%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC153+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 : n008.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 20:49:57 EDT 2023 % Result : Theorem 40.46s 6.25s % Output : Proof 53.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWC153+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n008.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 16:51:02 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.67/1.47 Prover 4: Preprocessing ... % 5.03/1.48 Prover 1: Preprocessing ... % 5.03/1.50 Prover 0: Preprocessing ... % 5.03/1.50 Prover 6: Preprocessing ... % 5.03/1.50 Prover 2: Preprocessing ... % 5.03/1.50 Prover 5: Preprocessing ... % 5.03/1.50 Prover 3: Preprocessing ... % 16.98/3.02 Prover 5: Constructing countermodel ... % 16.98/3.03 Prover 1: Constructing countermodel ... % 17.31/3.10 Prover 6: Proving ... % 18.00/3.14 Prover 3: Constructing countermodel ... % 18.38/3.23 Prover 2: Proving ... % 29.60/4.86 Prover 4: Constructing countermodel ... % 32.03/5.06 Prover 0: Proving ... % 40.46/6.25 Prover 3: proved (5606ms) % 40.46/6.25 % 40.46/6.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 40.46/6.25 % 40.46/6.25 Prover 5: stopped % 40.46/6.25 Prover 2: stopped % 40.46/6.26 Prover 0: stopped % 40.46/6.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 40.46/6.26 Prover 6: stopped % 40.46/6.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 40.46/6.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 40.46/6.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 40.46/6.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 42.30/6.43 Prover 7: Preprocessing ... % 42.30/6.50 Prover 10: Preprocessing ... % 43.05/6.53 Prover 8: Preprocessing ... % 43.05/6.53 Prover 11: Preprocessing ... % 43.05/6.56 Prover 13: Preprocessing ... % 43.77/6.63 Prover 7: Constructing countermodel ... % 43.77/6.66 Prover 10: Constructing countermodel ... % 45.42/6.84 Prover 8: Warning: ignoring some quantifiers % 45.42/6.86 Prover 8: Constructing countermodel ... % 46.10/6.92 Prover 13: Constructing countermodel ... % 48.40/7.23 Prover 10: Found proof (size 27) % 48.40/7.23 Prover 10: proved (969ms) % 48.40/7.23 Prover 4: stopped % 48.40/7.23 Prover 7: stopped % 48.40/7.23 Prover 8: stopped % 48.40/7.23 Prover 13: stopped % 48.40/7.23 Prover 1: stopped % 52.33/8.18 Prover 11: Constructing countermodel ... % 52.49/8.20 Prover 11: stopped % 52.49/8.21 % 52.49/8.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 52.49/8.21 % 52.49/8.22 % SZS output start Proof for theBenchmark % 52.49/8.23 Assumptions after simplification: % 52.49/8.23 --------------------------------- % 52.49/8.23 % 52.49/8.23 (ax1) % 52.66/8.24 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) | % 52.66/8.24 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) | % 52.66/8.24 ~ ssItem(v0)) % 52.66/8.24 % 52.66/8.24 (ax2) % 52.66/8.24 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) & % 52.66/8.24 ssItem(v0)) % 52.66/8.24 % 52.66/8.24 (ax29) % 52.66/8.24 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) % 52.66/8.24 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 52.70/8.24 % 52.70/8.24 (co1) % 52.70/8.30 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 52.70/8.30 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 52.70/8.30 [v10: $i] : ? [v11: $i] : ? [v12: $i] : (cons(v4, nil) = v5 & cons(v2, nil) % 52.70/8.30 = v3 & app(v10, v11) = v0 & app(v9, v5) = v10 & app(v7, v8) = v9 & app(v6, % 52.70/8.30 v3) = v7 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) % 52.70/8.30 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(v4, v2) & % 52.70/8.30 ssList(v11) & ssList(v8) & ssList(v6) & ssList(v1) & ssList(v0) & ssItem(v4) % 52.70/8.30 & ssItem(v2) & ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : % 52.70/8.30 ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! % 52.70/8.30 [v22: $i] : ! [v23: $i] : ( ~ (cons(v15, nil) = v16) | ~ (cons(v13, nil) = % 52.70/8.30 v14) | ~ (app(v21, v22) = v0) | ~ (app(v20, v16) = v21) | ~ (app(v18, % 52.70/8.30 v19) = v20) | ~ (app(v17, v14) = v18) | ~ $i(v23) | ~ $i(v22) | ~ % 52.70/8.30 $i(v19) | ~ $i(v17) | ~ $i(v15) | ~ $i(v13) | ~ leq(v15, v13) | ~ % 52.70/8.30 memberP(v19, v23) | ~ ssList(v22) | ~ ssList(v19) | ~ ssList(v17) | ~ % 52.70/8.30 ssItem(v23) | ~ ssItem(v15) | ~ ssItem(v13) | leq(v23, v15)) & ! [v13: % 52.70/8.30 $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: % 52.70/8.30 $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: % 52.70/8.30 $i] : ( ~ (cons(v15, nil) = v16) | ~ (cons(v13, nil) = v14) | ~ % 52.70/8.30 (app(v21, v22) = v0) | ~ (app(v20, v16) = v21) | ~ (app(v18, v19) = v20) % 52.70/8.30 | ~ (app(v17, v14) = v18) | ~ $i(v23) | ~ $i(v22) | ~ $i(v19) | ~ % 52.70/8.30 $i(v17) | ~ $i(v15) | ~ $i(v13) | ~ leq(v15, v13) | ~ memberP(v19, % 52.70/8.30 v23) | ~ ssList(v22) | ~ ssList(v19) | ~ ssList(v17) | ~ ssItem(v23) % 52.70/8.30 | ~ ssItem(v15) | ~ ssItem(v13) | leq(v13, v23)) & ! [v13: $i] : ! % 52.70/8.30 [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! % 52.70/8.30 [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ (cons(v15, nil) % 52.70/8.30 = v16) | ~ (cons(v13, nil) = v14) | ~ (app(v21, v22) = v0) | ~ % 52.70/8.30 (app(v20, v16) = v21) | ~ (app(v18, v19) = v20) | ~ (app(v17, v14) = % 52.70/8.30 v18) | ~ $i(v22) | ~ $i(v19) | ~ $i(v17) | ~ $i(v15) | ~ $i(v13) | % 52.70/8.30 ~ leq(v15, v13) | ~ ssList(v22) | ~ ssList(v19) | ~ ssList(v17) | ~ % 52.70/8.30 ssItem(v15) | ~ ssItem(v13) | leq(v13, v15)) & ( ~ leq(v2, v4) | % 52.70/8.30 (memberP(v8, v12) & ssItem(v12) & ( ~ leq(v12, v4) | ~ leq(v2, v12))))) % 52.70/8.30 % 52.70/8.30 Further assumptions not needed in the proof: % 52.70/8.30 -------------------------------------------- % 52.70/8.31 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22, % 52.70/8.31 ax23, ax24, ax25, ax26, ax27, ax28, ax3, ax30, ax31, ax32, ax33, ax34, ax35, % 52.70/8.31 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, % 52.70/8.31 ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, % 52.70/8.31 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, % 52.70/8.31 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, % 52.70/8.31 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, % 52.70/8.31 ax95 % 52.70/8.31 % 52.70/8.31 Those formulas are unsatisfiable: % 52.70/8.31 --------------------------------- % 52.70/8.31 % 52.70/8.31 Begin of proof % 53.00/8.31 | % 53.00/8.31 | ALPHA: (ax1) implies: % 53.00/8.31 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 53.00/8.31 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 53.00/8.31 | % 53.00/8.31 | ALPHA: (co1) implies: % 53.00/8.32 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 53.00/8.32 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 53.00/8.32 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : (cons(v4, nil) = v5 & % 53.00/8.32 | cons(v2, nil) = v3 & app(v10, v11) = v0 & app(v9, v5) = v10 & app(v7, % 53.00/8.32 | v8) = v9 & app(v6, v3) = v7 & $i(v12) & $i(v11) & $i(v10) & $i(v9) % 53.00/8.32 | & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 53.00/8.32 | $i(v1) & $i(v0) & leq(v4, v2) & ssList(v11) & ssList(v8) & ssList(v6) % 53.00/8.32 | & ssList(v1) & ssList(v0) & ssItem(v4) & ssItem(v2) & ! [v13: $i] : % 53.00/8.32 | ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: % 53.00/8.32 | $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : % 53.00/8.32 | ! [v23: $i] : ( ~ (cons(v15, nil) = v16) | ~ (cons(v13, nil) = v14) % 53.00/8.32 | | ~ (app(v21, v22) = v0) | ~ (app(v20, v16) = v21) | ~ (app(v18, % 53.00/8.32 | v19) = v20) | ~ (app(v17, v14) = v18) | ~ $i(v23) | ~ % 53.00/8.32 | $i(v22) | ~ $i(v19) | ~ $i(v17) | ~ $i(v15) | ~ $i(v13) | ~ % 53.00/8.32 | leq(v15, v13) | ~ memberP(v19, v23) | ~ ssList(v22) | ~ % 53.00/8.32 | ssList(v19) | ~ ssList(v17) | ~ ssItem(v23) | ~ ssItem(v15) | ~ % 53.00/8.32 | ssItem(v13) | leq(v23, v15)) & ! [v13: $i] : ! [v14: $i] : ! % 53.00/8.32 | [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] % 53.00/8.32 | : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ % 53.00/8.32 | (cons(v15, nil) = v16) | ~ (cons(v13, nil) = v14) | ~ (app(v21, % 53.00/8.32 | v22) = v0) | ~ (app(v20, v16) = v21) | ~ (app(v18, v19) = % 53.00/8.32 | v20) | ~ (app(v17, v14) = v18) | ~ $i(v23) | ~ $i(v22) | ~ % 53.00/8.32 | $i(v19) | ~ $i(v17) | ~ $i(v15) | ~ $i(v13) | ~ leq(v15, v13) | % 53.00/8.32 | ~ memberP(v19, v23) | ~ ssList(v22) | ~ ssList(v19) | ~ % 53.00/8.32 | ssList(v17) | ~ ssItem(v23) | ~ ssItem(v15) | ~ ssItem(v13) | % 53.00/8.33 | leq(v13, v23)) & ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! % 53.00/8.33 | [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] % 53.00/8.33 | : ! [v21: $i] : ! [v22: $i] : ( ~ (cons(v15, nil) = v16) | ~ % 53.00/8.33 | (cons(v13, nil) = v14) | ~ (app(v21, v22) = v0) | ~ (app(v20, % 53.00/8.33 | v16) = v21) | ~ (app(v18, v19) = v20) | ~ (app(v17, v14) = % 53.00/8.33 | v18) | ~ $i(v22) | ~ $i(v19) | ~ $i(v17) | ~ $i(v15) | ~ % 53.00/8.33 | $i(v13) | ~ leq(v15, v13) | ~ ssList(v22) | ~ ssList(v19) | ~ % 53.00/8.33 | ssList(v17) | ~ ssItem(v15) | ~ ssItem(v13) | leq(v13, v15)) & ( % 53.00/8.33 | ~ leq(v2, v4) | (memberP(v8, v12) & ssItem(v12) & ( ~ leq(v12, v4) % 53.00/8.33 | | ~ leq(v2, v12))))) % 53.00/8.33 | % 53.00/8.33 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives: % 53.00/8.33 | (3) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) & % 53.00/8.33 | ssItem(all_89_0) & ssItem(all_89_1) % 53.00/8.33 | % 53.00/8.33 | ALPHA: (3) implies: % 53.00/8.33 | (4) ~ (all_89_0 = all_89_1) % 53.00/8.33 | (5) ssItem(all_89_1) % 53.00/8.33 | (6) ssItem(all_89_0) % 53.00/8.33 | (7) $i(all_89_1) % 53.00/8.33 | (8) $i(all_89_0) % 53.00/8.33 | % 53.00/8.33 | DELTA: instantiating (2) with fresh symbols all_91_0, all_91_1, all_91_2, % 53.00/8.33 | all_91_3, all_91_4, all_91_5, all_91_6, all_91_7, all_91_8, all_91_9, % 53.00/8.33 | all_91_10, all_91_11, all_91_12 gives: % 53.00/8.34 | (9) cons(all_91_8, nil) = all_91_7 & cons(all_91_10, nil) = all_91_9 & % 53.00/8.34 | app(all_91_2, all_91_1) = all_91_12 & app(all_91_3, all_91_7) = % 53.00/8.34 | all_91_2 & app(all_91_5, all_91_4) = all_91_3 & app(all_91_6, all_91_9) % 53.00/8.34 | = all_91_5 & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) % 53.00/8.34 | & $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & $i(all_91_7) & % 53.00/8.34 | $i(all_91_8) & $i(all_91_9) & $i(all_91_10) & $i(all_91_11) & % 53.00/8.34 | $i(all_91_12) & leq(all_91_8, all_91_10) & ssList(all_91_1) & % 53.00/8.34 | ssList(all_91_4) & ssList(all_91_6) & ssList(all_91_11) & % 53.00/8.34 | ssList(all_91_12) & ssItem(all_91_8) & ssItem(all_91_10) & ! [v0: $i] % 53.00/8.34 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 53.00/8.34 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 53.00/8.34 | ( ~ (cons(v2, nil) = v3) | ~ (cons(v0, nil) = v1) | ~ (app(v8, v9) = % 53.00/8.34 | all_91_12) | ~ (app(v7, v3) = v8) | ~ (app(v5, v6) = v7) | ~ % 53.00/8.34 | (app(v4, v1) = v5) | ~ $i(v10) | ~ $i(v9) | ~ $i(v6) | ~ $i(v4) | % 53.00/8.34 | ~ $i(v2) | ~ $i(v0) | ~ leq(v2, v0) | ~ memberP(v6, v10) | ~ % 53.00/8.34 | ssList(v9) | ~ ssList(v6) | ~ ssList(v4) | ~ ssItem(v10) | ~ % 53.00/8.34 | ssItem(v2) | ~ ssItem(v0) | leq(v10, v2)) & ! [v0: $i] : ! [v1: % 53.00/8.34 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 53.00/8.34 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ % 53.00/8.34 | (cons(v2, nil) = v3) | ~ (cons(v0, nil) = v1) | ~ (app(v8, v9) = % 53.00/8.34 | all_91_12) | ~ (app(v7, v3) = v8) | ~ (app(v5, v6) = v7) | ~ % 53.00/8.34 | (app(v4, v1) = v5) | ~ $i(v10) | ~ $i(v9) | ~ $i(v6) | ~ $i(v4) | % 53.00/8.34 | ~ $i(v2) | ~ $i(v0) | ~ leq(v2, v0) | ~ memberP(v6, v10) | ~ % 53.00/8.34 | ssList(v9) | ~ ssList(v6) | ~ ssList(v4) | ~ ssItem(v10) | ~ % 53.00/8.34 | ssItem(v2) | ~ ssItem(v0) | leq(v0, v10)) & ! [v0: $i] : ! [v1: % 53.00/8.34 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 53.00/8.34 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (cons(v2, nil) = % 53.00/8.34 | v3) | ~ (cons(v0, nil) = v1) | ~ (app(v8, v9) = all_91_12) | ~ % 53.00/8.34 | (app(v7, v3) = v8) | ~ (app(v5, v6) = v7) | ~ (app(v4, v1) = v5) | % 53.00/8.34 | ~ $i(v9) | ~ $i(v6) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ leq(v2, % 53.00/8.34 | v0) | ~ ssList(v9) | ~ ssList(v6) | ~ ssList(v4) | ~ ssItem(v2) % 53.00/8.34 | | ~ ssItem(v0) | leq(v0, v2)) & ( ~ leq(all_91_10, all_91_8) | % 53.00/8.34 | (memberP(all_91_4, all_91_0) & ssItem(all_91_0) & ( ~ leq(all_91_0, % 53.00/8.34 | all_91_8) | ~ leq(all_91_10, all_91_0)))) % 53.00/8.34 | % 53.00/8.34 | ALPHA: (9) implies: % 53.00/8.34 | (10) ssItem(all_91_10) % 53.00/8.34 | (11) ssItem(all_91_8) % 53.00/8.34 | (12) ssList(all_91_6) % 53.00/8.34 | (13) ssList(all_91_4) % 53.00/8.34 | (14) ssList(all_91_1) % 53.00/8.34 | (15) leq(all_91_8, all_91_10) % 53.00/8.34 | (16) $i(all_91_10) % 53.00/8.34 | (17) $i(all_91_8) % 53.00/8.34 | (18) $i(all_91_6) % 53.00/8.34 | (19) $i(all_91_4) % 53.00/8.34 | (20) $i(all_91_1) % 53.00/8.34 | (21) $i(all_91_0) % 53.00/8.34 | (22) app(all_91_6, all_91_9) = all_91_5 % 53.00/8.34 | (23) app(all_91_5, all_91_4) = all_91_3 % 53.00/8.34 | (24) app(all_91_3, all_91_7) = all_91_2 % 53.00/8.34 | (25) app(all_91_2, all_91_1) = all_91_12 % 53.00/8.34 | (26) cons(all_91_10, nil) = all_91_9 % 53.00/8.34 | (27) cons(all_91_8, nil) = all_91_7 % 53.00/8.34 | (28) ~ leq(all_91_10, all_91_8) | (memberP(all_91_4, all_91_0) & % 53.00/8.34 | ssItem(all_91_0) & ( ~ leq(all_91_0, all_91_8) | ~ leq(all_91_10, % 53.00/8.34 | all_91_0))) % 53.00/8.35 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 53.00/8.35 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( % 53.00/8.35 | ~ (cons(v2, nil) = v3) | ~ (cons(v0, nil) = v1) | ~ (app(v8, v9) = % 53.00/8.35 | all_91_12) | ~ (app(v7, v3) = v8) | ~ (app(v5, v6) = v7) | ~ % 53.00/8.35 | (app(v4, v1) = v5) | ~ $i(v9) | ~ $i(v6) | ~ $i(v4) | ~ $i(v2) | % 53.00/8.35 | ~ $i(v0) | ~ leq(v2, v0) | ~ ssList(v9) | ~ ssList(v6) | ~ % 53.00/8.35 | ssList(v4) | ~ ssItem(v2) | ~ ssItem(v0) | leq(v0, v2)) % 53.00/8.35 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 53.00/8.35 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 53.00/8.35 | ! [v10: $i] : ( ~ (cons(v2, nil) = v3) | ~ (cons(v0, nil) = v1) | ~ % 53.00/8.35 | (app(v8, v9) = all_91_12) | ~ (app(v7, v3) = v8) | ~ (app(v5, v6) % 53.00/8.35 | = v7) | ~ (app(v4, v1) = v5) | ~ $i(v10) | ~ $i(v9) | ~ $i(v6) % 53.00/8.35 | | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ leq(v2, v0) | ~ % 53.00/8.35 | memberP(v6, v10) | ~ ssList(v9) | ~ ssList(v6) | ~ ssList(v4) | % 53.00/8.35 | ~ ssItem(v10) | ~ ssItem(v2) | ~ ssItem(v0) | leq(v0, v10)) % 53.00/8.35 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 53.00/8.35 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 53.00/8.35 | ! [v10: $i] : ( ~ (cons(v2, nil) = v3) | ~ (cons(v0, nil) = v1) | ~ % 53.00/8.35 | (app(v8, v9) = all_91_12) | ~ (app(v7, v3) = v8) | ~ (app(v5, v6) % 53.00/8.35 | = v7) | ~ (app(v4, v1) = v5) | ~ $i(v10) | ~ $i(v9) | ~ $i(v6) % 53.00/8.35 | | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ leq(v2, v0) | ~ % 53.00/8.35 | memberP(v6, v10) | ~ ssList(v9) | ~ ssList(v6) | ~ ssList(v4) | % 53.00/8.35 | ~ ssItem(v10) | ~ ssItem(v2) | ~ ssItem(v0) | leq(v10, v2)) % 53.00/8.35 | % 53.00/8.35 | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with (5), % 53.00/8.35 | (6), (7), (8) gives: % 53.00/8.35 | (32) all_89_0 = all_89_1 | neq(all_89_1, all_89_0) % 53.00/8.35 | % 53.00/8.35 | GROUND_INST: instantiating (29) with all_91_10, all_91_9, all_91_8, all_91_7, % 53.00/8.35 | all_91_6, all_91_5, all_91_4, all_91_3, all_91_2, all_91_1, % 53.00/8.35 | simplifying with (10), (11), (12), (13), (14), (15), (16), (17), % 53.00/8.35 | (18), (19), (20), (22), (23), (24), (25), (26), (27) gives: % 53.00/8.35 | (33) leq(all_91_10, all_91_8) % 53.00/8.35 | % 53.00/8.35 | BETA: splitting (28) gives: % 53.00/8.35 | % 53.00/8.35 | Case 1: % 53.00/8.35 | | % 53.00/8.35 | | (34) ~ leq(all_91_10, all_91_8) % 53.00/8.35 | | % 53.00/8.35 | | PRED_UNIFY: (33), (34) imply: % 53.00/8.35 | | (35) $false % 53.00/8.35 | | % 53.00/8.35 | | CLOSE: (35) is inconsistent. % 53.00/8.35 | | % 53.00/8.35 | Case 2: % 53.00/8.35 | | % 53.00/8.35 | | (36) memberP(all_91_4, all_91_0) & ssItem(all_91_0) & ( ~ leq(all_91_0, % 53.00/8.35 | | all_91_8) | ~ leq(all_91_10, all_91_0)) % 53.00/8.35 | | % 53.00/8.35 | | ALPHA: (36) implies: % 53.00/8.36 | | (37) ssItem(all_91_0) % 53.00/8.36 | | (38) memberP(all_91_4, all_91_0) % 53.00/8.36 | | (39) ~ leq(all_91_0, all_91_8) | ~ leq(all_91_10, all_91_0) % 53.00/8.36 | | % 53.00/8.36 | | BETA: splitting (32) gives: % 53.00/8.36 | | % 53.00/8.36 | | Case 1: % 53.00/8.36 | | | % 53.00/8.36 | | | % 53.00/8.36 | | | GROUND_INST: instantiating (31) with all_91_10, all_91_9, all_91_8, % 53.00/8.36 | | | all_91_7, all_91_6, all_91_5, all_91_4, all_91_3, all_91_2, % 53.00/8.36 | | | all_91_1, all_91_0, simplifying with (10), (11), (12), (13), % 53.00/8.36 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 53.00/8.36 | | | (24), (25), (26), (27), (37), (38) gives: % 53.00/8.36 | | | (40) leq(all_91_0, all_91_8) % 53.00/8.36 | | | % 53.00/8.36 | | | GROUND_INST: instantiating (30) with all_91_10, all_91_9, all_91_8, % 53.00/8.36 | | | all_91_7, all_91_6, all_91_5, all_91_4, all_91_3, all_91_2, % 53.00/8.36 | | | all_91_1, all_91_0, simplifying with (10), (11), (12), (13), % 53.00/8.36 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 53.00/8.36 | | | (24), (25), (26), (27), (37), (38) gives: % 53.00/8.36 | | | (41) leq(all_91_10, all_91_0) % 53.00/8.36 | | | % 53.00/8.36 | | | GROUND_INST: instantiating (ax29) with all_91_10, all_91_8, simplifying % 53.00/8.36 | | | with (10), (11), (15), (16), (17), (33) gives: % 53.00/8.36 | | | (42) all_91_8 = all_91_10 % 53.00/8.36 | | | % 53.00/8.36 | | | REDUCE: (40), (42) imply: % 53.00/8.36 | | | (43) leq(all_91_0, all_91_10) % 53.00/8.36 | | | % 53.00/8.36 | | | BETA: splitting (39) gives: % 53.00/8.36 | | | % 53.00/8.36 | | | Case 1: % 53.00/8.36 | | | | % 53.00/8.36 | | | | (44) ~ leq(all_91_0, all_91_8) % 53.00/8.36 | | | | % 53.00/8.36 | | | | REDUCE: (42), (44) imply: % 53.00/8.36 | | | | (45) ~ leq(all_91_0, all_91_10) % 53.00/8.36 | | | | % 53.00/8.36 | | | | PRED_UNIFY: (43), (45) imply: % 53.00/8.36 | | | | (46) $false % 53.00/8.36 | | | | % 53.00/8.36 | | | | CLOSE: (46) is inconsistent. % 53.00/8.36 | | | | % 53.00/8.36 | | | Case 2: % 53.00/8.36 | | | | % 53.00/8.36 | | | | (47) ~ leq(all_91_10, all_91_0) % 53.00/8.36 | | | | % 53.00/8.36 | | | | PRED_UNIFY: (41), (47) imply: % 53.00/8.36 | | | | (48) $false % 53.00/8.36 | | | | % 53.00/8.36 | | | | CLOSE: (48) is inconsistent. % 53.00/8.36 | | | | % 53.00/8.36 | | | End of split % 53.00/8.36 | | | % 53.00/8.36 | | Case 2: % 53.00/8.36 | | | % 53.00/8.36 | | | (49) all_89_0 = all_89_1 % 53.00/8.36 | | | % 53.00/8.36 | | | REDUCE: (4), (49) imply: % 53.00/8.36 | | | (50) $false % 53.00/8.36 | | | % 53.00/8.36 | | | CLOSE: (50) is inconsistent. % 53.00/8.36 | | | % 53.00/8.36 | | End of split % 53.00/8.36 | | % 53.00/8.36 | End of split % 53.00/8.36 | % 53.00/8.36 End of proof % 53.00/8.36 % SZS output end Proof for theBenchmark % 53.00/8.36 % 53.00/8.36 7743ms %------------------------------------------------------------------------------