%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC218+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 : n032.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 20:50:18 EDT 2023 % Result : Theorem 33.76s 5.14s % Output : Proof 56.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.10 % Problem : SWC218+1 : TPTP v8.1.2. Released v2.4.0. % 0.06/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 300 % 0.10/0.29 % DateTime : Mon Aug 28 18:28:01 EDT 2023 % 0.10/0.29 % CPUTime : % 0.14/0.51 ________ _____ % 0.14/0.51 ___ __ \_________(_)________________________________ % 0.14/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.14/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.14/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.14/0.51 % 0.14/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.14/0.51 (2023-06-19) % 0.14/0.51 % 0.14/0.51 (c) Philipp Rümmer, 2009-2023 % 0.14/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.14/0.51 Amanda Stjerna. % 0.14/0.51 Free software under BSD-3-Clause. % 0.14/0.51 % 0.14/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.14/0.51 % 0.14/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.14/0.53 Running up to 7 provers in parallel. % 0.14/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.14/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.14/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.14/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.14/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.14/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.14/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.88/1.26 Prover 4: Preprocessing ... % 3.88/1.26 Prover 1: Preprocessing ... % 4.74/1.33 Prover 6: Preprocessing ... % 4.74/1.33 Prover 2: Preprocessing ... % 4.74/1.33 Prover 5: Preprocessing ... % 4.74/1.33 Prover 3: Preprocessing ... % 4.74/1.33 Prover 0: Preprocessing ... % 13.51/2.52 Prover 2: Proving ... % 13.51/2.55 Prover 5: Constructing countermodel ... % 14.56/2.68 Prover 1: Constructing countermodel ... % 15.15/2.74 Prover 6: Proving ... % 15.15/2.76 Prover 3: Constructing countermodel ... % 20.66/3.42 Prover 4: Constructing countermodel ... % 22.02/3.60 Prover 0: Proving ... % 33.76/5.14 Prover 3: proved (4605ms) % 33.76/5.14 % 33.76/5.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 33.76/5.14 % 33.76/5.14 Prover 5: stopped % 33.76/5.16 Prover 0: stopped % 33.76/5.16 Prover 6: stopped % 33.76/5.16 Prover 2: stopped % 33.76/5.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 33.76/5.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 33.76/5.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 33.76/5.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 33.76/5.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 35.69/5.40 Prover 10: Preprocessing ... % 35.94/5.43 Prover 8: Preprocessing ... % 35.94/5.45 Prover 7: Preprocessing ... % 35.94/5.45 Prover 13: Preprocessing ... % 35.94/5.46 Prover 11: Preprocessing ... % 37.97/5.69 Prover 10: Constructing countermodel ... % 37.97/5.76 Prover 7: Constructing countermodel ... % 39.10/5.89 Prover 8: Warning: ignoring some quantifiers % 39.10/5.90 Prover 8: Constructing countermodel ... % 39.75/5.94 Prover 13: Constructing countermodel ... % 44.77/6.66 Prover 11: Constructing countermodel ... % 55.60/8.02 Prover 10: Found proof (size 76) % 55.60/8.02 Prover 10: proved (2861ms) % 55.60/8.02 Prover 13: stopped % 55.60/8.02 Prover 11: stopped % 55.60/8.02 Prover 8: stopped % 55.60/8.02 Prover 1: stopped % 55.60/8.02 Prover 7: stopped % 55.60/8.03 Prover 4: stopped % 55.60/8.03 % 55.60/8.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 55.60/8.03 % 55.60/8.04 % SZS output start Proof for theBenchmark % 55.60/8.04 Assumptions after simplification: % 55.60/8.04 --------------------------------- % 55.60/8.04 % 55.60/8.04 (ax1) % 55.60/8.05 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) | % 55.60/8.05 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) | % 55.60/8.05 ~ ssItem(v0)) % 55.60/8.05 % 55.60/8.05 (ax15) % 55.60/8.05 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 55.60/8.05 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ % 55.60/8.05 neq(v0, v0)) % 55.60/8.05 % 55.60/8.05 (ax16) % 56.10/8.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1) % 56.10/8.07 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) % 56.10/8.07 % 56.10/8.07 (ax17) % 56.10/8.07 $i(nil) & ssList(nil) % 56.10/8.07 % 56.10/8.07 (ax2) % 56.10/8.07 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) & % 56.10/8.07 ssItem(v0)) % 56.10/8.07 % 56.10/8.07 (ax27) % 56.10/8.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 56.10/8.08 (cons(v3, v2) = v4) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 56.10/8.08 $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | ? [v5: $i] : % 56.10/8.08 (cons(v3, v1) = v5 & app(v5, v0) = v4 & $i(v5) & $i(v4))) % 56.10/8.08 % 56.10/8.08 (ax28) % 56.10/8.08 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 56.10/8.08 $i(v0) | ~ ssList(v0)) % 56.10/8.08 % 56.10/8.08 (ax39) % 56.10/8.08 $i(nil) & ~ singletonP(nil) % 56.10/8.08 % 56.10/8.08 (ax4) % 56.18/8.08 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | % 56.18/8.08 ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0: $i] : ( % 56.18/8.08 ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1: $i] : (cons(v1, nil) % 56.18/8.08 = v0 & $i(v1) & ssItem(v1))) % 56.18/8.08 % 56.18/8.08 (ax46) % 56.18/8.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 56.18/8.08 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 56.18/8.08 % 56.18/8.08 (ax5) % 56.18/8.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 56.18/8.08 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 56.18/8.08 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 56.18/8.08 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 56.18/8.08 v2) = v0 & $i(v2) & ssList(v2))) % 56.18/8.08 % 56.18/8.08 (ax52) % 56.18/8.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~ % 56.18/8.08 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil)) % 56.18/8.08 % 56.18/8.08 (ax54) % 56.18/8.08 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ segmentP(v1, % 56.18/8.08 v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 56.18/8.08 % 56.18/8.08 (ax57) % 56.18/8.08 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil)) % 56.18/8.08 % 56.18/8.08 (ax58) % 56.18/8.09 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 56.18/8.09 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 56.18/8.09 % 56.18/8.09 (ax6) % 56.18/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 56.18/8.09 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 56.18/8.09 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 56.18/8.09 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 56.18/8.09 v1) = v0 & $i(v2) & ssList(v2))) % 56.18/8.09 % 56.18/8.09 (ax7) % 56.18/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 56.18/8.09 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 56.18/8.09 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 56.18/8.09 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 56.18/8.09 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 56.18/8.09 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 56.18/8.09 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 56.18/8.09 % 56.18/8.09 (ax82) % 56.18/8.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 56.18/8.09 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 56.18/8.09 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 56.18/8.09 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 56.18/8.09 % 56.18/8.09 (ax83) % 56.18/8.09 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 56.18/8.09 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 56.18/8.09 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 56.18/8.09 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 56.18/8.09 v0) | ~ ssList(nil)) % 56.18/8.09 % 56.18/8.09 (ax84) % 56.18/8.09 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 56.18/8.09 $i(v0) | ~ ssList(v0)) % 56.18/8.09 % 56.18/8.09 (co1) % 56.18/8.10 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 56.18/8.10 : ? [v5: $i] : ? [v6: $i] : (cons(v4, nil) = v5 & app(v6, v3) = v0 & app(v2, % 56.18/8.10 v5) = v6 & app(v2, v3) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 56.18/8.10 $i(v1) & $i(v0) & ssList(v3) & ssList(v2) & ssList(v1) & ssList(v0) & % 56.18/8.10 ssItem(v4) & ~ neq(v0, nil)) % 56.18/8.10 % 56.18/8.10 (function-axioms) % 56.18/8.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.18/8.10 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 56.18/8.10 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 56.18/8.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 56.18/8.10 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 56.18/8.10 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 56.18/8.10 % 56.18/8.10 Further assumptions not needed in the proof: % 56.18/8.10 -------------------------------------------- % 56.18/8.10 ax10, ax11, ax12, ax13, ax14, ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, % 56.18/8.10 ax26, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax40, % 56.18/8.10 ax41, ax42, ax43, ax44, ax45, ax47, ax48, ax49, ax50, ax51, ax53, ax55, ax56, % 56.18/8.10 ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71, % 56.18/8.10 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax85, ax86, % 56.18/8.10 ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 56.18/8.10 % 56.18/8.10 Those formulas are unsatisfiable: % 56.18/8.10 --------------------------------- % 56.18/8.10 % 56.18/8.10 Begin of proof % 56.18/8.10 | % 56.18/8.10 | ALPHA: (ax1) implies: % 56.18/8.10 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 56.18/8.10 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 56.18/8.10 | % 56.18/8.10 | ALPHA: (ax4) implies: % 56.18/8.10 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | ~ % 56.18/8.10 | $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) % 56.18/8.10 | % 56.18/8.10 | ALPHA: (ax5) implies: % 56.18/8.11 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 56.18/8.11 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 56.18/8.11 | v0 & $i(v2) & ssList(v2))) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax6) implies: % 56.18/8.11 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 56.18/8.11 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 56.18/8.11 | v0 & $i(v2) & ssList(v2))) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax7) implies: % 56.18/8.11 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 56.18/8.11 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 56.18/8.11 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 56.18/8.11 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax15) implies: % 56.18/8.11 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 56.18/8.11 | ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax17) implies: % 56.18/8.11 | (7) ssList(nil) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax28) implies: % 56.18/8.11 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 56.18/8.11 | $i(v0) | ~ ssList(v0)) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax39) implies: % 56.18/8.11 | (9) ~ singletonP(nil) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax46) implies: % 56.18/8.11 | (10) ~ ssList(nil) | frontsegP(nil, nil) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax52) implies: % 56.18/8.11 | (11) ~ ssList(nil) | rearsegP(nil, nil) % 56.18/8.11 | % 56.18/8.11 | ALPHA: (ax57) implies: % 56.36/8.11 | (12) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil)) % 56.36/8.11 | % 56.36/8.11 | ALPHA: (ax58) implies: % 56.36/8.11 | (13) ~ ssList(nil) | segmentP(nil, nil) % 56.36/8.11 | % 56.36/8.11 | ALPHA: (ax83) implies: % 56.36/8.11 | (14) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 56.36/8.11 | % 56.36/8.11 | ALPHA: (ax84) implies: % 56.36/8.11 | (15) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 56.36/8.11 | $i(v0) | ~ ssList(v0)) % 56.36/8.11 | % 56.36/8.11 | ALPHA: (co1) implies: % 56.36/8.12 | (16) $i(nil) % 56.36/8.12 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 56.36/8.12 | ? [v5: $i] : ? [v6: $i] : (cons(v4, nil) = v5 & app(v6, v3) = v0 & % 56.36/8.12 | app(v2, v5) = v6 & app(v2, v3) = v1 & $i(v6) & $i(v5) & $i(v4) & % 56.36/8.12 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v3) & ssList(v2) & % 56.36/8.12 | ssList(v1) & ssList(v0) & ssItem(v4) & ~ neq(v0, nil)) % 56.36/8.12 | % 56.36/8.12 | ALPHA: (function-axioms) implies: % 56.36/8.12 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.36/8.12 | (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 56.36/8.12 | % 56.36/8.12 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives: % 56.36/8.12 | (19) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) & % 56.36/8.12 | ssItem(all_89_0) & ssItem(all_89_1) % 56.36/8.12 | % 56.36/8.12 | ALPHA: (19) implies: % 56.36/8.12 | (20) ~ (all_89_0 = all_89_1) % 56.36/8.12 | (21) ssItem(all_89_1) % 56.36/8.12 | (22) ssItem(all_89_0) % 56.36/8.12 | (23) $i(all_89_1) % 56.36/8.12 | (24) $i(all_89_0) % 56.36/8.12 | % 56.36/8.12 | DELTA: instantiating (17) with fresh symbols all_91_0, all_91_1, all_91_2, % 56.36/8.12 | all_91_3, all_91_4, all_91_5, all_91_6 gives: % 56.36/8.12 | (25) cons(all_91_2, nil) = all_91_1 & app(all_91_0, all_91_3) = all_91_6 & % 56.36/8.12 | app(all_91_4, all_91_1) = all_91_0 & app(all_91_4, all_91_3) = % 56.36/8.12 | all_91_5 & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & % 56.36/8.12 | $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_3) & % 56.36/8.12 | ssList(all_91_4) & ssList(all_91_5) & ssList(all_91_6) & % 56.36/8.12 | ssItem(all_91_2) & ~ neq(all_91_6, nil) % 56.36/8.12 | % 56.36/8.12 | ALPHA: (25) implies: % 56.36/8.12 | (26) ~ neq(all_91_6, nil) % 56.36/8.12 | (27) ssItem(all_91_2) % 56.36/8.12 | (28) ssList(all_91_6) % 56.36/8.12 | (29) ssList(all_91_4) % 56.36/8.12 | (30) ssList(all_91_3) % 56.36/8.12 | (31) $i(all_91_6) % 56.36/8.12 | (32) $i(all_91_4) % 56.36/8.12 | (33) $i(all_91_3) % 56.36/8.12 | (34) $i(all_91_2) % 56.36/8.12 | (35) $i(all_91_1) % 56.36/8.12 | (36) app(all_91_4, all_91_1) = all_91_0 % 56.36/8.12 | (37) app(all_91_0, all_91_3) = all_91_6 % 56.36/8.12 | (38) cons(all_91_2, nil) = all_91_1 % 56.36/8.12 | % 56.36/8.12 | BETA: splitting (10) gives: % 56.36/8.12 | % 56.36/8.13 | Case 1: % 56.36/8.13 | | % 56.36/8.13 | | (39) ~ ssList(nil) % 56.36/8.13 | | % 56.36/8.13 | | PRED_UNIFY: (7), (39) imply: % 56.36/8.13 | | (40) $false % 56.36/8.13 | | % 56.36/8.13 | | CLOSE: (40) is inconsistent. % 56.36/8.13 | | % 56.36/8.13 | Case 2: % 56.36/8.13 | | % 56.36/8.13 | | (41) frontsegP(nil, nil) % 56.36/8.13 | | % 56.36/8.13 | | BETA: splitting (11) gives: % 56.36/8.13 | | % 56.36/8.13 | | Case 1: % 56.36/8.13 | | | % 56.36/8.13 | | | (42) ~ ssList(nil) % 56.36/8.13 | | | % 56.36/8.13 | | | PRED_UNIFY: (7), (42) imply: % 56.36/8.13 | | | (43) $false % 56.36/8.13 | | | % 56.36/8.13 | | | CLOSE: (43) is inconsistent. % 56.36/8.13 | | | % 56.36/8.13 | | Case 2: % 56.36/8.13 | | | % 56.36/8.13 | | | (44) rearsegP(nil, nil) % 56.36/8.13 | | | % 56.36/8.13 | | | BETA: splitting (13) gives: % 56.36/8.13 | | | % 56.36/8.13 | | | Case 1: % 56.36/8.13 | | | | % 56.36/8.13 | | | | (45) ~ ssList(nil) % 56.36/8.13 | | | | % 56.36/8.13 | | | | PRED_UNIFY: (7), (45) imply: % 56.36/8.13 | | | | (46) $false % 56.36/8.13 | | | | % 56.36/8.13 | | | | CLOSE: (46) is inconsistent. % 56.36/8.13 | | | | % 56.36/8.13 | | | Case 2: % 56.36/8.13 | | | | % 56.45/8.13 | | | | % 56.45/8.13 | | | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with % 56.45/8.13 | | | | (21), (22), (23), (24) gives: % 56.45/8.13 | | | | (47) all_89_0 = all_89_1 | neq(all_89_1, all_89_0) % 56.45/8.13 | | | | % 56.45/8.13 | | | | GROUND_INST: instantiating (6) with all_91_6, nil, simplifying with (7), % 56.45/8.13 | | | | (16), (26), (28), (31) gives: % 56.45/8.13 | | | | (48) all_91_6 = nil % 56.45/8.13 | | | | % 56.45/8.13 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (7), % 56.45/8.13 | | | | (16), (41) gives: % 56.45/8.13 | | | | (49) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 56.45/8.13 | | | | % 56.45/8.13 | | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (7), % 56.45/8.13 | | | | (16), (44) gives: % 56.45/8.13 | | | | (50) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0)) % 56.45/8.13 | | | | % 56.45/8.14 | | | | GROUND_INST: instantiating (ax16) with nil, all_91_2, all_91_1, % 56.45/8.14 | | | | simplifying with (7), (16), (27), (34), (38) gives: % 56.45/8.14 | | | | (51) ssList(all_91_1) % 56.45/8.14 | | | | % 56.45/8.14 | | | | DELTA: instantiating (50) with fresh symbol all_111_0 gives: % 56.45/8.14 | | | | (52) app(all_111_0, nil) = nil & $i(all_111_0) & ssList(all_111_0) % 56.45/8.14 | | | | % 56.45/8.14 | | | | ALPHA: (52) implies: % 56.45/8.14 | | | | (53) ssList(all_111_0) % 56.45/8.14 | | | | (54) $i(all_111_0) % 56.45/8.14 | | | | (55) app(all_111_0, nil) = nil % 56.45/8.14 | | | | % 56.45/8.14 | | | | DELTA: instantiating (49) with fresh symbol all_113_0 gives: % 56.45/8.14 | | | | (56) app(nil, all_113_0) = nil & $i(all_113_0) & ssList(all_113_0) % 56.45/8.14 | | | | % 56.45/8.14 | | | | ALPHA: (56) implies: % 56.45/8.14 | | | | (57) ssList(all_113_0) % 56.45/8.14 | | | | (58) $i(all_113_0) % 56.45/8.14 | | | | (59) app(nil, all_113_0) = nil % 56.45/8.14 | | | | % 56.45/8.14 | | | | REDUCE: (37), (48) imply: % 56.45/8.14 | | | | (60) app(all_91_0, all_91_3) = nil % 56.45/8.14 | | | | % 56.45/8.14 | | | | BETA: splitting (47) gives: % 56.45/8.14 | | | | % 56.45/8.14 | | | | Case 1: % 56.45/8.14 | | | | | % 56.45/8.14 | | | | | % 56.45/8.14 | | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_2, simplifying % 56.45/8.14 | | | | | with (27), (34), (35), (38), (51) gives: % 56.45/8.14 | | | | | (61) singletonP(all_91_1) % 56.45/8.14 | | | | | % 56.45/8.14 | | | | | GROUND_INST: instantiating (12) with all_91_1, simplifying with (35), % 56.45/8.14 | | | | | (51) gives: % 56.45/8.14 | | | | | (62) segmentP(all_91_1, nil) % 56.45/8.14 | | | | | % 56.45/8.14 | | | | | GROUND_INST: instantiating (ax27) with all_113_0, nil, nil, all_91_2, % 56.45/8.14 | | | | | all_91_1, simplifying with (7), (16), (27), (34), (38), % 56.45/8.14 | | | | | (57), (58), (59) gives: % 56.45/8.14 | | | | | (63) ? [v0: $i] : (cons(all_91_2, nil) = v0 & app(v0, all_113_0) = % 56.45/8.14 | | | | | all_91_1 & $i(v0) & $i(all_91_1)) % 56.45/8.14 | | | | | % 56.45/8.14 | | | | | GROUND_INST: instantiating (ax82) with nil, all_113_0, nil, all_113_0, % 56.45/8.14 | | | | | nil, simplifying with (7), (16), (57), (58), (59) gives: % 56.45/8.15 | | | | | (64) ? [v0: $i] : (app(all_113_0, all_113_0) = v0 & app(nil, v0) = % 56.45/8.15 | | | | | nil & $i(v0)) % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | GROUND_INST: instantiating (8) with all_113_0, nil, simplifying with % 56.45/8.15 | | | | | (57), (58), (59) gives: % 56.45/8.15 | | | | | (65) all_113_0 = nil % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | GROUND_INST: instantiating (5) with nil, all_91_1, all_91_4, all_91_0, % 56.45/8.15 | | | | | all_91_3, simplifying with (7), (16), (29), (30), (32), % 56.45/8.15 | | | | | (33), (35), (36), (51), (60) gives: % 56.45/8.15 | | | | | (66) segmentP(nil, all_91_1) % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | GROUND_INST: instantiating (ax27) with nil, all_111_0, nil, all_91_2, % 56.45/8.15 | | | | | all_91_1, simplifying with (7), (16), (27), (34), (38), % 56.45/8.15 | | | | | (53), (54), (55) gives: % 56.45/8.15 | | | | | (67) ? [v0: $i] : (cons(all_91_2, all_111_0) = v0 & app(v0, nil) = % 56.45/8.15 | | | | | all_91_1 & $i(v0) & $i(all_91_1)) % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | GROUND_INST: instantiating (15) with all_111_0, nil, simplifying with % 56.45/8.15 | | | | | (53), (54), (55) gives: % 56.45/8.15 | | | | | (68) all_111_0 = nil % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | DELTA: instantiating (64) with fresh symbol all_141_0 gives: % 56.45/8.15 | | | | | (69) app(all_113_0, all_113_0) = all_141_0 & app(nil, all_141_0) = % 56.45/8.15 | | | | | nil & $i(all_141_0) % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | ALPHA: (69) implies: % 56.45/8.15 | | | | | (70) $i(all_141_0) % 56.45/8.15 | | | | | (71) app(all_113_0, all_113_0) = all_141_0 % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | DELTA: instantiating (67) with fresh symbol all_165_0 gives: % 56.45/8.15 | | | | | (72) cons(all_91_2, all_111_0) = all_165_0 & app(all_165_0, nil) = % 56.45/8.15 | | | | | all_91_1 & $i(all_165_0) & $i(all_91_1) % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | ALPHA: (72) implies: % 56.45/8.15 | | | | | (73) $i(all_165_0) % 56.45/8.15 | | | | | (74) cons(all_91_2, all_111_0) = all_165_0 % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | DELTA: instantiating (63) with fresh symbol all_167_0 gives: % 56.45/8.15 | | | | | (75) cons(all_91_2, nil) = all_167_0 & app(all_167_0, all_113_0) = % 56.45/8.15 | | | | | all_91_1 & $i(all_167_0) & $i(all_91_1) % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | ALPHA: (75) implies: % 56.45/8.15 | | | | | (76) cons(all_91_2, nil) = all_167_0 % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | REDUCE: (68), (74) imply: % 56.45/8.15 | | | | | (77) cons(all_91_2, nil) = all_165_0 % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | REDUCE: (65), (71) imply: % 56.45/8.15 | | | | | (78) app(nil, nil) = all_141_0 % 56.45/8.15 | | | | | % 56.45/8.15 | | | | | GROUND_INST: instantiating (14) with all_141_0, simplifying with (7), % 56.45/8.16 | | | | | (78) gives: % 56.45/8.16 | | | | | (79) all_141_0 = nil % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | GROUND_INST: instantiating (18) with all_91_1, all_167_0, nil, % 56.45/8.16 | | | | | all_91_2, simplifying with (38), (76) gives: % 56.45/8.16 | | | | | (80) all_167_0 = all_91_1 % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | GROUND_INST: instantiating (18) with all_165_0, all_167_0, nil, % 56.45/8.16 | | | | | all_91_2, simplifying with (76), (77) gives: % 56.45/8.16 | | | | | (81) all_167_0 = all_165_0 % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | COMBINE_EQS: (80), (81) imply: % 56.45/8.16 | | | | | (82) all_165_0 = all_91_1 % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | GROUND_INST: instantiating (ax54) with nil, all_91_1, simplifying with % 56.45/8.16 | | | | | (7), (16), (35), (51), (62), (66) gives: % 56.45/8.16 | | | | | (83) all_91_1 = nil % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | REDUCE: (61), (83) imply: % 56.45/8.16 | | | | | (84) singletonP(nil) % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | PRED_UNIFY: (9), (84) imply: % 56.45/8.16 | | | | | (85) $false % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | CLOSE: (85) is inconsistent. % 56.45/8.16 | | | | | % 56.45/8.16 | | | | Case 2: % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | (86) all_89_0 = all_89_1 % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | REDUCE: (20), (86) imply: % 56.45/8.16 | | | | | (87) $false % 56.45/8.16 | | | | | % 56.45/8.16 | | | | | CLOSE: (87) is inconsistent. % 56.45/8.16 | | | | | % 56.45/8.16 | | | | End of split % 56.45/8.16 | | | | % 56.45/8.16 | | | End of split % 56.45/8.16 | | | % 56.45/8.16 | | End of split % 56.45/8.16 | | % 56.45/8.16 | End of split % 56.45/8.16 | % 56.45/8.16 End of proof % 56.45/8.16 % SZS output end Proof for theBenchmark % 56.45/8.16 % 56.45/8.16 7645ms %------------------------------------------------------------------------------