%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC095+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 : n028.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 20:49:37 EDT 2023 % Result : Theorem 26.26s 4.13s % Output : Proof 35.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWC095+1 : TPTP v8.1.2. Released v2.4.0. % 0.12/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Mon Aug 28 15:00:39 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.58 ________ _____ % 0.19/0.58 ___ __ \_________(_)________________________________ % 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.58 (2023-06-19) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2023 % 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.58 Amanda Stjerna. % 0.19/0.58 Free software under BSD-3-Clause. % 0.19/0.58 % 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 6.93/1.59 Prover 4: Preprocessing ... % 6.93/1.60 Prover 1: Preprocessing ... % 7.14/1.63 Prover 3: Preprocessing ... % 7.14/1.63 Prover 0: Preprocessing ... % 7.14/1.63 Prover 2: Preprocessing ... % 7.14/1.63 Prover 5: Preprocessing ... % 7.14/1.63 Prover 6: Preprocessing ... % 16.61/2.91 Prover 2: Proving ... % 17.41/3.03 Prover 1: Constructing countermodel ... % 17.87/3.05 Prover 5: Constructing countermodel ... % 17.87/3.06 Prover 6: Proving ... % 18.25/3.12 Prover 3: Constructing countermodel ... % 22.49/3.74 Prover 4: Constructing countermodel ... % 24.66/3.95 Prover 0: Proving ... % 26.26/4.12 Prover 0: proved (3522ms) % 26.26/4.13 % 26.26/4.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.26/4.13 % 26.26/4.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 26.26/4.13 Prover 2: stopped % 26.26/4.14 Prover 5: stopped % 26.26/4.15 Prover 3: stopped % 26.26/4.16 Prover 6: stopped % 26.26/4.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.26/4.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.26/4.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 26.26/4.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 27.47/4.37 Prover 13: Preprocessing ... % 27.47/4.37 Prover 10: Preprocessing ... % 27.47/4.38 Prover 8: Preprocessing ... % 27.47/4.39 Prover 7: Preprocessing ... % 28.72/4.47 Prover 11: Preprocessing ... % 30.43/4.71 Prover 10: Constructing countermodel ... % 30.43/4.73 Prover 7: Constructing countermodel ... % 30.43/4.74 Prover 13: Constructing countermodel ... % 31.07/4.77 Prover 8: Warning: ignoring some quantifiers % 31.26/4.79 Prover 8: Constructing countermodel ... % 33.08/5.09 Prover 10: Found proof (size 17) % 33.08/5.09 Prover 10: proved (946ms) % 33.08/5.09 Prover 4: stopped % 33.08/5.09 Prover 7: stopped % 33.08/5.09 Prover 8: stopped % 33.08/5.09 Prover 1: stopped % 33.08/5.09 Prover 13: stopped % 34.91/5.46 Prover 11: Constructing countermodel ... % 34.91/5.48 Prover 11: stopped % 35.24/5.48 % 35.24/5.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 35.24/5.48 % 35.24/5.49 % SZS output start Proof for theBenchmark % 35.24/5.49 Assumptions after simplification: % 35.24/5.49 --------------------------------- % 35.24/5.49 % 35.24/5.49 (ax17) % 35.24/5.50 $i(nil) & ssList(nil) % 35.24/5.50 % 35.24/5.50 (ax58) % 35.24/5.50 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 35.24/5.50 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 35.24/5.50 % 35.24/5.50 (co1) % 35.24/5.55 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 35.24/5.55 $i] : (app(v4, v5) = v0 & app(v2, v5) = v1 & app(v2, v3) = v4 & $i(v5) & % 35.24/5.55 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v5) & ssList(v3) & % 35.24/5.55 ssList(v2) & ssList(v1) & ssList(v0) & ! [v6: $i] : ! [v7: $i] : ! [v8: % 35.24/5.55 $i] : ! [v9: $i] : ( ~ (app(v8, v9) = v0) | ~ (app(v6, v7) = v8) | ~ % 35.24/5.55 $i(v9) | ~ $i(v7) | ~ $i(v6) | ~ ssList(v9) | ~ ssList(v7) | ~ % 35.24/5.55 ssList(v6) | ? [v10: $i] : ( ~ (v10 = v1) & app(v6, v9) = v10 & % 35.24/5.55 $i(v10)))) % 35.24/5.55 % 35.24/5.55 (function-axioms) % 35.24/5.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 35.24/5.55 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 35.24/5.55 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 35.24/5.55 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 35.24/5.55 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 35.24/5.55 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 35.24/5.55 % 35.24/5.55 Further assumptions not needed in the proof: % 35.24/5.55 -------------------------------------------- % 35.24/5.55 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, % 35.24/5.55 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, % 35.24/5.55 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, % 35.24/5.55 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, % 35.24/5.55 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, % 35.24/5.55 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 35.24/5.55 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 35.24/5.55 ax94, ax95 % 35.24/5.55 % 35.24/5.55 Those formulas are unsatisfiable: % 35.24/5.55 --------------------------------- % 35.24/5.55 % 35.24/5.55 Begin of proof % 35.24/5.55 | % 35.24/5.55 | ALPHA: (ax17) implies: % 35.24/5.56 | (1) ssList(nil) % 35.24/5.56 | % 35.24/5.56 | ALPHA: (ax58) implies: % 35.24/5.56 | (2) ~ ssList(nil) | segmentP(nil, nil) % 35.24/5.56 | % 35.24/5.56 | ALPHA: (function-axioms) implies: % 35.24/5.56 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 35.24/5.56 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 35.24/5.56 | % 35.24/5.56 | DELTA: instantiating (co1) with fresh symbols all_91_0, all_91_1, all_91_2, % 35.24/5.56 | all_91_3, all_91_4, all_91_5 gives: % 35.24/5.56 | (4) app(all_91_1, all_91_0) = all_91_5 & app(all_91_3, all_91_0) = all_91_4 % 35.24/5.56 | & app(all_91_3, all_91_2) = all_91_1 & $i(all_91_0) & $i(all_91_1) & % 35.24/5.56 | $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & $i(all_91_5) & % 35.24/5.56 | ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_3) & % 35.24/5.56 | ssList(all_91_4) & ssList(all_91_5) & ! [v0: $i] : ! [v1: $i] : ! % 35.24/5.56 | [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v3) = all_91_5) | ~ (app(v0, v1) % 35.24/5.56 | = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v3) | ~ % 35.24/5.56 | ssList(v1) | ~ ssList(v0) | ? [v4: any] : ( ~ (v4 = all_91_4) & % 35.24/5.56 | app(v0, v3) = v4 & $i(v4))) % 35.24/5.56 | % 35.24/5.56 | ALPHA: (4) implies: % 35.24/5.56 | (5) ssList(all_91_3) % 35.24/5.57 | (6) ssList(all_91_2) % 35.24/5.57 | (7) ssList(all_91_0) % 35.24/5.57 | (8) $i(all_91_3) % 35.24/5.57 | (9) $i(all_91_2) % 35.24/5.57 | (10) $i(all_91_0) % 35.24/5.57 | (11) app(all_91_3, all_91_2) = all_91_1 % 35.24/5.57 | (12) app(all_91_3, all_91_0) = all_91_4 % 35.24/5.57 | (13) app(all_91_1, all_91_0) = all_91_5 % 35.24/5.57 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, % 35.24/5.57 | v3) = all_91_5) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) % 35.24/5.57 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? % 35.24/5.57 | [v4: any] : ( ~ (v4 = all_91_4) & app(v0, v3) = v4 & $i(v4))) % 35.24/5.57 | % 35.24/5.57 | BETA: splitting (2) gives: % 35.24/5.57 | % 35.24/5.57 | Case 1: % 35.24/5.57 | | % 35.24/5.57 | | (15) ~ ssList(nil) % 35.24/5.57 | | % 35.24/5.57 | | PRED_UNIFY: (1), (15) imply: % 35.24/5.57 | | (16) $false % 35.24/5.57 | | % 35.24/5.57 | | CLOSE: (16) is inconsistent. % 35.24/5.57 | | % 35.24/5.57 | Case 2: % 35.24/5.57 | | % 35.24/5.57 | | % 35.24/5.57 | | GROUND_INST: instantiating (14) with all_91_3, all_91_2, all_91_1, all_91_0, % 35.24/5.57 | | simplifying with (5), (6), (7), (8), (9), (10), (11), (13) % 35.24/5.57 | | gives: % 35.24/5.57 | | (17) ? [v0: any] : ( ~ (v0 = all_91_4) & app(all_91_3, all_91_0) = v0 & % 35.24/5.57 | | $i(v0)) % 35.24/5.57 | | % 35.24/5.57 | | DELTA: instantiating (17) with fresh symbol all_114_0 gives: % 35.67/5.57 | | (18) ~ (all_114_0 = all_91_4) & app(all_91_3, all_91_0) = all_114_0 & % 35.67/5.57 | | $i(all_114_0) % 35.67/5.57 | | % 35.67/5.57 | | ALPHA: (18) implies: % 35.67/5.58 | | (19) ~ (all_114_0 = all_91_4) % 35.67/5.58 | | (20) app(all_91_3, all_91_0) = all_114_0 % 35.67/5.58 | | % 35.67/5.58 | | GROUND_INST: instantiating (3) with all_91_4, all_114_0, all_91_0, all_91_3, % 35.67/5.58 | | simplifying with (12), (20) gives: % 35.67/5.58 | | (21) all_114_0 = all_91_4 % 35.67/5.58 | | % 35.67/5.58 | | REDUCE: (19), (21) imply: % 35.67/5.58 | | (22) $false % 35.67/5.58 | | % 35.67/5.58 | | CLOSE: (22) is inconsistent. % 35.67/5.58 | | % 35.67/5.58 | End of split % 35.67/5.58 | % 35.67/5.58 End of proof % 35.67/5.58 % SZS output end Proof for theBenchmark % 35.67/5.58 % 35.67/5.58 4993ms %------------------------------------------------------------------------------