%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC273+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 : n003.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 20:50:34 EDT 2023 % Result : Theorem 139.11s 18.85s % Output : Proof 139.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC273+1 : TPTP v8.1.2. Released v2.4.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n003.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 18:01:25 EDT 2023 % 0.13/0.34 % CPUTime : % 0.58/0.59 ________ _____ % 0.58/0.59 ___ __ \_________(_)________________________________ % 0.58/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.58/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.58/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.58/0.59 (2023-06-19) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2023 % 0.58/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.58/0.59 Amanda Stjerna. % 0.58/0.59 Free software under BSD-3-Clause. % 0.58/0.59 % 0.58/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.58/0.60 Running up to 7 provers in parallel. % 0.58/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.58/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.58/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.58/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.58/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.58/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.58/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 6.62/1.62 Prover 4: Preprocessing ... % 6.62/1.64 Prover 1: Preprocessing ... % 6.95/1.65 Prover 3: Preprocessing ... % 6.95/1.65 Prover 2: Preprocessing ... % 6.95/1.65 Prover 0: Preprocessing ... % 6.95/1.65 Prover 5: Preprocessing ... % 6.95/1.65 Prover 6: Preprocessing ... % 16.63/2.98 Prover 2: Proving ... % 16.97/3.03 Prover 5: Constructing countermodel ... % 17.38/3.06 Prover 6: Proving ... % 17.73/3.10 Prover 1: Constructing countermodel ... % 17.73/3.13 Prover 3: Constructing countermodel ... % 22.62/3.77 Prover 4: Constructing countermodel ... % 22.62/3.84 Prover 0: Proving ... % 73.54/10.38 Prover 2: stopped % 73.54/10.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.29/10.54 Prover 7: Preprocessing ... % 76.97/10.79 Prover 7: Constructing countermodel ... % 101.13/13.95 Prover 5: stopped % 101.13/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 101.95/14.07 Prover 8: Preprocessing ... % 103.97/14.29 Prover 8: Warning: ignoring some quantifiers % 103.97/14.30 Prover 8: Constructing countermodel ... % 116.59/15.95 Prover 1: stopped % 116.59/15.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 117.43/16.10 Prover 9: Preprocessing ... % 123.20/16.76 Prover 9: Constructing countermodel ... % 131.76/17.86 Prover 6: stopped % 131.76/17.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.52/17.97 Prover 10: Preprocessing ... % 133.16/18.09 Prover 10: Constructing countermodel ... % 138.68/18.80 Prover 10: Found proof (size 19) % 138.68/18.81 Prover 10: proved (936ms) % 138.68/18.81 Prover 9: stopped % 138.68/18.81 Prover 0: stopped % 138.68/18.81 Prover 3: stopped % 138.68/18.81 Prover 8: stopped % 138.68/18.81 Prover 7: stopped % 139.11/18.85 Prover 4: stopped % 139.11/18.85 % 139.11/18.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 139.11/18.85 % 139.11/18.85 % SZS output start Proof for theBenchmark % 139.32/18.86 Assumptions after simplification: % 139.32/18.86 --------------------------------- % 139.32/18.86 % 139.32/18.86 (ax11) % 139.32/18.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 139.32/18.91 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v7) = v8) | ~ % 139.32/18.91 (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ % 139.32/18.91 $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 139.32/18.91 totalorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ % 139.32/18.91 ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v1, v2)) & ! [v0: $i] : ( % 139.32/18.91 ~ $i(v0) | ~ ssList(v0) | totalorderedP(v0) | ? [v1: $i] : ? [v2: $i] : % 139.32/18.91 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 139.32/18.91 $i] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, % 139.32/18.91 v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 139.32/18.91 & $i(v1) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) % 139.32/18.91 & ~ leq(v1, v2))) % 139.32/18.91 % 139.32/18.91 (ax12) % 139.32/18.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 139.32/18.92 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v7) = v8) | ~ % 139.32/18.92 (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ % 139.32/18.92 $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 139.32/18.92 strictorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ % 139.32/18.92 ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v1, v2)) & ! [v0: $i] : ( ~ % 139.32/18.92 $i(v0) | ~ ssList(v0) | strictorderedP(v0) | ? [v1: $i] : ? [v2: $i] : ? % 139.32/18.92 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 139.32/18.92 $i] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, % 139.32/18.92 v5) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 139.32/18.92 & $i(v1) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) % 139.32/18.92 & ~ lt(v1, v2))) % 139.32/18.92 % 139.32/18.92 (ax17) % 139.32/18.92 $i(nil) & ssList(nil) % 139.32/18.92 % 139.32/18.92 (ax58) % 139.32/18.92 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 139.32/18.92 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 139.32/18.92 % 139.32/18.92 (ax93) % 139.32/18.92 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 139.32/18.92 | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) & ! [v0: $i] : ! [v1: $i] : % 139.32/18.92 ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | % 139.32/18.92 leq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ lt(v0, v0) | ~ ssItem(v0)) % 139.32/18.93 % 139.32/18.93 (co1) % 139.32/18.93 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & strictorderedP(v0) & % 139.32/18.93 segmentP(v1, v0) & ssList(v1) & ssList(v0) & ~ totalorderedP(v0) & ! [v2: % 139.32/18.93 $i] : ( ~ $i(v2) | ~ strictorderedP(v2) | ~ segmentP(v2, v0) | ~ % 139.32/18.93 segmentP(v1, v2) | ~ ssList(v2) | ~ neq(v0, v2))) % 139.32/18.93 % 139.32/18.93 Further assumptions not needed in the proof: % 139.32/18.93 -------------------------------------------- % 139.32/18.93 ax1, ax10, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, ax22, ax23, % 139.32/18.93 ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, % 139.32/18.93 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, % 139.32/18.93 ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6, % 139.32/18.93 ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, % 139.32/18.93 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, % 139.32/18.93 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax94, ax95 % 139.32/18.93 % 139.32/18.93 Those formulas are unsatisfiable: % 139.32/18.93 --------------------------------- % 139.32/18.93 % 139.32/18.93 Begin of proof % 139.32/18.93 | % 139.32/18.93 | ALPHA: (ax11) implies: % 139.32/18.93 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | totalorderedP(v0) | ? [v1: % 139.32/18.93 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 139.32/18.93 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : (cons(v2, v7) = v8 & cons(v1, % 139.32/18.93 | v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & $i(v8) & $i(v7) % 139.32/18.93 | & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & ssList(v7) % 139.32/18.93 | & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ leq(v1, % 139.32/18.93 | v2))) % 139.32/18.93 | % 139.32/18.93 | ALPHA: (ax12) implies: % 139.32/18.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 139.32/18.93 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, % 139.32/18.93 | v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ % 139.32/18.93 | (app(v3, v5) = v6) | ~ $i(v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 139.32/18.93 | ~ $i(v1) | ~ $i(v0) | ~ strictorderedP(v0) | ~ ssList(v7) | ~ % 139.32/18.93 | ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ % 139.32/18.93 | ssItem(v1) | lt(v1, v2)) % 139.32/18.93 | % 139.32/18.93 | ALPHA: (ax17) implies: % 139.32/18.93 | (3) ssList(nil) % 139.32/18.93 | % 139.32/18.93 | ALPHA: (ax58) implies: % 139.32/18.93 | (4) ~ ssList(nil) | segmentP(nil, nil) % 139.32/18.93 | % 139.32/18.93 | ALPHA: (ax93) implies: % 139.32/18.93 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~ % 139.32/18.93 | ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) % 139.32/18.93 | % 139.32/18.93 | DELTA: instantiating (co1) with fresh symbols all_91_0, all_91_1 gives: % 139.32/18.94 | (6) $i(all_91_0) & $i(all_91_1) & strictorderedP(all_91_1) & % 139.32/18.94 | segmentP(all_91_0, all_91_1) & ssList(all_91_0) & ssList(all_91_1) & ~ % 139.32/18.94 | totalorderedP(all_91_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 139.32/18.94 | strictorderedP(v0) | ~ segmentP(v0, all_91_1) | ~ % 139.32/18.94 | segmentP(all_91_0, v0) | ~ ssList(v0) | ~ neq(all_91_1, v0)) % 139.32/18.94 | % 139.32/18.94 | ALPHA: (6) implies: % 139.32/18.94 | (7) ~ totalorderedP(all_91_1) % 139.32/18.94 | (8) ssList(all_91_1) % 139.32/18.94 | (9) strictorderedP(all_91_1) % 139.32/18.94 | (10) $i(all_91_1) % 139.32/18.94 | % 139.32/18.94 | BETA: splitting (4) gives: % 139.32/18.94 | % 139.32/18.94 | Case 1: % 139.32/18.94 | | % 139.32/18.94 | | (11) ~ ssList(nil) % 139.32/18.94 | | % 139.32/18.94 | | PRED_UNIFY: (3), (11) imply: % 139.32/18.94 | | (12) $false % 139.71/18.94 | | % 139.71/18.94 | | CLOSE: (12) is inconsistent. % 139.71/18.94 | | % 139.71/18.94 | Case 2: % 139.71/18.94 | | % 139.71/18.94 | | % 139.71/18.94 | | GROUND_INST: instantiating (1) with all_91_1, simplifying with (7), (8), % 139.71/18.94 | | (10) gives: % 139.71/18.94 | | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 139.71/18.94 | | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (cons(v1, v6) = v7 & % 139.71/18.94 | | cons(v0, v3) = v4 & app(v5, v7) = all_91_1 & app(v2, v4) = v5 & % 139.71/18.94 | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 139.71/18.94 | | $i(v0) & ssList(v6) & ssList(v3) & ssList(v2) & ssItem(v1) & % 139.71/18.94 | | ssItem(v0) & ~ leq(v0, v1)) % 139.71/18.94 | | % 139.71/18.94 | | DELTA: instantiating (13) with fresh symbols all_120_0, all_120_1, % 139.71/18.94 | | all_120_2, all_120_3, all_120_4, all_120_5, all_120_6, all_120_7 % 139.71/18.94 | | gives: % 139.71/18.94 | | (14) cons(all_120_6, all_120_1) = all_120_0 & cons(all_120_7, all_120_4) % 139.71/18.94 | | = all_120_3 & app(all_120_2, all_120_0) = all_91_1 & app(all_120_5, % 139.71/18.94 | | all_120_3) = all_120_2 & $i(all_120_0) & $i(all_120_1) & % 139.71/18.94 | | $i(all_120_2) & $i(all_120_3) & $i(all_120_4) & $i(all_120_5) & % 139.71/18.94 | | $i(all_120_6) & $i(all_120_7) & ssList(all_120_1) & % 139.71/18.94 | | ssList(all_120_4) & ssList(all_120_5) & ssItem(all_120_6) & % 139.71/18.94 | | ssItem(all_120_7) & ~ leq(all_120_7, all_120_6) % 139.71/18.94 | | % 139.71/18.94 | | ALPHA: (14) implies: % 139.71/18.94 | | (15) ~ leq(all_120_7, all_120_6) % 139.71/18.94 | | (16) ssItem(all_120_7) % 139.71/18.94 | | (17) ssItem(all_120_6) % 139.71/18.94 | | (18) ssList(all_120_5) % 139.71/18.94 | | (19) ssList(all_120_4) % 139.71/18.94 | | (20) ssList(all_120_1) % 139.71/18.94 | | (21) $i(all_120_7) % 139.71/18.94 | | (22) $i(all_120_6) % 139.71/18.94 | | (23) $i(all_120_5) % 139.71/18.94 | | (24) $i(all_120_4) % 139.71/18.94 | | (25) $i(all_120_1) % 139.71/18.94 | | (26) app(all_120_5, all_120_3) = all_120_2 % 139.71/18.94 | | (27) app(all_120_2, all_120_0) = all_91_1 % 139.71/18.94 | | (28) cons(all_120_7, all_120_4) = all_120_3 % 139.71/18.94 | | (29) cons(all_120_6, all_120_1) = all_120_0 % 139.71/18.94 | | % 139.71/18.94 | | GROUND_INST: instantiating (2) with all_91_1, all_120_7, all_120_6, % 139.71/18.94 | | all_120_5, all_120_4, all_120_3, all_120_2, all_120_1, % 139.71/18.94 | | all_120_0, simplifying with (8), (9), (10), (16), (17), (18), % 139.71/18.94 | | (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), % 139.71/18.94 | | (29) gives: % 139.71/18.94 | | (30) lt(all_120_7, all_120_6) % 139.71/18.94 | | % 139.71/18.95 | | GROUND_INST: instantiating (5) with all_120_7, all_120_6, simplifying with % 139.71/18.95 | | (15), (16), (17), (21), (22), (30) gives: % 139.71/18.95 | | (31) $false % 139.71/18.95 | | % 139.71/18.95 | | CLOSE: (31) is inconsistent. % 139.71/18.95 | | % 139.71/18.95 | End of split % 139.71/18.95 | % 139.71/18.95 End of proof % 139.71/18.95 % SZS output end Proof for theBenchmark % 139.71/18.95 % 139.71/18.95 18355ms %------------------------------------------------------------------------------