%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC241+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 : n029.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 20:50:24 EDT 2023 % Result : Theorem 31.85s 4.86s % Output : Proof 40.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWC241+1 : TPTP v8.1.2. Released v2.4.0. % 0.04/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 19:25:26 EDT 2023 % 0.12/0.33 % CPUTime : % 0.57/0.59 ________ _____ % 0.57/0.59 ___ __ \_________(_)________________________________ % 0.57/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.60 % 0.57/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.60 (2023-06-19) % 0.57/0.60 % 0.57/0.60 (c) Philipp Rümmer, 2009-2023 % 0.57/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.60 Amanda Stjerna. % 0.57/0.60 Free software under BSD-3-Clause. % 0.57/0.60 % 0.57/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.60 % 0.57/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.57/0.61 Running up to 7 provers in parallel. % 0.57/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.09/1.44 Prover 1: Preprocessing ... % 5.09/1.44 Prover 4: Preprocessing ... % 5.72/1.48 Prover 2: Preprocessing ... % 5.72/1.48 Prover 5: Preprocessing ... % 5.96/1.48 Prover 6: Preprocessing ... % 5.96/1.49 Prover 0: Preprocessing ... % 5.96/1.49 Prover 3: Preprocessing ... % 16.27/2.87 Prover 2: Proving ... % 16.70/2.95 Prover 5: Constructing countermodel ... % 17.22/2.97 Prover 3: Constructing countermodel ... % 17.22/2.98 Prover 6: Proving ... % 17.55/3.01 Prover 1: Constructing countermodel ... % 21.27/3.49 Prover 4: Constructing countermodel ... % 22.59/3.67 Prover 0: Proving ... % 31.85/4.86 Prover 3: proved (4239ms) % 31.85/4.86 % 31.85/4.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 31.85/4.86 % 31.85/4.86 Prover 5: stopped % 31.85/4.86 Prover 6: stopped % 31.85/4.88 Prover 2: stopped % 31.85/4.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 31.85/4.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 31.85/4.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 31.85/4.89 Prover 0: stopped % 31.85/4.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 31.85/4.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 33.94/5.11 Prover 7: Preprocessing ... % 34.08/5.14 Prover 13: Preprocessing ... % 34.08/5.19 Prover 11: Preprocessing ... % 34.08/5.19 Prover 10: Preprocessing ... % 34.08/5.20 Prover 8: Preprocessing ... % 35.90/5.36 Prover 10: Constructing countermodel ... % 35.90/5.37 Prover 13: Constructing countermodel ... % 36.03/5.40 Prover 7: Constructing countermodel ... % 37.70/5.63 Prover 8: Warning: ignoring some quantifiers % 37.70/5.65 Prover 8: Constructing countermodel ... % 38.57/5.72 Prover 10: Found proof (size 17) % 38.57/5.72 Prover 10: proved (838ms) % 38.57/5.72 Prover 13: stopped % 38.57/5.72 Prover 7: stopped % 38.57/5.72 Prover 1: stopped % 38.57/5.72 Prover 8: stopped % 38.57/5.72 Prover 4: stopped % 40.05/6.07 Prover 11: Constructing countermodel ... % 40.05/6.09 Prover 11: stopped % 40.05/6.10 % 40.05/6.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 40.05/6.10 % 40.05/6.10 % SZS output start Proof for theBenchmark % 40.05/6.11 Assumptions after simplification: % 40.05/6.11 --------------------------------- % 40.05/6.11 % 40.05/6.11 (ax17) % 40.05/6.12 $i(nil) & ssList(nil) % 40.05/6.12 % 40.05/6.12 (ax58) % 40.05/6.12 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 40.05/6.12 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 40.05/6.12 % 40.05/6.12 (ax93) % 40.05/6.12 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 40.05/6.12 | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) & ! [v0: $i] : ! [v1: $i] : % 40.05/6.12 ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | % 40.05/6.12 leq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ lt(v0, v0) | ~ ssItem(v0)) % 40.05/6.12 % 40.05/6.13 (co1) % 40.45/6.17 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 40.45/6.17 : ? [v5: $i] : ? [v6: $i] : ( ~ (v0 = nil) & cons(v2, nil) = v3 & app(v5, % 40.45/6.17 v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 40.45/6.17 $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) & % 40.45/6.17 ssItem(v2) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! % 40.45/6.17 [v11: $i] : ( ~ (cons(v7, nil) = v8) | ~ (app(v10, v11) = v0) | ~ (app(v9, % 40.45/6.17 v8) = v10) | ~ $i(v11) | ~ $i(v9) | ~ $i(v7) | ~ ssList(v11) | ~ % 40.45/6.17 ssList(v9) | ~ ssItem(v7) | ? [v12: $i] : ($i(v12) & lt(v7, v12) & % 40.45/6.17 memberP(v11, v12) & memberP(v9, v12) & ssItem(v12) & ~ leq(v7, v12))) & % 40.45/6.17 ! [v7: $i] : ( ~ $i(v7) | ~ leq(v2, v7) | ~ memberP(v6, v7) | ~ % 40.45/6.17 memberP(v4, v7) | ~ ssItem(v7) | leq(v7, v2))) % 40.45/6.17 % 40.45/6.17 Further assumptions not needed in the proof: % 40.45/6.17 -------------------------------------------- % 40.45/6.17 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, % 40.45/6.17 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, % 40.45/6.17 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, % 40.45/6.17 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, % 40.45/6.17 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, % 40.45/6.17 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, % 40.45/6.17 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax94, % 40.45/6.17 ax95 % 40.45/6.17 % 40.45/6.17 Those formulas are unsatisfiable: % 40.45/6.17 --------------------------------- % 40.45/6.17 % 40.45/6.17 Begin of proof % 40.45/6.17 | % 40.45/6.17 | ALPHA: (ax17) implies: % 40.45/6.17 | (1) ssList(nil) % 40.45/6.17 | % 40.45/6.17 | ALPHA: (ax58) implies: % 40.45/6.17 | (2) ~ ssList(nil) | segmentP(nil, nil) % 40.45/6.17 | % 40.45/6.17 | ALPHA: (ax93) implies: % 40.45/6.17 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~ % 40.45/6.17 | ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) % 40.45/6.17 | % 40.45/6.17 | ALPHA: (co1) implies: % 40.45/6.18 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 40.45/6.18 | ? [v5: $i] : ? [v6: $i] : ( ~ (v0 = nil) & cons(v2, nil) = v3 & % 40.45/6.18 | app(v5, v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & % 40.45/6.18 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & % 40.45/6.18 | ssList(v1) & ssList(v0) & ssItem(v2) & ! [v7: $i] : ! [v8: $i] : ! % 40.45/6.18 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ (cons(v7, nil) = v8) | % 40.45/6.18 | ~ (app(v10, v11) = v0) | ~ (app(v9, v8) = v10) | ~ $i(v11) | ~ % 40.45/6.18 | $i(v9) | ~ $i(v7) | ~ ssList(v11) | ~ ssList(v9) | ~ ssItem(v7) % 40.45/6.18 | | ? [v12: $i] : ($i(v12) & lt(v7, v12) & memberP(v11, v12) & % 40.45/6.18 | memberP(v9, v12) & ssItem(v12) & ~ leq(v7, v12))) & ! [v7: $i] % 40.45/6.18 | : ( ~ $i(v7) | ~ leq(v2, v7) | ~ memberP(v6, v7) | ~ memberP(v4, % 40.45/6.18 | v7) | ~ ssItem(v7) | leq(v7, v2))) % 40.45/6.18 | % 40.45/6.18 | DELTA: instantiating (4) with fresh symbols all_91_0, all_91_1, all_91_2, % 40.45/6.18 | all_91_3, all_91_4, all_91_5, all_91_6 gives: % 40.45/6.18 | (5) ~ (all_91_6 = nil) & cons(all_91_4, nil) = all_91_3 & app(all_91_1, % 40.45/6.18 | all_91_0) = all_91_6 & app(all_91_2, all_91_3) = all_91_1 & % 40.45/6.18 | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & % 40.45/6.18 | $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_0) & % 40.45/6.18 | ssList(all_91_2) & ssList(all_91_5) & ssList(all_91_6) & % 40.45/6.18 | ssItem(all_91_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 40.45/6.18 | $i] : ! [v4: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = % 40.45/6.18 | all_91_6) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 40.45/6.18 | $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i] % 40.45/6.18 | : ($i(v5) & lt(v0, v5) & memberP(v4, v5) & memberP(v2, v5) & % 40.45/6.18 | ssItem(v5) & ~ leq(v0, v5))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 40.45/6.18 | leq(all_91_4, v0) | ~ memberP(all_91_0, v0) | ~ memberP(all_91_2, % 40.45/6.18 | v0) | ~ ssItem(v0) | leq(v0, all_91_4)) % 40.45/6.18 | % 40.45/6.18 | ALPHA: (5) implies: % 40.45/6.18 | (6) ssItem(all_91_4) % 40.45/6.18 | (7) ssList(all_91_2) % 40.45/6.18 | (8) ssList(all_91_0) % 40.45/6.18 | (9) $i(all_91_4) % 40.45/6.18 | (10) $i(all_91_2) % 40.45/6.18 | (11) $i(all_91_0) % 40.45/6.18 | (12) app(all_91_2, all_91_3) = all_91_1 % 40.45/6.18 | (13) app(all_91_1, all_91_0) = all_91_6 % 40.45/6.18 | (14) cons(all_91_4, nil) = all_91_3 % 40.45/6.18 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 40.45/6.18 | ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = all_91_6) | ~ (app(v2, % 40.45/6.18 | v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) | % 40.45/6.18 | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i] : ($i(v5) & lt(v0, v5) & % 40.45/6.18 | memberP(v4, v5) & memberP(v2, v5) & ssItem(v5) & ~ leq(v0, v5))) % 40.45/6.18 | % 40.45/6.18 | BETA: splitting (2) gives: % 40.45/6.18 | % 40.45/6.18 | Case 1: % 40.45/6.18 | | % 40.45/6.18 | | (16) ~ ssList(nil) % 40.45/6.18 | | % 40.45/6.18 | | PRED_UNIFY: (1), (16) imply: % 40.45/6.19 | | (17) $false % 40.45/6.19 | | % 40.45/6.19 | | CLOSE: (17) is inconsistent. % 40.45/6.19 | | % 40.45/6.19 | Case 2: % 40.45/6.19 | | % 40.45/6.19 | | % 40.45/6.19 | | GROUND_INST: instantiating (15) with all_91_4, all_91_3, all_91_2, all_91_1, % 40.45/6.19 | | all_91_0, simplifying with (6), (7), (8), (9), (10), (11), % 40.45/6.19 | | (12), (13), (14) gives: % 40.45/6.19 | | (18) ? [v0: $i] : ($i(v0) & lt(all_91_4, v0) & memberP(all_91_0, v0) & % 40.45/6.19 | | memberP(all_91_2, v0) & ssItem(v0) & ~ leq(all_91_4, v0)) % 40.45/6.19 | | % 40.45/6.19 | | DELTA: instantiating (18) with fresh symbol all_116_0 gives: % 40.45/6.19 | | (19) $i(all_116_0) & lt(all_91_4, all_116_0) & memberP(all_91_0, % 40.45/6.19 | | all_116_0) & memberP(all_91_2, all_116_0) & ssItem(all_116_0) & ~ % 40.45/6.19 | | leq(all_91_4, all_116_0) % 40.45/6.19 | | % 40.45/6.19 | | ALPHA: (19) implies: % 40.45/6.19 | | (20) ~ leq(all_91_4, all_116_0) % 40.45/6.19 | | (21) ssItem(all_116_0) % 40.45/6.19 | | (22) lt(all_91_4, all_116_0) % 40.45/6.19 | | (23) $i(all_116_0) % 40.45/6.19 | | % 40.45/6.19 | | GROUND_INST: instantiating (3) with all_91_4, all_116_0, simplifying with % 40.45/6.19 | | (6), (9), (20), (21), (22), (23) gives: % 40.45/6.19 | | (24) $false % 40.45/6.19 | | % 40.45/6.19 | | CLOSE: (24) is inconsistent. % 40.45/6.19 | | % 40.45/6.19 | End of split % 40.45/6.19 | % 40.45/6.19 End of proof % 40.45/6.19 % SZS output end Proof for theBenchmark % 40.45/6.19 % 40.45/6.19 5594ms %------------------------------------------------------------------------------