%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC010+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 20:49:09 EDT 2023 % Result : Theorem 22.87s 3.88s % Output : Proof 33.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWC010+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n008.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Mon Aug 28 18:02:47 EDT 2023 % 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.60/1.45 Prover 1: Preprocessing ... % 4.60/1.45 Prover 4: Preprocessing ... % 4.60/1.49 Prover 3: Preprocessing ... % 4.60/1.49 Prover 6: Preprocessing ... % 4.60/1.49 Prover 5: Preprocessing ... % 4.60/1.49 Prover 0: Preprocessing ... % 4.60/1.49 Prover 2: Preprocessing ... % 14.23/2.70 Prover 2: Proving ... % 14.23/2.74 Prover 5: Constructing countermodel ... % 14.23/2.75 Prover 1: Constructing countermodel ... % 14.82/2.79 Prover 6: Proving ... % 14.82/2.88 Prover 3: Constructing countermodel ... % 21.52/3.66 Prover 4: Constructing countermodel ... % 22.87/3.85 Prover 0: Proving ... % 22.87/3.87 Prover 3: proved (3216ms) % 22.87/3.88 % 22.87/3.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.87/3.88 % 22.87/3.89 Prover 5: stopped % 22.87/3.89 Prover 2: stopped % 22.87/3.89 Prover 6: stopped % 22.87/3.89 Prover 0: stopped % 23.20/3.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.20/3.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.20/3.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.20/3.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.20/3.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.98/4.15 Prover 11: Preprocessing ... % 24.90/4.20 Prover 10: Preprocessing ... % 24.90/4.21 Prover 7: Preprocessing ... % 24.90/4.22 Prover 13: Preprocessing ... % 24.90/4.22 Prover 8: Preprocessing ... % 27.26/4.45 Prover 10: Constructing countermodel ... % 27.26/4.46 Prover 7: Constructing countermodel ... % 27.26/4.53 Prover 13: Constructing countermodel ... % 28.80/4.66 Prover 8: Warning: ignoring some quantifiers % 28.80/4.67 Prover 8: Constructing countermodel ... % 29.19/4.80 Prover 10: Found proof (size 18) % 29.19/4.80 Prover 10: proved (887ms) % 29.19/4.80 Prover 13: stopped % 29.19/4.80 Prover 7: stopped % 29.19/4.80 Prover 4: stopped % 29.19/4.80 Prover 8: stopped % 29.19/4.81 Prover 1: stopped % 32.38/5.54 Prover 11: Constructing countermodel ... % 32.38/5.58 Prover 11: stopped % 32.38/5.58 % 32.38/5.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 32.38/5.59 % 32.38/5.59 % SZS output start Proof for theBenchmark % 32.38/5.60 Assumptions after simplification: % 32.38/5.60 --------------------------------- % 32.38/5.60 % 32.38/5.60 (ax17) % 32.38/5.61 $i(nil) & ssList(nil) % 32.38/5.61 % 32.38/5.61 (ax58) % 32.38/5.61 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 32.38/5.61 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 32.38/5.62 % 32.38/5.62 (co1) % 33.02/5.66 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 33.02/5.66 : ? [v5: $i] : ? [v6: $i] : (cons(v2, nil) = v3 & app(v5, v6) = v1 & app(v4, % 33.02/5.66 v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 33.02/5.66 $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) & % 33.02/5.66 neq(v1, nil) & ssItem(v2) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 33.02/5.66 [v10: $i] : ! [v11: $i] : ( ~ (cons(v7, nil) = v8) | ~ (app(v10, v11) = % 33.02/5.66 v1) | ~ (app(v9, v8) = v10) | ~ $i(v11) | ~ $i(v9) | ~ $i(v7) | ~ % 33.02/5.66 ssList(v11) | ~ ssList(v9) | ~ ssItem(v7) | ? [v12: $i] : ( ~ (v12 = % 33.02/5.66 v0) & app(v9, v11) = v12 & $i(v12))) & ! [v7: $i] : (v7 = v2 | ~ % 33.02/5.66 $i(v7) | ~ geq(v7, v2) | ~ memberP(v1, v7) | ~ ssItem(v7))) % 33.02/5.66 % 33.02/5.66 (function-axioms) % 33.02/5.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.02/5.67 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 33.02/5.67 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 33.02/5.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 33.02/5.67 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 33.02/5.67 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 33.02/5.67 % 33.02/5.67 Further assumptions not needed in the proof: % 33.02/5.67 -------------------------------------------- % 33.02/5.67 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, % 33.02/5.67 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, % 33.02/5.67 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, % 33.02/5.67 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, % 33.02/5.67 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, % 33.02/5.67 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 33.02/5.67 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 33.02/5.67 ax94, ax95 % 33.02/5.67 % 33.02/5.67 Those formulas are unsatisfiable: % 33.02/5.67 --------------------------------- % 33.02/5.67 % 33.02/5.67 Begin of proof % 33.02/5.67 | % 33.02/5.67 | ALPHA: (ax17) implies: % 33.02/5.67 | (1) ssList(nil) % 33.02/5.67 | % 33.02/5.67 | ALPHA: (ax58) implies: % 33.02/5.68 | (2) ~ ssList(nil) | segmentP(nil, nil) % 33.02/5.68 | % 33.02/5.68 | ALPHA: (co1) implies: % 33.02/5.68 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 33.02/5.68 | ? [v5: $i] : ? [v6: $i] : (cons(v2, nil) = v3 & app(v5, v6) = v1 & % 33.02/5.68 | app(v4, v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & % 33.02/5.68 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & % 33.02/5.68 | ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v7: $i] : % 33.02/5.68 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 33.02/5.68 | (cons(v7, nil) = v8) | ~ (app(v10, v11) = v1) | ~ (app(v9, v8) = % 33.02/5.68 | v10) | ~ $i(v11) | ~ $i(v9) | ~ $i(v7) | ~ ssList(v11) | ~ % 33.02/5.68 | ssList(v9) | ~ ssItem(v7) | ? [v12: $i] : ( ~ (v12 = v0) & % 33.02/5.68 | app(v9, v11) = v12 & $i(v12))) & ! [v7: $i] : (v7 = v2 | ~ % 33.02/5.68 | $i(v7) | ~ geq(v7, v2) | ~ memberP(v1, v7) | ~ ssItem(v7))) % 33.02/5.68 | % 33.02/5.68 | ALPHA: (function-axioms) implies: % 33.02/5.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.02/5.68 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 33.02/5.68 | % 33.02/5.69 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2, % 33.02/5.69 | all_91_3, all_91_4, all_91_5, all_91_6 gives: % 33.02/5.69 | (5) cons(all_91_4, nil) = all_91_3 & app(all_91_1, all_91_0) = all_91_5 & % 33.02/5.69 | app(all_91_2, all_91_0) = all_91_6 & app(all_91_2, all_91_3) = all_91_1 % 33.02/5.69 | & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & % 33.02/5.69 | $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_0) & % 33.02/5.69 | ssList(all_91_2) & ssList(all_91_5) & ssList(all_91_6) & neq(all_91_5, % 33.02/5.69 | nil) & ssItem(all_91_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 33.02/5.69 | ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = % 33.02/5.69 | all_91_5) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 33.02/5.69 | $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: any] % 33.02/5.69 | : ( ~ (v5 = all_91_6) & app(v2, v4) = v5 & $i(v5))) & ! [v0: any] : % 33.02/5.69 | (v0 = all_91_4 | ~ $i(v0) | ~ geq(v0, all_91_4) | ~ % 33.02/5.69 | memberP(all_91_5, v0) | ~ ssItem(v0)) % 33.02/5.69 | % 33.02/5.69 | ALPHA: (5) implies: % 33.02/5.70 | (6) ssItem(all_91_4) % 33.02/5.70 | (7) ssList(all_91_2) % 33.02/5.70 | (8) ssList(all_91_0) % 33.02/5.70 | (9) $i(all_91_4) % 33.02/5.70 | (10) $i(all_91_2) % 33.02/5.70 | (11) $i(all_91_0) % 33.02/5.70 | (12) app(all_91_2, all_91_3) = all_91_1 % 33.02/5.70 | (13) app(all_91_2, all_91_0) = all_91_6 % 33.02/5.70 | (14) app(all_91_1, all_91_0) = all_91_5 % 33.02/5.70 | (15) cons(all_91_4, nil) = all_91_3 % 33.02/5.70 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 33.02/5.70 | ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = all_91_5) | ~ (app(v2, % 33.02/5.70 | v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) | % 33.02/5.70 | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: any] : ( ~ (v5 = all_91_6) & % 33.02/5.70 | app(v2, v4) = v5 & $i(v5))) % 33.02/5.70 | % 33.02/5.70 | BETA: splitting (2) gives: % 33.02/5.70 | % 33.02/5.70 | Case 1: % 33.02/5.70 | | % 33.02/5.70 | | (17) ~ ssList(nil) % 33.02/5.70 | | % 33.02/5.70 | | PRED_UNIFY: (1), (17) imply: % 33.02/5.70 | | (18) $false % 33.02/5.70 | | % 33.02/5.70 | | CLOSE: (18) is inconsistent. % 33.02/5.70 | | % 33.02/5.71 | Case 2: % 33.02/5.71 | | % 33.02/5.71 | | % 33.02/5.71 | | GROUND_INST: instantiating (16) with all_91_4, all_91_3, all_91_2, all_91_1, % 33.02/5.71 | | all_91_0, simplifying with (6), (7), (8), (9), (10), (11), % 33.02/5.71 | | (12), (14), (15) gives: % 33.02/5.71 | | (19) ? [v0: any] : ( ~ (v0 = all_91_6) & app(all_91_2, all_91_0) = v0 & % 33.02/5.71 | | $i(v0)) % 33.02/5.71 | | % 33.02/5.71 | | DELTA: instantiating (19) with fresh symbol all_112_0 gives: % 33.02/5.71 | | (20) ~ (all_112_0 = all_91_6) & app(all_91_2, all_91_0) = all_112_0 & % 33.02/5.71 | | $i(all_112_0) % 33.02/5.71 | | % 33.02/5.71 | | ALPHA: (20) implies: % 33.02/5.71 | | (21) ~ (all_112_0 = all_91_6) % 33.02/5.71 | | (22) app(all_91_2, all_91_0) = all_112_0 % 33.02/5.71 | | % 33.02/5.71 | | GROUND_INST: instantiating (4) with all_91_6, all_112_0, all_91_0, all_91_2, % 33.02/5.71 | | simplifying with (13), (22) gives: % 33.02/5.71 | | (23) all_112_0 = all_91_6 % 33.02/5.71 | | % 33.02/5.71 | | REDUCE: (21), (23) imply: % 33.02/5.71 | | (24) $false % 33.02/5.71 | | % 33.02/5.71 | | CLOSE: (24) is inconsistent. % 33.02/5.71 | | % 33.02/5.71 | End of split % 33.02/5.71 | % 33.02/5.71 End of proof % 33.02/5.71 % SZS output end Proof for theBenchmark % 33.02/5.71 % 33.02/5.71 5086ms %------------------------------------------------------------------------------