%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC422+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 : n012.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 20:51:22 EDT 2023 % Result : Theorem 25.05s 4.15s % Output : Proof 34.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC422+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 17:43:39 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 7.44/1.70 Prover 4: Preprocessing ... % 7.44/1.71 Prover 1: Preprocessing ... % 7.44/1.71 Prover 5: Preprocessing ... % 7.44/1.72 Prover 6: Preprocessing ... % 7.44/1.72 Prover 0: Preprocessing ... % 7.44/1.72 Prover 3: Preprocessing ... % 7.44/1.73 Prover 2: Preprocessing ... % 17.71/3.12 Prover 2: Proving ... % 18.07/3.13 Prover 5: Constructing countermodel ... % 18.20/3.18 Prover 6: Proving ... % 18.20/3.19 Prover 1: Constructing countermodel ... % 18.20/3.20 Prover 3: Constructing countermodel ... % 23.42/3.87 Prover 4: Constructing countermodel ... % 24.52/4.00 Prover 0: Proving ... % 25.05/4.15 Prover 3: proved (3518ms) % 25.05/4.15 % 25.05/4.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 25.05/4.15 % 25.05/4.16 Prover 5: stopped % 25.05/4.16 Prover 2: stopped % 25.05/4.16 Prover 6: stopped % 25.05/4.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 25.05/4.17 Prover 0: proved (3531ms) % 25.05/4.17 % 25.05/4.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 25.05/4.17 % 25.05/4.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 25.05/4.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 25.05/4.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 25.05/4.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 27.51/4.40 Prover 10: Preprocessing ... % 27.75/4.43 Prover 7: Preprocessing ... % 27.81/4.47 Prover 11: Preprocessing ... % 27.81/4.47 Prover 8: Preprocessing ... % 27.81/4.48 Prover 13: Preprocessing ... % 28.91/4.66 Prover 7: Constructing countermodel ... % 29.65/4.68 Prover 10: Constructing countermodel ... % 29.83/4.72 Prover 13: Constructing countermodel ... % 30.18/4.92 Prover 8: Warning: ignoring some quantifiers % 30.18/4.93 Prover 8: Constructing countermodel ... % 32.22/5.07 Prover 10: Found proof (size 20) % 32.62/5.07 Prover 10: proved (907ms) % 32.62/5.07 Prover 4: stopped % 32.62/5.07 Prover 7: stopped % 32.62/5.07 Prover 13: stopped % 32.62/5.07 Prover 1: stopped % 32.62/5.07 Prover 8: stopped % 34.15/5.48 Prover 11: Constructing countermodel ... % 34.15/5.51 Prover 11: stopped % 34.15/5.51 % 34.15/5.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 34.15/5.51 % 34.15/5.51 % SZS output start Proof for theBenchmark % 34.15/5.52 Assumptions after simplification: % 34.15/5.52 --------------------------------- % 34.15/5.52 % 34.15/5.52 (ax17) % 34.15/5.53 $i(nil) & ssList(nil) % 34.15/5.53 % 34.15/5.53 (ax58) % 34.15/5.53 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 34.15/5.53 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 34.15/5.53 % 34.15/5.53 (co1) % 34.15/5.57 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 34.15/5.58 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (cons(v2, nil) = v3 & app(v7, v4) % 34.15/5.58 = v0 & app(v6, v3) = v7 & app(v5, v6) = v1 & app(v4, v3) = v5 & $i(v7) & % 34.15/5.58 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) & % 34.15/5.58 ssList(v4) & ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v8: % 34.15/5.58 $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ % 34.15/5.58 (cons(v8, nil) = v9) | ~ (app(v11, v12) = v1) | ~ (app(v10, v9) = v11) | % 34.15/5.58 ~ $i(v12) | ~ $i(v10) | ~ $i(v8) | ~ ssList(v12) | ~ ssList(v10) | ~ % 34.15/5.58 ssItem(v8) | ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = v0) & app(v13, v10) % 34.15/5.58 = v14 & app(v12, v9) = v13 & $i(v14) & $i(v13)))) % 34.15/5.58 % 34.15/5.58 (function-axioms) % 34.30/5.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.30/5.58 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 34.30/5.58 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 34.30/5.58 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 34.30/5.58 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 34.30/5.58 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 34.30/5.58 % 34.30/5.58 Further assumptions not needed in the proof: % 34.30/5.58 -------------------------------------------- % 34.30/5.58 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, % 34.30/5.58 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, % 34.30/5.58 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, % 34.30/5.58 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, % 34.30/5.58 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, % 34.30/5.58 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 34.30/5.58 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 34.30/5.58 ax94, ax95 % 34.30/5.58 % 34.30/5.58 Those formulas are unsatisfiable: % 34.30/5.58 --------------------------------- % 34.30/5.58 % 34.30/5.58 Begin of proof % 34.30/5.58 | % 34.30/5.58 | ALPHA: (ax17) implies: % 34.30/5.59 | (1) ssList(nil) % 34.30/5.59 | % 34.30/5.59 | ALPHA: (ax58) implies: % 34.30/5.59 | (2) ~ ssList(nil) | segmentP(nil, nil) % 34.30/5.59 | % 34.30/5.59 | ALPHA: (co1) implies: % 34.30/5.59 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 34.30/5.59 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (cons(v2, nil) = v3 & app(v7, % 34.30/5.59 | v4) = v0 & app(v6, v3) = v7 & app(v5, v6) = v1 & app(v4, v3) = v5 & % 34.30/5.59 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) % 34.30/5.59 | & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) & neq(v1, nil) & % 34.30/5.59 | ssItem(v2) & ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] % 34.30/5.59 | : ! [v12: $i] : ( ~ (cons(v8, nil) = v9) | ~ (app(v11, v12) = v1) | % 34.30/5.59 | ~ (app(v10, v9) = v11) | ~ $i(v12) | ~ $i(v10) | ~ $i(v8) | ~ % 34.30/5.59 | ssList(v12) | ~ ssList(v10) | ~ ssItem(v8) | ? [v13: $i] : ? % 34.30/5.59 | [v14: $i] : ( ~ (v14 = v0) & app(v13, v10) = v14 & app(v12, v9) = % 34.30/5.59 | v13 & $i(v14) & $i(v13)))) % 34.30/5.59 | % 34.30/5.59 | ALPHA: (function-axioms) implies: % 34.30/5.59 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.30/5.59 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 34.30/5.59 | % 34.30/5.59 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2, % 34.30/5.59 | all_91_3, all_91_4, all_91_5, all_91_6, all_91_7 gives: % 34.30/5.60 | (5) cons(all_91_5, nil) = all_91_4 & app(all_91_0, all_91_3) = all_91_7 & % 34.30/5.60 | app(all_91_1, all_91_4) = all_91_0 & app(all_91_2, all_91_1) = all_91_6 % 34.30/5.60 | & app(all_91_3, all_91_4) = all_91_2 & $i(all_91_0) & $i(all_91_1) & % 34.30/5.60 | $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & $i(all_91_5) & % 34.30/5.60 | $i(all_91_6) & $i(all_91_7) & ssList(all_91_1) & ssList(all_91_3) & % 34.30/5.60 | ssList(all_91_6) & ssList(all_91_7) & neq(all_91_6, nil) & % 34.30/5.60 | ssItem(all_91_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 34.30/5.60 | $i] : ! [v4: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = % 34.30/5.60 | all_91_6) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 34.30/5.60 | $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i] % 34.30/5.60 | : ? [v6: any] : ( ~ (v6 = all_91_7) & app(v5, v2) = v6 & app(v4, v1) % 34.30/5.60 | = v5 & $i(v6) & $i(v5))) % 34.30/5.60 | % 34.30/5.60 | ALPHA: (5) implies: % 34.30/5.60 | (6) ssItem(all_91_5) % 34.30/5.60 | (7) ssList(all_91_3) % 34.30/5.60 | (8) ssList(all_91_1) % 34.30/5.60 | (9) $i(all_91_5) % 34.30/5.60 | (10) $i(all_91_3) % 34.30/5.60 | (11) $i(all_91_1) % 34.30/5.60 | (12) app(all_91_3, all_91_4) = all_91_2 % 34.30/5.60 | (13) app(all_91_2, all_91_1) = all_91_6 % 34.30/5.60 | (14) app(all_91_1, all_91_4) = all_91_0 % 34.30/5.60 | (15) app(all_91_0, all_91_3) = all_91_7 % 34.30/5.60 | (16) cons(all_91_5, nil) = all_91_4 % 34.30/5.61 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 34.30/5.61 | ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = all_91_6) | ~ (app(v2, % 34.30/5.61 | v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) | % 34.30/5.61 | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i] : ? [v6: any] : ( ~ (v6 % 34.30/5.61 | = all_91_7) & app(v5, v2) = v6 & app(v4, v1) = v5 & $i(v6) & % 34.30/5.61 | $i(v5))) % 34.30/5.61 | % 34.30/5.61 | BETA: splitting (2) gives: % 34.30/5.61 | % 34.30/5.61 | Case 1: % 34.30/5.61 | | % 34.30/5.61 | | (18) ~ ssList(nil) % 34.30/5.61 | | % 34.30/5.61 | | PRED_UNIFY: (1), (18) imply: % 34.30/5.61 | | (19) $false % 34.30/5.61 | | % 34.30/5.61 | | CLOSE: (19) is inconsistent. % 34.30/5.61 | | % 34.30/5.61 | Case 2: % 34.30/5.61 | | % 34.30/5.61 | | % 34.30/5.61 | | GROUND_INST: instantiating (17) with all_91_5, all_91_4, all_91_3, all_91_2, % 34.30/5.61 | | all_91_1, simplifying with (6), (7), (8), (9), (10), (11), % 34.30/5.61 | | (12), (13), (16) gives: % 34.30/5.61 | | (20) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_91_7) & app(v0, all_91_3) % 34.30/5.61 | | = v1 & app(all_91_1, all_91_4) = v0 & $i(v1) & $i(v0)) % 34.30/5.61 | | % 34.30/5.61 | | DELTA: instantiating (20) with fresh symbols all_116_0, all_116_1 gives: % 34.30/5.61 | | (21) ~ (all_116_0 = all_91_7) & app(all_116_1, all_91_3) = all_116_0 & % 34.30/5.61 | | app(all_91_1, all_91_4) = all_116_1 & $i(all_116_0) & $i(all_116_1) % 34.30/5.61 | | % 34.30/5.61 | | ALPHA: (21) implies: % 34.30/5.61 | | (22) ~ (all_116_0 = all_91_7) % 34.30/5.61 | | (23) app(all_91_1, all_91_4) = all_116_1 % 34.30/5.61 | | (24) app(all_116_1, all_91_3) = all_116_0 % 34.30/5.61 | | % 34.30/5.61 | | GROUND_INST: instantiating (4) with all_91_0, all_116_1, all_91_4, all_91_1, % 34.30/5.61 | | simplifying with (14), (23) gives: % 34.30/5.61 | | (25) all_116_1 = all_91_0 % 34.30/5.61 | | % 34.30/5.61 | | REDUCE: (24), (25) imply: % 34.30/5.61 | | (26) app(all_91_0, all_91_3) = all_116_0 % 34.30/5.61 | | % 34.30/5.61 | | GROUND_INST: instantiating (4) with all_91_7, all_116_0, all_91_3, all_91_0, % 34.30/5.61 | | simplifying with (15), (26) gives: % 34.30/5.61 | | (27) all_116_0 = all_91_7 % 34.30/5.61 | | % 34.30/5.61 | | REDUCE: (22), (27) imply: % 34.30/5.61 | | (28) $false % 34.30/5.61 | | % 34.30/5.61 | | CLOSE: (28) is inconsistent. % 34.30/5.61 | | % 34.30/5.61 | End of split % 34.30/5.61 | % 34.30/5.61 End of proof % 34.30/5.61 % SZS output end Proof for theBenchmark % 34.30/5.61 % 34.30/5.61 5004ms %------------------------------------------------------------------------------