singletonP(all_91_3) % 52.30/10.56 | | | | | % 52.62/10.56 | | | | | GROUND_INST: instantiating (5) with nil, all_91_3, all_91_2, all_91_1, % 52.62/10.56 | | | | | all_91_0, simplifying with (14), (25), (26), (27), (29), % 52.62/10.56 | | | | | (30), (31), (32), (33), (46) gives: % 52.62/10.56 | | | | | (56) segmentP(nil, all_91_3) % 52.62/10.56 | | | | | % 52.62/10.56 | | | | | GROUND_INST: instantiating (10) with all_91_3, simplifying with (29), % 52.62/10.56 | | | | | (46) gives: % 52.62/10.56 | | | | | (57) segmentP(all_91_3, nil) % 52.62/10.56 | | | | | % 52.62/10.57 | | | | | GROUND_INST: instantiating (ax27) with all_113_0, nil, nil, all_91_4, % 52.62/10.57 | | | | | all_91_3, simplifying with (14), (24), (25), (28), (34), % 52.63/10.57 | | | | | (52), (53), (54) gives: % 52.63/10.57 | | | | | (58) ? [v0: $i] : (cons(all_91_4, nil) = v0 & app(v0, all_113_0) = % 52.63/10.57 | | | | | all_91_3 & $i(v0) & $i(all_91_3)) % 52.63/10.57 | | | | | % 52.63/10.57 | | | | | GROUND_INST: instantiating (ax82) with nil, all_113_0, nil, all_113_0, % 52.63/10.57 | | | | | nil, simplifying with (14), (25), (52), (53), (54) gives: % 52.63/10.58 | | | | | (59) ? [v0: $i] : (app(all_113_0, all_113_0) = v0 & app(nil, v0) = % 52.63/10.58 | | | | | nil & $i(v0)) % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | GROUND_INST: instantiating (6) with all_113_0, nil, simplifying with % 52.63/10.58 | | | | | (52), (53), (54) gives: % 52.63/10.58 | | | | | (60) all_113_0 = nil % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | GROUND_INST: instantiating (ax27) with nil, all_111_0, nil, all_91_4, % 52.63/10.58 | | | | | all_91_3, simplifying with (14), (24), (25), (28), (34), % 52.63/10.58 | | | | | (48), (49), (50) gives: % 52.63/10.58 | | | | | (61) ? [v0: $i] : (cons(all_91_4, all_111_0) = v0 & app(v0, nil) = % 52.63/10.58 | | | | | all_91_3 & $i(v0) & $i(all_91_3)) % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | GROUND_INST: instantiating (13) with all_111_0, nil, simplifying with % 52.63/10.58 | | | | | (48), (49), (50) gives: % 52.63/10.58 | | | | | (62) all_111_0 = nil % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | DELTA: instantiating (59) with fresh symbol all_159_0 gives: % 52.63/10.58 | | | | | (63) app(all_113_0, all_113_0) = all_159_0 & app(nil, all_159_0) = % 52.63/10.58 | | | | | nil & $i(all_159_0) % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | ALPHA: (63) implies: % 52.63/10.58 | | | | | (64) $i(all_159_0) % 52.63/10.58 | | | | | (65) app(all_113_0, all_113_0) = all_159_0 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | DELTA: instantiating (61) with fresh symbol all_161_0 gives: % 52.63/10.58 | | | | | (66) cons(all_91_4, all_111_0) = all_161_0 & app(all_161_0, nil) = % 52.63/10.58 | | | | | all_91_3 & $i(all_161_0) & $i(all_91_3) % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | ALPHA: (66) implies: % 52.63/10.58 | | | | | (67) $i(all_161_0) % 52.63/10.58 | | | | | (68) cons(all_91_4, all_111_0) = all_161_0 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | DELTA: instantiating (58) with fresh symbol all_163_0 gives: % 52.63/10.58 | | | | | (69) cons(all_91_4, nil) = all_163_0 & app(all_163_0, all_113_0) = % 52.63/10.58 | | | | | all_91_3 & $i(all_163_0) & $i(all_91_3) % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | ALPHA: (69) implies: % 52.63/10.58 | | | | | (70) cons(all_91_4, nil) = all_163_0 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | REDUCE: (62), (68) imply: % 52.63/10.58 | | | | | (71) cons(all_91_4, nil) = all_161_0 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | REDUCE: (60), (65) imply: % 52.63/10.58 | | | | | (72) app(nil, nil) = all_159_0 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | GROUND_INST: instantiating (12) with all_159_0, simplifying with (25), % 52.63/10.58 | | | | | (72) gives: % 52.63/10.58 | | | | | (73) all_159_0 = nil % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | GROUND_INST: instantiating (16) with all_91_3, all_163_0, nil, % 52.63/10.58 | | | | | all_91_4, simplifying with (34), (70) gives: % 52.63/10.58 | | | | | (74) all_163_0 = all_91_3 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | GROUND_INST: instantiating (16) with all_161_0, all_163_0, nil, % 52.63/10.58 | | | | | all_91_4, simplifying with (70), (71) gives: % 52.63/10.58 | | | | | (75) all_163_0 = all_161_0 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | COMBINE_EQS: (74), (75) imply: % 52.63/10.58 | | | | | (76) all_161_0 = all_91_3 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | GROUND_INST: instantiating (ax54) with nil, all_91_3, simplifying with % 52.63/10.58 | | | | | (14), (25), (29), (46), (56), (57) gives: % 52.63/10.58 | | | | | (77) all_91_3 = nil % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | REDUCE: (55), (77) imply: % 52.63/10.58 | | | | | (78) singletonP(nil) % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | PRED_UNIFY: (7), (78) imply: % 52.63/10.58 | | | | | (79) $false % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | CLOSE: (79) is inconsistent. % 52.63/10.58 | | | | | % 52.63/10.58 | | | | Case 2: % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | (80) all_89_0 = all_89_1 % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | REDUCE: (18), (80) imply: % 52.63/10.58 | | | | | (81) $false % 52.63/10.58 | | | | | % 52.63/10.58 | | | | | CLOSE: (81) is inconsistent. % 52.63/10.59 | | | | | % 52.63/10.59 | | | | End of split % 52.63/10.59 | | | | % 52.63/10.59 | | | End of split % 52.63/10.59 | | | % 52.63/10.59 | | End of split % 52.63/10.59 | | % 52.63/10.59 | End of split % 52.63/10.59 | % 52.63/10.59 End of proof % 52.63/10.59 % SZS output end Proof for theBenchmark % 52.63/10.59 % 52.63/10.59 9958ms %------------------------------------------------------------------------------