%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC200+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 : n004.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 20:50:12 EDT 2023 % Result : Theorem 57.89s 8.35s % Output : Proof 86.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SWC200+1 : TPTP v8.1.2. Released v2.4.0. % 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n004.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 17:32:07 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.57/1.39 Prover 4: Preprocessing ... % 4.57/1.40 Prover 1: Preprocessing ... % 5.26/1.44 Prover 0: Preprocessing ... % 5.26/1.44 Prover 2: Preprocessing ... % 5.26/1.44 Prover 5: Preprocessing ... % 5.26/1.44 Prover 6: Preprocessing ... % 5.26/1.44 Prover 3: Preprocessing ... % 14.96/2.73 Prover 2: Proving ... % 15.38/2.83 Prover 5: Constructing countermodel ... % 15.38/2.83 Prover 1: Constructing countermodel ... % 15.38/2.84 Prover 6: Proving ... % 16.10/2.90 Prover 3: Constructing countermodel ... % 20.84/3.56 Prover 4: Constructing countermodel ... % 21.84/3.66 Prover 0: Proving ... % 57.89/8.34 Prover 3: proved (7718ms) % 57.89/8.34 % 57.89/8.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 57.89/8.35 % 57.89/8.37 Prover 6: stopped % 57.89/8.37 Prover 2: stopped % 57.89/8.37 Prover 5: stopped % 58.21/8.38 Prover 0: stopped % 58.21/8.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 58.21/8.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 58.21/8.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 58.21/8.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 58.21/8.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 60.21/8.59 Prover 13: Preprocessing ... % 60.21/8.60 Prover 10: Preprocessing ... % 60.21/8.62 Prover 7: Preprocessing ... % 60.21/8.64 Prover 11: Preprocessing ... % 60.21/8.65 Prover 8: Preprocessing ... % 61.20/8.73 Prover 10: Constructing countermodel ... % 61.20/8.78 Prover 7: Constructing countermodel ... % 61.97/8.89 Prover 13: Constructing countermodel ... % 63.87/9.07 Prover 8: Warning: ignoring some quantifiers % 64.04/9.09 Prover 8: Constructing countermodel ... % 68.45/9.76 Prover 11: Constructing countermodel ... % 86.33/12.01 Prover 10: Found proof (size 53) % 86.33/12.01 Prover 10: proved (3623ms) % 86.33/12.01 Prover 8: stopped % 86.33/12.01 Prover 1: stopped % 86.33/12.01 Prover 7: stopped % 86.33/12.01 Prover 11: stopped % 86.33/12.01 Prover 4: stopped % 86.33/12.01 Prover 13: stopped % 86.33/12.01 % 86.33/12.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 86.33/12.01 % 86.33/12.02 % SZS output start Proof for theBenchmark % 86.33/12.02 Assumptions after simplification: % 86.33/12.02 --------------------------------- % 86.33/12.02 % 86.33/12.02 (ax1) % 86.33/12.03 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) | % 86.33/12.03 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) | % 86.33/12.03 ~ ssItem(v0)) % 86.33/12.03 % 86.33/12.03 (ax17) % 86.33/12.03 $i(nil) & ssList(nil) % 86.33/12.03 % 86.33/12.03 (ax2) % 86.33/12.03 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) & % 86.33/12.03 ssItem(v0)) % 86.33/12.03 % 86.33/12.03 (ax28) % 86.75/12.05 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 86.75/12.05 $i(v0) | ~ ssList(v0)) % 86.75/12.05 % 86.75/12.05 (ax37) % 86.75/12.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 86.75/12.05 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v3, v0) % 86.75/12.05 | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0: % 86.75/12.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, v2) = v3) | ~ % 86.75/12.05 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ % 86.75/12.05 ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0: $i] : ! [v1: $i] : % 86.75/12.05 ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 86.75/12.05 ~ ssItem(v0) | memberP(v2, v0)) % 86.75/12.06 % 86.75/12.06 (ax38) % 86.75/12.06 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ memberP(nil, v0) | ~ ssItem(v0)) % 86.75/12.06 % 86.75/12.06 (ax4) % 86.75/12.06 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | % 86.75/12.06 ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0: $i] : ( % 86.75/12.06 ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1: $i] : (cons(v1, nil) % 86.75/12.06 = v0 & $i(v1) & ssItem(v1))) % 86.75/12.06 % 86.75/12.06 (ax46) % 86.75/12.06 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 86.75/12.06 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 86.75/12.06 % 86.75/12.06 (ax5) % 86.75/12.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 86.75/12.06 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 86.75/12.06 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 86.75/12.06 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 86.75/12.06 v2) = v0 & $i(v2) & ssList(v2))) % 86.75/12.06 % 86.75/12.06 (ax58) % 86.75/12.06 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 86.75/12.06 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 86.75/12.06 % 86.75/12.06 (ax82) % 86.75/12.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 86.75/12.06 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 86.75/12.06 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 86.75/12.06 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 86.75/12.06 % 86.75/12.06 (ax83) % 86.75/12.06 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 86.75/12.06 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 86.75/12.06 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 86.75/12.06 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 86.75/12.06 v0) | ~ ssList(nil)) % 86.75/12.06 % 86.75/12.06 (ax86) % 86.75/12.07 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = nil | % 86.75/12.07 ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 86.75/12.07 ssList(v2) | ~ ssList(v0) | ? [v4: $i] : (tl(v4) = v3 & app(v0, v2) = v4 & % 86.75/12.07 $i(v4) & $i(v3))) % 86.75/12.07 % 86.75/12.07 (co1) % 86.75/12.07 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & singletonP(v0) & ssList(v1) & % 86.75/12.07 ssList(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ ssItem(v2) | ? [v3: $i] : ( ~ % 86.75/12.07 (v3 = v2) & $i(v3) & memberP(v0, v3) & ssItem(v3)))) % 86.75/12.07 % 86.75/12.07 Further assumptions not needed in the proof: % 86.75/12.07 -------------------------------------------- % 86.75/12.07 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax20, ax21, ax22, ax23, % 86.75/12.07 ax24, ax25, ax26, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 86.75/12.07 ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax47, ax48, ax49, ax50, ax51, ax52, % 86.75/12.07 ax53, ax54, ax55, ax56, ax57, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, % 86.75/12.07 ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, % 86.75/12.07 ax78, ax79, ax8, ax80, ax81, ax84, ax85, ax87, ax88, ax89, ax9, ax90, ax91, % 86.75/12.07 ax92, ax93, ax94, ax95 % 86.75/12.07 % 86.75/12.07 Those formulas are unsatisfiable: % 86.75/12.07 --------------------------------- % 86.75/12.07 % 86.75/12.07 Begin of proof % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax1) implies: % 86.75/12.07 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 86.75/12.07 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax4) implies: % 86.75/12.07 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1: % 86.75/12.07 | $i] : (cons(v1, nil) = v0 & $i(v1) & ssItem(v1))) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax5) implies: % 86.75/12.07 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 86.75/12.07 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 86.75/12.07 | v0 & $i(v2) & ssList(v2))) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax17) implies: % 86.75/12.07 | (4) ssList(nil) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax28) implies: % 86.75/12.07 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 86.75/12.07 | $i(v0) | ~ ssList(v0)) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax37) implies: % 86.75/12.07 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 86.75/12.07 | (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 86.75/12.07 | memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | % 86.75/12.07 | memberP(v2, v0)) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax38) implies: % 86.75/12.07 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ memberP(nil, v0) | ~ ssItem(v0)) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax46) implies: % 86.75/12.07 | (8) ~ ssList(nil) | frontsegP(nil, nil) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax58) implies: % 86.75/12.07 | (9) ~ ssList(nil) | segmentP(nil, nil) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax83) implies: % 86.75/12.07 | (10) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 86.75/12.07 | % 86.75/12.07 | ALPHA: (ax86) implies: % 86.75/12.07 | (11) $i(nil) % 86.75/12.07 | % 86.75/12.07 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives: % 86.75/12.08 | (12) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) & % 86.75/12.08 | ssItem(all_89_0) & ssItem(all_89_1) % 86.75/12.08 | % 86.75/12.08 | ALPHA: (12) implies: % 86.75/12.08 | (13) ~ (all_89_0 = all_89_1) % 86.75/12.08 | (14) ssItem(all_89_1) % 86.75/12.08 | (15) ssItem(all_89_0) % 86.75/12.08 | (16) $i(all_89_1) % 86.75/12.08 | (17) $i(all_89_0) % 86.75/12.08 | % 86.75/12.08 | DELTA: instantiating (co1) with fresh symbols all_91_0, all_91_1 gives: % 86.75/12.08 | (18) $i(all_91_0) & $i(all_91_1) & singletonP(all_91_1) & ssList(all_91_0) % 86.75/12.08 | & ssList(all_91_1) & ! [v0: $i] : ( ~ $i(v0) | ~ ssItem(v0) | ? % 86.75/12.08 | [v1: $i] : ( ~ (v1 = v0) & $i(v1) & memberP(all_91_1, v1) & % 86.75/12.08 | ssItem(v1))) % 86.75/12.08 | % 86.75/12.08 | ALPHA: (18) implies: % 86.75/12.08 | (19) ssList(all_91_1) % 86.75/12.08 | (20) singletonP(all_91_1) % 86.75/12.08 | (21) $i(all_91_1) % 86.75/12.08 | (22) ! [v0: $i] : ( ~ $i(v0) | ~ ssItem(v0) | ? [v1: $i] : ( ~ (v1 = v0) % 86.75/12.08 | & $i(v1) & memberP(all_91_1, v1) & ssItem(v1))) % 86.75/12.08 | % 86.75/12.08 | BETA: splitting (8) gives: % 86.75/12.08 | % 86.75/12.08 | Case 1: % 86.75/12.08 | | % 86.75/12.08 | | (23) ~ ssList(nil) % 86.75/12.08 | | % 86.75/12.08 | | PRED_UNIFY: (4), (23) imply: % 86.75/12.08 | | (24) $false % 86.75/12.08 | | % 86.75/12.08 | | CLOSE: (24) is inconsistent. % 86.75/12.08 | | % 86.75/12.08 | Case 2: % 86.75/12.08 | | % 86.75/12.08 | | (25) frontsegP(nil, nil) % 86.75/12.08 | | % 86.75/12.08 | | BETA: splitting (9) gives: % 86.75/12.08 | | % 86.75/12.08 | | Case 1: % 86.75/12.08 | | | % 86.75/12.08 | | | (26) ~ ssList(nil) % 86.75/12.08 | | | % 86.75/12.08 | | | PRED_UNIFY: (4), (26) imply: % 86.75/12.08 | | | (27) $false % 86.75/12.08 | | | % 86.75/12.08 | | | CLOSE: (27) is inconsistent. % 86.75/12.08 | | | % 86.75/12.08 | | Case 2: % 86.75/12.08 | | | % 86.75/12.08 | | | % 86.75/12.08 | | | GROUND_INST: instantiating (1) with all_89_0, all_89_1, simplifying with % 86.75/12.08 | | | (14), (15), (16), (17) gives: % 86.75/12.08 | | | (28) all_89_0 = all_89_1 | neq(all_89_0, all_89_1) % 86.75/12.08 | | | % 86.75/12.08 | | | GROUND_INST: instantiating (2) with all_91_1, simplifying with (19), (20), % 86.75/12.08 | | | (21) gives: % 86.75/12.08 | | | (29) ? [v0: $i] : (cons(v0, nil) = all_91_1 & $i(v0) & ssItem(v0)) % 86.75/12.08 | | | % 86.75/12.08 | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (4), (11), % 86.75/12.08 | | | (25) gives: % 86.75/12.08 | | | (30) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 86.75/12.08 | | | % 86.75/12.08 | | | DELTA: instantiating (30) with fresh symbol all_112_0 gives: % 86.75/12.08 | | | (31) app(nil, all_112_0) = nil & $i(all_112_0) & ssList(all_112_0) % 86.75/12.08 | | | % 86.75/12.08 | | | ALPHA: (31) implies: % 86.75/12.08 | | | (32) ssList(all_112_0) % 86.75/12.08 | | | (33) $i(all_112_0) % 86.75/12.08 | | | (34) app(nil, all_112_0) = nil % 86.75/12.08 | | | % 86.75/12.08 | | | DELTA: instantiating (29) with fresh symbol all_114_0 gives: % 86.75/12.08 | | | (35) cons(all_114_0, nil) = all_91_1 & $i(all_114_0) & % 86.75/12.08 | | | ssItem(all_114_0) % 86.75/12.08 | | | % 86.75/12.08 | | | ALPHA: (35) implies: % 86.75/12.08 | | | (36) ssItem(all_114_0) % 86.75/12.09 | | | (37) $i(all_114_0) % 86.75/12.09 | | | (38) cons(all_114_0, nil) = all_91_1 % 86.75/12.09 | | | % 86.75/12.09 | | | BETA: splitting (28) gives: % 86.75/12.09 | | | % 86.75/12.09 | | | Case 1: % 86.75/12.09 | | | | % 86.75/12.09 | | | | % 86.75/12.09 | | | | GROUND_INST: instantiating (22) with all_114_0, simplifying with (36), % 86.75/12.09 | | | | (37) gives: % 86.75/12.09 | | | | (39) ? [v0: any] : ( ~ (v0 = all_114_0) & $i(v0) & memberP(all_91_1, % 86.75/12.09 | | | | v0) & ssItem(v0)) % 86.75/12.09 | | | | % 86.75/12.09 | | | | GROUND_INST: instantiating (ax82) with nil, all_112_0, nil, all_112_0, % 86.75/12.09 | | | | nil, simplifying with (4), (11), (32), (33), (34) gives: % 86.75/12.09 | | | | (40) ? [v0: $i] : (app(all_112_0, all_112_0) = v0 & app(nil, v0) = % 86.75/12.09 | | | | nil & $i(v0)) % 86.75/12.09 | | | | % 86.75/12.09 | | | | GROUND_INST: instantiating (5) with all_112_0, nil, simplifying with % 86.75/12.09 | | | | (32), (33), (34) gives: % 86.75/12.09 | | | | (41) all_112_0 = nil % 86.75/12.09 | | | | % 86.75/12.09 | | | | DELTA: instantiating (40) with fresh symbol all_148_0 gives: % 86.75/12.09 | | | | (42) app(all_112_0, all_112_0) = all_148_0 & app(nil, all_148_0) = % 86.75/12.09 | | | | nil & $i(all_148_0) % 86.75/12.09 | | | | % 86.75/12.09 | | | | ALPHA: (42) implies: % 86.75/12.09 | | | | (43) $i(all_148_0) % 86.75/12.09 | | | | (44) app(all_112_0, all_112_0) = all_148_0 % 86.75/12.09 | | | | % 86.75/12.09 | | | | DELTA: instantiating (39) with fresh symbol all_162_0 gives: % 86.75/12.09 | | | | (45) ~ (all_162_0 = all_114_0) & $i(all_162_0) & memberP(all_91_1, % 86.75/12.09 | | | | all_162_0) & ssItem(all_162_0) % 86.75/12.09 | | | | % 86.75/12.09 | | | | ALPHA: (45) implies: % 86.75/12.09 | | | | (46) ~ (all_162_0 = all_114_0) % 86.75/12.09 | | | | (47) ssItem(all_162_0) % 86.75/12.09 | | | | (48) memberP(all_91_1, all_162_0) % 86.75/12.09 | | | | (49) $i(all_162_0) % 86.75/12.09 | | | | % 86.75/12.09 | | | | REDUCE: (41), (44) imply: % 86.75/12.09 | | | | (50) app(nil, nil) = all_148_0 % 86.75/12.09 | | | | % 86.75/12.09 | | | | GROUND_INST: instantiating (10) with all_148_0, simplifying with (4), % 86.75/12.09 | | | | (50) gives: % 86.75/12.09 | | | | (51) all_148_0 = nil % 86.75/12.09 | | | | % 86.75/12.09 | | | | GROUND_INST: instantiating (6) with all_162_0, all_114_0, nil, all_91_1, % 86.75/12.09 | | | | simplifying with (4), (11), (36), (37), (38), (47), (48), % 86.75/12.09 | | | | (49) gives: % 86.75/12.09 | | | | (52) all_162_0 = all_114_0 | memberP(nil, all_162_0) % 86.75/12.09 | | | | % 86.75/12.09 | | | | BETA: splitting (52) gives: % 86.75/12.09 | | | | % 86.75/12.09 | | | | Case 1: % 86.75/12.09 | | | | | % 86.75/12.09 | | | | | (53) memberP(nil, all_162_0) % 86.75/12.09 | | | | | % 86.75/12.09 | | | | | GROUND_INST: instantiating (7) with all_162_0, simplifying with (47), % 86.75/12.09 | | | | | (49), (53) gives: % 86.75/12.09 | | | | | (54) $false % 86.75/12.09 | | | | | % 86.75/12.09 | | | | | CLOSE: (54) is inconsistent. % 86.75/12.09 | | | | | % 86.75/12.09 | | | | Case 2: % 86.75/12.09 | | | | | % 86.75/12.09 | | | | | (55) all_162_0 = all_114_0 % 86.75/12.09 | | | | | % 86.75/12.09 | | | | | REDUCE: (46), (55) imply: % 86.75/12.09 | | | | | (56) $false % 86.75/12.09 | | | | | % 86.75/12.09 | | | | | CLOSE: (56) is inconsistent. % 86.75/12.09 | | | | | % 86.75/12.09 | | | | End of split % 86.75/12.09 | | | | % 86.75/12.09 | | | Case 2: % 86.75/12.09 | | | | % 86.75/12.09 | | | | (57) all_89_0 = all_89_1 % 86.75/12.09 | | | | % 86.75/12.09 | | | | REDUCE: (13), (57) imply: % 86.75/12.09 | | | | (58) $false % 86.75/12.09 | | | | % 86.75/12.09 | | | | CLOSE: (58) is inconsistent. % 86.75/12.09 | | | | % 86.75/12.09 | | | End of split % 86.75/12.09 | | | % 86.75/12.09 | | End of split % 86.75/12.09 | | % 86.75/12.09 | End of split % 86.75/12.09 | % 86.75/12.09 End of proof % 86.75/12.09 % SZS output end Proof for theBenchmark % 86.75/12.09 % 86.75/12.09 11494ms %------------------------------------------------------------------------------