%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC380+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 : n006.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 20:51:08 EDT 2023 % Result : Theorem 39.92s 6.14s % Output : Proof 75.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWC380+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n006.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Mon Aug 28 15:03:06 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.65 Running up to 7 provers in parallel. % 0.62/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.62/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.62/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.62/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.62/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.62/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.62/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.36/1.63 Prover 1: Preprocessing ... % 6.36/1.63 Prover 4: Preprocessing ... % 6.72/1.68 Prover 0: Preprocessing ... % 6.72/1.68 Prover 2: Preprocessing ... % 6.72/1.68 Prover 6: Preprocessing ... % 6.72/1.68 Prover 3: Preprocessing ... % 6.72/1.68 Prover 5: Preprocessing ... % 22.29/3.78 Prover 2: Proving ... % 22.29/3.78 Prover 1: Constructing countermodel ... % 22.29/3.78 Prover 3: Constructing countermodel ... % 22.29/3.79 Prover 5: Constructing countermodel ... % 22.29/3.79 Prover 6: Proving ... % 31.13/4.97 Prover 4: Constructing countermodel ... % 32.30/5.15 Prover 0: Proving ... % 39.92/6.13 Prover 3: proved (5467ms) % 39.92/6.14 % 39.92/6.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 39.92/6.14 % 39.92/6.14 Prover 5: stopped % 39.92/6.15 Prover 2: stopped % 40.53/6.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 40.53/6.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 40.53/6.17 Prover 6: stopped % 40.53/6.17 Prover 0: stopped % 40.53/6.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 40.53/6.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 40.64/6.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 42.91/6.52 Prover 8: Preprocessing ... % 42.91/6.59 Prover 10: Preprocessing ... % 43.93/6.64 Prover 7: Preprocessing ... % 43.93/6.65 Prover 11: Preprocessing ... % 44.59/6.75 Prover 13: Preprocessing ... % 46.91/7.04 Prover 7: Constructing countermodel ... % 46.91/7.06 Prover 10: Constructing countermodel ... % 47.53/7.10 Prover 8: Warning: ignoring some quantifiers % 47.53/7.12 Prover 8: Constructing countermodel ... % 49.23/7.35 Prover 13: Constructing countermodel ... % 58.62/8.66 Prover 11: Constructing countermodel ... % 74.98/10.67 Prover 10: Found proof (size 35) % 74.98/10.67 Prover 10: proved (4499ms) % 74.98/10.67 Prover 13: stopped % 74.98/10.67 Prover 7: stopped % 74.98/10.67 Prover 8: stopped % 74.98/10.67 Prover 11: stopped % 74.98/10.67 Prover 1: stopped % 74.98/10.67 Prover 4: stopped % 74.98/10.67 % 74.98/10.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 74.98/10.67 % 74.98/10.68 % SZS output start Proof for theBenchmark % 74.98/10.68 Assumptions after simplification: % 74.98/10.68 --------------------------------- % 74.98/10.68 % 74.98/10.68 (ax1) % 74.98/10.69 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) | % 74.98/10.69 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) | % 74.98/10.69 ~ ssItem(v0)) % 74.98/10.69 % 74.98/10.69 (ax17) % 74.98/10.70 $i(nil) & ssList(nil) % 74.98/10.70 % 74.98/10.70 (ax2) % 74.98/10.70 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) & % 74.98/10.70 ssItem(v0)) % 74.98/10.70 % 74.98/10.70 (ax23) % 75.25/10.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1) % 75.25/10.74 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) % 75.25/10.74 % 75.25/10.74 (ax25) % 75.25/10.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1) % 75.25/10.74 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) % 75.25/10.74 % 75.25/10.74 (ax37) % 75.25/10.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.25/10.74 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v3, v0) % 75.25/10.74 | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0: % 75.25/10.74 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, v2) = v3) | ~ % 75.25/10.74 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ % 75.25/10.74 ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0: $i] : ! [v1: $i] : % 75.25/10.74 ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 75.25/10.74 ~ ssItem(v0) | memberP(v2, v0)) % 75.25/10.74 % 75.25/10.74 (ax58) % 75.25/10.75 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 75.25/10.75 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 75.25/10.75 % 75.25/10.75 (ax77) % 75.43/10.75 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~ % 75.43/10.75 ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3 = v0 | % 75.43/10.75 v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~ ssList(v3) | ? % 75.43/10.75 [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 & $i(v4))))) % 75.43/10.75 % 75.43/10.75 (ax81) % 75.43/10.75 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 75.43/10.75 (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 75.43/10.75 ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3))) % 75.43/10.75 % 75.43/10.75 (co1) % 75.43/10.76 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2, % 75.43/10.76 nil) = v0 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 75.43/10.76 ssList(v3) & ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v4: % 75.43/10.76 $i] : ( ~ (cons(v4, nil) = v0) | ~ $i(v4) | ~ memberP(v1, v4) | ~ % 75.43/10.76 ssItem(v4))) % 75.43/10.76 % 75.43/10.76 (function-axioms) % 75.43/10.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.43/10.76 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 75.43/10.76 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 75.43/10.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 75.43/10.76 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 75.43/10.76 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 75.43/10.76 % 75.43/10.76 Further assumptions not needed in the proof: % 75.43/10.76 -------------------------------------------- % 75.43/10.76 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax20, ax21, ax22, ax24, % 75.43/10.76 ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax38, % 75.43/10.76 ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, % 75.43/10.76 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6, ax60, ax61, ax62, % 75.43/10.76 ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73, ax74, % 75.43/10.76 ax75, ax76, ax78, ax79, ax8, ax80, ax82, ax83, ax84, ax85, ax86, ax87, ax88, % 75.43/10.76 ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 75.43/10.76 % 75.43/10.76 Those formulas are unsatisfiable: % 75.43/10.76 --------------------------------- % 75.43/10.76 % 75.43/10.76 Begin of proof % 75.43/10.76 | % 75.43/10.76 | ALPHA: (ax1) implies: % 75.43/10.77 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 75.43/10.77 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 75.43/10.77 | % 75.43/10.77 | ALPHA: (ax17) implies: % 75.43/10.77 | (2) ssList(nil) % 75.43/10.77 | % 75.43/10.77 | ALPHA: (ax37) implies: % 75.43/10.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~ % 75.43/10.77 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 75.43/10.77 | % 75.43/10.77 | ALPHA: (ax58) implies: % 75.43/10.77 | (4) ~ ssList(nil) | segmentP(nil, nil) % 75.43/10.77 | % 75.43/10.77 | ALPHA: (ax77) implies: % 75.43/10.77 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~ % 75.43/10.77 | ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3 % 75.43/10.77 | = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~ % 75.43/10.77 | ssList(v3) | ? [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 & % 75.43/10.77 | $i(v4))))) % 75.43/10.77 | % 75.43/10.77 | ALPHA: (ax81) implies: % 75.43/10.77 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, % 75.43/10.77 | nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 75.43/10.77 | ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3))) % 75.43/10.77 | % 75.43/10.77 | ALPHA: (co1) implies: % 75.43/10.78 | (7) $i(nil) % 75.43/10.78 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) % 75.43/10.78 | = v0 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 75.43/10.78 | ssList(v3) & ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! % 75.43/10.78 | [v4: $i] : ( ~ (cons(v4, nil) = v0) | ~ $i(v4) | ~ memberP(v1, v4) % 75.43/10.78 | | ~ ssItem(v4))) % 75.43/10.78 | % 75.43/10.78 | ALPHA: (function-axioms) implies: % 75.43/10.78 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (hd(v2) = v1) | % 75.43/10.78 | ~ (hd(v2) = v0)) % 75.43/10.78 | % 75.43/10.78 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives: % 75.43/10.78 | (10) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) & % 75.43/10.78 | ssItem(all_89_0) & ssItem(all_89_1) % 75.43/10.78 | % 75.43/10.78 | ALPHA: (10) implies: % 75.43/10.78 | (11) ~ (all_89_0 = all_89_1) % 75.43/10.78 | (12) ssItem(all_89_1) % 75.43/10.78 | (13) ssItem(all_89_0) % 75.43/10.78 | (14) $i(all_89_1) % 75.43/10.78 | (15) $i(all_89_0) % 75.43/10.78 | % 75.43/10.78 | DELTA: instantiating (8) with fresh symbols all_91_0, all_91_1, all_91_2, % 75.43/10.78 | all_91_3 gives: % 75.43/10.79 | (16) cons(all_91_1, nil) = all_91_3 & app(all_91_3, all_91_0) = all_91_2 & % 75.43/10.79 | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & % 75.43/10.79 | ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_3) & neq(all_91_2, % 75.43/10.79 | nil) & ssItem(all_91_1) & ! [v0: $i] : ( ~ (cons(v0, nil) = % 75.43/10.79 | all_91_3) | ~ $i(v0) | ~ memberP(all_91_2, v0) | ~ ssItem(v0)) % 75.43/10.79 | % 75.43/10.79 | ALPHA: (16) implies: % 75.43/10.79 | (17) ssItem(all_91_1) % 75.43/10.79 | (18) ssList(all_91_3) % 75.43/10.79 | (19) ssList(all_91_0) % 75.43/10.79 | (20) $i(all_91_3) % 75.43/10.79 | (21) $i(all_91_1) % 75.43/10.79 | (22) $i(all_91_0) % 75.43/10.79 | (23) app(all_91_3, all_91_0) = all_91_2 % 75.43/10.79 | (24) cons(all_91_1, nil) = all_91_3 % 75.43/10.79 | (25) ! [v0: $i] : ( ~ (cons(v0, nil) = all_91_3) | ~ $i(v0) | ~ % 75.43/10.79 | memberP(all_91_2, v0) | ~ ssItem(v0)) % 75.43/10.79 | % 75.43/10.79 | BETA: splitting (4) gives: % 75.43/10.79 | % 75.43/10.79 | Case 1: % 75.43/10.79 | | % 75.43/10.79 | | (26) ~ ssList(nil) % 75.43/10.79 | | % 75.43/10.79 | | PRED_UNIFY: (2), (26) imply: % 75.43/10.79 | | (27) $false % 75.43/10.79 | | % 75.43/10.79 | | CLOSE: (27) is inconsistent. % 75.43/10.79 | | % 75.43/10.79 | Case 2: % 75.43/10.79 | | % 75.43/10.79 | | % 75.43/10.79 | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with % 75.43/10.79 | | (12), (13), (14), (15) gives: % 75.43/10.79 | | (28) all_89_0 = all_89_1 | neq(all_89_1, all_89_0) % 75.43/10.79 | | % 75.43/10.80 | | GROUND_INST: instantiating (ax25) with nil, all_91_1, all_91_3, simplifying % 75.43/10.80 | | with (2), (7), (17), (21), (24) gives: % 75.43/10.80 | | (29) tl(all_91_3) = nil % 75.43/10.80 | | % 75.43/10.80 | | GROUND_INST: instantiating (ax23) with nil, all_91_1, all_91_3, simplifying % 75.43/10.80 | | with (2), (7), (17), (21), (24) gives: % 75.43/10.80 | | (30) hd(all_91_3) = all_91_1 % 75.43/10.80 | | % 75.43/10.80 | | GROUND_INST: instantiating (6) with all_91_0, all_91_1, all_91_3, all_91_2, % 75.43/10.80 | | simplifying with (17), (19), (21), (22), (23), (24) gives: % 75.43/10.80 | | (31) cons(all_91_1, all_91_0) = all_91_2 & $i(all_91_2) % 75.43/10.80 | | % 75.43/10.80 | | ALPHA: (31) implies: % 75.43/10.80 | | (32) cons(all_91_1, all_91_0) = all_91_2 % 75.43/10.80 | | % 75.43/10.80 | | BETA: splitting (28) gives: % 75.43/10.80 | | % 75.43/10.80 | | Case 1: % 75.43/10.80 | | | % 75.43/10.80 | | | % 75.43/10.80 | | | GROUND_INST: instantiating (3) with all_91_1, all_91_0, all_91_2, % 75.43/10.80 | | | simplifying with (17), (19), (21), (22), (32) gives: % 75.43/10.80 | | | (33) memberP(all_91_2, all_91_1) % 75.43/10.80 | | | % 75.43/10.80 | | | GROUND_INST: instantiating (5) with all_91_3, nil, simplifying with (18), % 75.43/10.80 | | | (20), (29) gives: % 75.43/10.80 | | | (34) ? [v0: $i] : (hd(all_91_3) = v0 & $i(v0) & ! [v1: any] : (v1 = % 75.43/10.80 | | | all_91_3 | v1 = nil | all_91_3 = nil | ~ (tl(v1) = nil) | ~ % 75.43/10.80 | | | $i(v1) | ~ ssList(v1) | ? [v2: $i] : ( ~ (v2 = v0) & hd(v1) % 75.43/10.80 | | | = v2 & $i(v2)))) % 75.43/10.80 | | | % 75.43/10.80 | | | DELTA: instantiating (34) with fresh symbol all_180_0 gives: % 75.43/10.81 | | | (35) hd(all_91_3) = all_180_0 & $i(all_180_0) & ! [v0: any] : (v0 = % 75.43/10.81 | | | all_91_3 | v0 = nil | all_91_3 = nil | ~ (tl(v0) = nil) | ~ % 75.43/10.81 | | | $i(v0) | ~ ssList(v0) | ? [v1: any] : ( ~ (v1 = all_180_0) & % 75.43/10.81 | | | hd(v0) = v1 & $i(v1))) % 75.43/10.81 | | | % 75.43/10.81 | | | ALPHA: (35) implies: % 75.43/10.81 | | | (36) $i(all_180_0) % 75.43/10.81 | | | (37) hd(all_91_3) = all_180_0 % 75.43/10.81 | | | % 75.43/10.81 | | | GROUND_INST: instantiating (9) with all_91_1, all_180_0, all_91_3, % 75.43/10.81 | | | simplifying with (30), (37) gives: % 75.43/10.81 | | | (38) all_180_0 = all_91_1 % 75.43/10.81 | | | % 75.43/10.81 | | | GROUND_INST: instantiating (25) with all_91_1, simplifying with (17), % 75.43/10.81 | | | (21), (24), (33) gives: % 75.43/10.81 | | | (39) $false % 75.43/10.81 | | | % 75.43/10.81 | | | CLOSE: (39) is inconsistent. % 75.43/10.81 | | | % 75.43/10.81 | | Case 2: % 75.43/10.81 | | | % 75.43/10.81 | | | (40) all_89_0 = all_89_1 % 75.43/10.81 | | | % 75.43/10.81 | | | REDUCE: (11), (40) imply: % 75.43/10.81 | | | (41) $false % 75.43/10.81 | | | % 75.43/10.81 | | | CLOSE: (41) is inconsistent. % 75.43/10.81 | | | % 75.43/10.81 | | End of split % 75.43/10.81 | | % 75.43/10.81 | End of split % 75.43/10.81 | % 75.43/10.81 End of proof % 75.43/10.81 % SZS output end Proof for theBenchmark % 75.43/10.81 % 75.43/10.81 10177ms %------------------------------------------------------------------------------