%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC317+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 : n024.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 20:50:48 EDT 2023 % Result : Theorem 23.37s 3.76s % Output : Proof 31.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC317+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.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 15:05:23 EDT 2023 % 0.13/0.34 % 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. % 0.20/0.64 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 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 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 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 % 5.83/1.48 Prover 4: Preprocessing ... % 5.83/1.48 Prover 2: Preprocessing ... % 5.83/1.48 Prover 0: Preprocessing ... % 5.83/1.48 Prover 3: Preprocessing ... % 5.83/1.49 Prover 5: Preprocessing ... % 6.17/1.50 Prover 6: Preprocessing ... % 6.17/1.52 Prover 1: Preprocessing ... % 15.38/2.74 Prover 1: Constructing countermodel ... % 15.38/2.75 Prover 2: Proving ... % 15.38/2.75 Prover 3: Constructing countermodel ... % 15.38/2.76 Prover 5: Constructing countermodel ... % 15.38/2.79 Prover 6: Proving ... % 21.67/3.55 Prover 4: Constructing countermodel ... % 22.52/3.65 Prover 0: Proving ... % 23.37/3.76 Prover 0: proved (3126ms) % 23.37/3.76 % 23.37/3.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.37/3.76 % 23.37/3.77 Prover 5: stopped % 23.37/3.78 Prover 3: proved (3128ms) % 23.37/3.78 % 23.37/3.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.37/3.78 % 23.37/3.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.37/3.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.37/3.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.37/3.78 Prover 6: stopped % 23.37/3.78 Prover 2: stopped % 23.37/3.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.37/3.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.86/3.97 Prover 8: Preprocessing ... % 24.86/3.99 Prover 13: Preprocessing ... % 24.86/4.01 Prover 11: Preprocessing ... % 25.40/4.03 Prover 7: Preprocessing ... % 25.40/4.03 Prover 10: Preprocessing ... % 27.06/4.25 Prover 10: Constructing countermodel ... % 27.22/4.27 Prover 7: Constructing countermodel ... % 27.75/4.34 Prover 13: Constructing countermodel ... % 28.11/4.39 Prover 8: Warning: ignoring some quantifiers % 28.11/4.41 Prover 8: Constructing countermodel ... % 28.73/4.55 Prover 10: Found proof (size 18) % 28.73/4.55 Prover 10: proved (768ms) % 28.73/4.55 Prover 4: stopped % 28.73/4.55 Prover 7: stopped % 28.73/4.55 Prover 1: stopped % 28.73/4.55 Prover 8: stopped % 28.73/4.55 Prover 13: stopped % 31.41/5.03 Prover 11: Constructing countermodel ... % 31.41/5.05 Prover 11: stopped % 31.41/5.05 % 31.41/5.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 31.41/5.05 % 31.41/5.06 % SZS output start Proof for theBenchmark % 31.41/5.07 Assumptions after simplification: % 31.41/5.07 --------------------------------- % 31.41/5.07 % 31.41/5.07 (ax17) % 31.41/5.07 $i(nil) & ssList(nil) % 31.41/5.07 % 31.41/5.07 (ax58) % 31.41/5.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 31.41/5.08 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 31.41/5.08 % 31.41/5.08 (co1) % 31.67/5.12 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 31.67/5.12 : (cons(v2, nil) = v3 & app(v4, v3) = v1 & app(v3, v4) = v0 & $i(v4) & $i(v3) % 31.67/5.12 & $i(v2) & $i(v1) & $i(v0) & ssList(v4) & ssList(v1) & ssList(v0) & neq(v1, % 31.67/5.12 nil) & ssItem(v2) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 31.67/5.12 (cons(v5, nil) = v6) | ~ (app(v6, v7) = v0) | ~ $i(v7) | ~ $i(v5) | ~ % 31.67/5.12 ssList(v7) | ~ ssItem(v5) | ? [v8: $i] : ( ~ (v8 = v1) & app(v7, v6) = % 31.67/5.12 v8 & $i(v8)))) % 31.67/5.12 % 31.67/5.12 (function-axioms) % 31.67/5.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.67/5.12 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 31.67/5.12 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 31.67/5.12 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 31.67/5.13 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 31.67/5.13 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 31.67/5.13 % 31.67/5.13 Further assumptions not needed in the proof: % 31.67/5.13 -------------------------------------------- % 31.67/5.13 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, % 31.67/5.13 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, % 31.67/5.13 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, % 31.67/5.13 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, % 31.67/5.13 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, % 31.67/5.13 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 31.67/5.13 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, % 31.67/5.13 ax94, ax95 % 31.67/5.13 % 31.67/5.13 Those formulas are unsatisfiable: % 31.67/5.13 --------------------------------- % 31.67/5.13 % 31.67/5.13 Begin of proof % 31.67/5.13 | % 31.67/5.13 | ALPHA: (ax17) implies: % 31.67/5.13 | (1) ssList(nil) % 31.67/5.13 | % 31.67/5.13 | ALPHA: (ax58) implies: % 31.67/5.13 | (2) ~ ssList(nil) | segmentP(nil, nil) % 31.67/5.13 | % 31.67/5.13 | ALPHA: (co1) implies: % 31.67/5.13 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 31.67/5.13 | (cons(v2, nil) = v3 & app(v4, v3) = v1 & app(v3, v4) = v0 & $i(v4) & % 31.67/5.13 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v4) & ssList(v1) & % 31.67/5.13 | ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v5: $i] : ! [v6: $i] : % 31.67/5.13 | ! [v7: $i] : ( ~ (cons(v5, nil) = v6) | ~ (app(v6, v7) = v0) | ~ % 31.67/5.13 | $i(v7) | ~ $i(v5) | ~ ssList(v7) | ~ ssItem(v5) | ? [v8: $i] : % 31.67/5.13 | ( ~ (v8 = v1) & app(v7, v6) = v8 & $i(v8)))) % 31.67/5.13 | % 31.67/5.13 | ALPHA: (function-axioms) implies: % 31.67/5.14 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.67/5.14 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 31.67/5.14 | % 31.67/5.14 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2, % 31.67/5.14 | all_91_3, all_91_4 gives: % 31.67/5.14 | (5) cons(all_91_2, nil) = all_91_1 & app(all_91_0, all_91_1) = all_91_3 & % 31.67/5.14 | app(all_91_1, all_91_0) = all_91_4 & $i(all_91_0) & $i(all_91_1) & % 31.67/5.14 | $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & ssList(all_91_0) & % 31.67/5.14 | ssList(all_91_3) & ssList(all_91_4) & neq(all_91_3, nil) & % 31.67/5.14 | ssItem(all_91_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 31.67/5.14 | (cons(v0, nil) = v1) | ~ (app(v1, v2) = all_91_4) | ~ $i(v2) | ~ % 31.67/5.14 | $i(v0) | ~ ssList(v2) | ~ ssItem(v0) | ? [v3: any] : ( ~ (v3 = % 31.67/5.14 | all_91_3) & app(v2, v1) = v3 & $i(v3))) % 31.67/5.14 | % 31.67/5.14 | ALPHA: (5) implies: % 31.67/5.14 | (6) ssItem(all_91_2) % 31.67/5.14 | (7) ssList(all_91_0) % 31.67/5.14 | (8) $i(all_91_2) % 31.67/5.14 | (9) $i(all_91_0) % 31.67/5.14 | (10) app(all_91_1, all_91_0) = all_91_4 % 31.67/5.14 | (11) app(all_91_0, all_91_1) = all_91_3 % 31.67/5.14 | (12) cons(all_91_2, nil) = all_91_1 % 31.67/5.14 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, nil) = v1) | % 31.67/5.14 | ~ (app(v1, v2) = all_91_4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v2) | % 31.67/5.14 | ~ ssItem(v0) | ? [v3: any] : ( ~ (v3 = all_91_3) & app(v2, v1) = % 31.67/5.14 | v3 & $i(v3))) % 31.67/5.14 | % 31.67/5.14 | BETA: splitting (2) gives: % 31.67/5.14 | % 31.67/5.15 | Case 1: % 31.67/5.15 | | % 31.67/5.15 | | (14) ~ ssList(nil) % 31.67/5.15 | | % 31.67/5.15 | | PRED_UNIFY: (1), (14) imply: % 31.67/5.15 | | (15) $false % 31.67/5.15 | | % 31.67/5.15 | | CLOSE: (15) is inconsistent. % 31.67/5.15 | | % 31.67/5.15 | Case 2: % 31.67/5.15 | | % 31.67/5.15 | | % 31.67/5.15 | | GROUND_INST: instantiating (13) with all_91_2, all_91_1, all_91_0, % 31.67/5.15 | | simplifying with (6), (7), (8), (9), (10), (12) gives: % 31.67/5.15 | | (16) ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_91_0, all_91_1) = v0 & % 31.67/5.15 | | $i(v0)) % 31.67/5.15 | | % 31.67/5.15 | | DELTA: instantiating (16) with fresh symbol all_116_0 gives: % 31.67/5.15 | | (17) ~ (all_116_0 = all_91_3) & app(all_91_0, all_91_1) = all_116_0 & % 31.67/5.15 | | $i(all_116_0) % 31.67/5.15 | | % 31.67/5.15 | | ALPHA: (17) implies: % 31.67/5.15 | | (18) ~ (all_116_0 = all_91_3) % 31.67/5.15 | | (19) app(all_91_0, all_91_1) = all_116_0 % 31.67/5.15 | | % 31.67/5.15 | | GROUND_INST: instantiating (4) with all_91_3, all_116_0, all_91_1, all_91_0, % 31.67/5.15 | | simplifying with (11), (19) gives: % 31.67/5.15 | | (20) all_116_0 = all_91_3 % 31.67/5.15 | | % 31.67/5.15 | | REDUCE: (18), (20) imply: % 31.67/5.15 | | (21) $false % 31.67/5.15 | | % 31.67/5.15 | | CLOSE: (21) is inconsistent. % 31.67/5.15 | | % 31.67/5.15 | End of split % 31.67/5.15 | % 31.67/5.15 End of proof % 31.67/5.15 % SZS output end Proof for theBenchmark % 31.67/5.15 % 31.67/5.15 4534ms %------------------------------------------------------------------------------