%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC364+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 : n005.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 20:51:03 EDT 2023 % Result : Theorem 88.30s 17.79s % Output : Proof 88.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SWC364+1 : TPTP v8.1.2. Released v2.4.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n005.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 16:54:08 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.46/1.65 Prover 1: Preprocessing ... % 4.46/1.66 Prover 4: Preprocessing ... % 4.46/1.69 Prover 6: Preprocessing ... % 4.46/1.69 Prover 2: Preprocessing ... % 4.46/1.69 Prover 0: Preprocessing ... % 4.46/1.69 Prover 3: Preprocessing ... % 4.82/1.72 Prover 5: Preprocessing ... % 13.98/3.59 Prover 2: Proving ... % 14.18/3.64 Prover 5: Constructing countermodel ... % 14.18/3.73 Prover 1: Constructing countermodel ... % 14.18/3.74 Prover 6: Proving ... % 14.48/3.79 Prover 3: Constructing countermodel ... % 20.63/4.96 Prover 4: Constructing countermodel ... % 22.16/5.32 Prover 0: Proving ... % 56.61/11.96 Prover 2: stopped % 56.61/11.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 58.18/12.19 Prover 7: Preprocessing ... % 59.92/12.48 Prover 7: Constructing countermodel ... % 67.39/14.00 Prover 5: stopped % 67.39/14.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 68.81/14.17 Prover 8: Preprocessing ... % 68.81/14.18 Prover 3: gave up % 68.81/14.20 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 69.65/14.33 Prover 9: Preprocessing ... % 70.74/14.66 Prover 8: Warning: ignoring some quantifiers % 71.31/14.68 Prover 8: Constructing countermodel ... % 77.54/15.92 Prover 9: Constructing countermodel ... % 77.54/15.99 Prover 1: stopped % 77.89/16.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 78.64/16.12 Prover 10: Preprocessing ... % 79.57/16.30 Prover 10: Constructing countermodel ... % 88.30/17.77 Prover 10: Found proof (size 31) % 88.30/17.77 Prover 10: proved (1770ms) % 88.30/17.77 Prover 0: stopped % 88.30/17.77 Prover 7: stopped % 88.30/17.77 Prover 9: stopped % 88.30/17.78 Prover 8: stopped % 88.30/17.78 Prover 6: stopped % 88.30/17.78 Prover 4: stopped % 88.30/17.78 % 88.30/17.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 88.30/17.79 % 88.30/17.79 % SZS output start Proof for theBenchmark % 88.52/17.80 Assumptions after simplification: % 88.52/17.80 --------------------------------- % 88.52/17.80 % 88.52/17.80 (ax1) % 88.52/17.81 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) | % 88.52/17.81 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) | % 88.52/17.81 ~ ssItem(v0)) % 88.52/17.81 % 88.52/17.81 (ax16) % 88.71/17.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1) % 88.71/17.85 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) % 88.71/17.85 % 88.71/17.85 (ax17) % 88.71/17.85 $i(nil) & ssList(nil) % 88.71/17.85 % 88.71/17.85 (ax2) % 88.71/17.85 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) & % 88.71/17.85 ssItem(v0)) % 88.71/17.85 % 88.71/17.85 (ax42) % 88.71/17.85 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0)) % 88.71/17.85 % 88.71/17.85 (ax5) % 88.71/17.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 88.71/17.86 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 88.71/17.86 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 88.71/17.86 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 88.71/17.86 v2) = v0 & $i(v2) & ssList(v2))) % 88.71/17.86 % 88.71/17.86 (ax58) % 88.71/17.86 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 88.71/17.86 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 88.71/17.86 % 88.71/17.86 (ax7) % 88.71/17.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 88.71/17.86 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 88.71/17.86 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 88.71/17.86 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 88.71/17.86 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 88.71/17.86 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 88.71/17.86 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 88.71/17.86 % 88.71/17.86 (ax81) % 88.71/17.87 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 88.71/17.87 (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 88.71/17.87 ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3))) % 88.71/17.87 % 88.71/17.87 (co1) % 88.71/17.87 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2, % 88.71/17.87 nil) = v3 & app(v3, v0) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 88.71/17.87 ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ~ segmentP(v1, v0)) % 88.71/17.87 % 88.71/17.87 Further assumptions not needed in the proof: % 88.71/17.87 -------------------------------------------- % 88.71/17.87 ax10, ax11, ax12, ax13, ax14, ax15, ax18, ax19, ax20, ax21, ax22, ax23, ax24, % 88.71/17.87 ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 88.71/17.87 ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax45, ax46, ax47, ax48, ax49, % 88.71/17.87 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6, ax60, ax61, ax62, % 88.71/17.87 ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, % 88.71/17.87 ax76, ax77, ax78, ax79, ax8, ax80, ax82, ax83, ax84, ax85, ax86, ax87, ax88, % 88.71/17.87 ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 88.71/17.87 % 88.71/17.87 Those formulas are unsatisfiable: % 88.71/17.87 --------------------------------- % 88.71/17.87 % 88.71/17.87 Begin of proof % 88.71/17.87 | % 88.71/17.87 | ALPHA: (ax1) implies: % 88.71/17.87 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 88.71/17.87 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 88.71/17.87 | % 88.71/17.87 | ALPHA: (ax5) implies: % 88.71/17.87 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 88.71/17.87 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 88.71/17.87 | v0 & $i(v2) & ssList(v2))) % 88.71/17.88 | % 88.71/17.88 | ALPHA: (ax7) implies: % 88.71/17.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 88.71/17.88 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 88.71/17.88 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 88.71/17.88 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 88.71/17.88 | % 88.71/17.88 | ALPHA: (ax17) implies: % 88.71/17.88 | (4) ssList(nil) % 88.71/17.88 | % 88.71/17.88 | ALPHA: (ax58) implies: % 88.71/17.88 | (5) ~ ssList(nil) | segmentP(nil, nil) % 88.71/17.88 | % 88.71/17.88 | ALPHA: (ax81) implies: % 88.71/17.88 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, % 88.71/17.88 | nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 88.71/17.88 | ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3))) % 88.71/17.88 | % 88.71/17.88 | ALPHA: (co1) implies: % 88.71/17.88 | (7) $i(nil) % 88.71/17.88 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) % 88.71/17.88 | = v3 & app(v3, v0) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 88.71/17.88 | ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ~ segmentP(v1, % 88.71/17.88 | v0)) % 88.71/17.88 | % 88.71/17.89 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives: % 88.71/17.89 | (9) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) & % 88.71/17.89 | ssItem(all_89_0) & ssItem(all_89_1) % 88.71/17.89 | % 88.71/17.89 | ALPHA: (9) implies: % 88.71/17.89 | (10) ~ (all_89_0 = all_89_1) % 88.71/17.89 | (11) ssItem(all_89_1) % 88.71/17.89 | (12) ssItem(all_89_0) % 88.71/17.89 | (13) $i(all_89_1) % 88.71/17.89 | (14) $i(all_89_0) % 88.71/17.89 | % 88.71/17.89 | DELTA: instantiating (8) with fresh symbols all_91_0, all_91_1, all_91_2, % 88.71/17.89 | all_91_3 gives: % 88.71/17.89 | (15) cons(all_91_1, nil) = all_91_0 & app(all_91_0, all_91_3) = all_91_2 & % 88.71/17.89 | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & % 88.71/17.89 | ssList(all_91_2) & ssList(all_91_3) & neq(all_91_2, nil) & % 88.71/17.89 | ssItem(all_91_1) & ~ segmentP(all_91_2, all_91_3) % 88.71/17.89 | % 88.71/17.89 | ALPHA: (15) implies: % 88.71/17.89 | (16) ~ segmentP(all_91_2, all_91_3) % 88.71/17.89 | (17) ssItem(all_91_1) % 88.71/17.89 | (18) ssList(all_91_3) % 88.71/17.89 | (19) ssList(all_91_2) % 88.71/17.89 | (20) $i(all_91_3) % 88.71/17.89 | (21) $i(all_91_2) % 88.71/17.89 | (22) $i(all_91_1) % 88.71/17.89 | (23) $i(all_91_0) % 88.71/17.89 | (24) app(all_91_0, all_91_3) = all_91_2 % 88.71/17.89 | (25) cons(all_91_1, nil) = all_91_0 % 88.71/17.89 | % 88.71/17.89 | BETA: splitting (5) gives: % 88.71/17.89 | % 88.71/17.89 | Case 1: % 88.71/17.89 | | % 88.71/17.89 | | (26) ~ ssList(nil) % 88.71/17.89 | | % 88.71/17.89 | | PRED_UNIFY: (4), (26) imply: % 88.71/17.89 | | (27) $false % 88.71/17.90 | | % 88.71/17.90 | | CLOSE: (27) is inconsistent. % 88.71/17.90 | | % 88.71/17.90 | Case 2: % 88.71/17.90 | | % 88.71/17.90 | | % 88.71/17.90 | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with % 88.71/17.90 | | (11), (12), (13), (14) gives: % 88.71/17.90 | | (28) all_89_0 = all_89_1 | neq(all_89_1, all_89_0) % 88.71/17.90 | | % 88.71/17.90 | | GROUND_INST: instantiating (ax42) with all_91_2, simplifying with (19), (21) % 88.71/17.90 | | gives: % 88.71/17.90 | | (29) frontsegP(all_91_2, all_91_2) % 88.71/17.90 | | % 88.71/17.90 | | GROUND_INST: instantiating (ax16) with nil, all_91_1, all_91_0, simplifying % 88.71/17.90 | | with (4), (7), (17), (22), (25) gives: % 88.71/17.90 | | (30) ssList(all_91_0) % 88.71/17.90 | | % 88.71/17.90 | | GROUND_INST: instantiating (6) with all_91_3, all_91_1, all_91_0, all_91_2, % 88.71/17.90 | | simplifying with (17), (18), (20), (22), (24), (25) gives: % 88.71/17.90 | | (31) cons(all_91_1, all_91_3) = all_91_2 & $i(all_91_2) % 88.71/17.90 | | % 88.71/17.90 | | BETA: splitting (28) gives: % 88.71/17.90 | | % 88.71/17.90 | | Case 1: % 88.71/17.90 | | | % 88.71/17.90 | | | % 88.71/17.90 | | | GROUND_INST: instantiating (2) with all_91_2, all_91_2, simplifying with % 88.71/17.90 | | | (19), (21), (29) gives: % 88.71/17.90 | | | (32) ? [v0: $i] : (app(all_91_2, v0) = all_91_2 & $i(v0) & ssList(v0)) % 88.71/17.90 | | | % 88.71/17.90 | | | DELTA: instantiating (32) with fresh symbol all_141_0 gives: % 88.71/17.90 | | | (33) app(all_91_2, all_141_0) = all_91_2 & $i(all_141_0) & % 88.71/17.90 | | | ssList(all_141_0) % 88.71/17.90 | | | % 88.71/17.90 | | | ALPHA: (33) implies: % 88.71/17.90 | | | (34) ssList(all_141_0) % 88.71/17.90 | | | (35) $i(all_141_0) % 88.71/17.91 | | | (36) app(all_91_2, all_141_0) = all_91_2 % 88.71/17.91 | | | % 88.71/17.91 | | | GROUND_INST: instantiating (3) with all_91_2, all_91_3, all_91_0, % 88.71/17.91 | | | all_91_2, all_141_0, simplifying with (16), (18), (19), (20), % 88.71/17.91 | | | (21), (23), (24), (30), (34), (35), (36) gives: % 88.71/17.91 | | | (37) $false % 88.71/17.91 | | | % 88.71/17.91 | | | CLOSE: (37) is inconsistent. % 88.71/17.91 | | | % 88.71/17.91 | | Case 2: % 88.71/17.91 | | | % 88.71/17.91 | | | (38) all_89_0 = all_89_1 % 88.71/17.91 | | | % 88.71/17.91 | | | REDUCE: (10), (38) imply: % 88.71/17.91 | | | (39) $false % 88.71/17.91 | | | % 88.71/17.91 | | | CLOSE: (39) is inconsistent. % 88.71/17.91 | | | % 88.71/17.91 | | End of split % 88.71/17.91 | | % 88.71/17.91 | End of split % 88.71/17.91 | % 88.71/17.91 End of proof % 88.71/17.91 % SZS output end Proof for theBenchmark % 88.71/17.91 % 88.71/17.91 17305ms %------------------------------------------------------------------------------