%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC024+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 : n010.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 20:49:14 EDT 2023 % Result : Theorem 80.68s 11.61s % Output : Proof 81.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWC024+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n010.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Mon Aug 28 15:41:34 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.69 ________ _____ % 0.21/0.69 ___ __ \_________(_)________________________________ % 0.21/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.69 % 0.21/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.69 (2023-06-19) % 0.21/0.69 % 0.21/0.69 (c) Philipp Rümmer, 2009-2023 % 0.21/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.69 Amanda Stjerna. % 0.21/0.69 Free software under BSD-3-Clause. % 0.21/0.69 % 0.21/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.69 % 0.21/0.69 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.71 Running up to 7 provers in parallel. % 0.74/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.74/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.74/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.57/1.60 Prover 4: Preprocessing ... % 5.57/1.60 Prover 1: Preprocessing ... % 5.57/1.65 Prover 3: Preprocessing ... % 5.57/1.65 Prover 6: Preprocessing ... % 5.57/1.65 Prover 5: Preprocessing ... % 5.57/1.65 Prover 2: Preprocessing ... % 5.57/1.65 Prover 0: Preprocessing ... % 17.39/3.25 Prover 2: Proving ... % 17.39/3.28 Prover 1: Constructing countermodel ... % 17.39/3.30 Prover 5: Constructing countermodel ... % 17.85/3.32 Prover 6: Proving ... % 17.85/3.38 Prover 3: Constructing countermodel ... % 23.05/4.03 Prover 4: Constructing countermodel ... % 24.53/4.21 Prover 0: Proving ... % 70.92/10.33 Prover 2: stopped % 70.92/10.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.08/10.48 Prover 7: Preprocessing ... % 73.28/10.60 Prover 7: Constructing countermodel ... % 80.68/11.60 Prover 7: Found proof (size 34) % 80.68/11.60 Prover 7: proved (1256ms) % 80.68/11.60 Prover 3: stopped % 80.68/11.60 Prover 6: stopped % 80.68/11.61 Prover 1: stopped % 80.68/11.61 Prover 5: stopped % 80.68/11.61 Prover 0: stopped % 80.68/11.61 Prover 4: stopped % 80.68/11.61 % 80.68/11.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 80.68/11.61 % 80.68/11.62 % SZS output start Proof for theBenchmark % 80.68/11.62 Assumptions after simplification: % 80.68/11.62 --------------------------------- % 80.68/11.62 % 80.68/11.62 (ax15) % 81.32/11.63 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 81.32/11.63 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ % 81.32/11.63 neq(v0, v0)) % 81.32/11.63 % 81.32/11.63 (ax17) % 81.32/11.63 $i(nil) & ssList(nil) % 81.32/11.63 % 81.32/11.63 (ax28) % 81.32/11.65 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 81.32/11.65 $i(v0) | ~ ssList(v0)) % 81.32/11.65 % 81.32/11.65 (ax42) % 81.32/11.65 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0)) % 81.32/11.65 % 81.32/11.65 (ax46) % 81.32/11.65 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 81.32/11.65 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 81.32/11.65 % 81.32/11.65 (ax5) % 81.32/11.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 81.32/11.66 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 81.32/11.66 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 81.32/11.66 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 81.32/11.66 v2) = v0 & $i(v2) & ssList(v2))) % 81.32/11.66 % 81.32/11.66 (co1) % 81.32/11.66 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) % 81.32/11.66 & $i(v1) & $i(v0) & equalelemsP(v0) & ssList(v2) & ssList(v1) & ssList(v0) & % 81.32/11.66 neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 81.32/11.66 (cons(v3, nil) = v4) | ~ (app(v6, v4) = v0) | ~ (app(v4, v5) = v2) | ~ % 81.32/11.66 $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ ssList(v6) | ~ ssList(v5) | ~ % 81.32/11.66 ssItem(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ frontsegP(v1, v3) | ~ % 81.32/11.66 frontsegP(v0, v3) | ~ ssList(v3) | ~ neq(v3, nil)) & ( ~ (v0 = nil) | v1 % 81.32/11.66 = nil)) % 81.32/11.66 % 81.32/11.66 Further assumptions not needed in the proof: % 81.32/11.66 -------------------------------------------- % 81.32/11.66 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 81.32/11.66 ax23, ax24, ax25, ax26, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, % 81.32/11.66 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax45, ax47, ax48, ax49, % 81.32/11.66 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60, ax61, % 81.32/11.66 ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73, % 81.32/11.66 ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, % 81.32/11.66 ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 81.32/11.66 % 81.32/11.66 Those formulas are unsatisfiable: % 81.32/11.66 --------------------------------- % 81.32/11.66 % 81.32/11.66 Begin of proof % 81.32/11.66 | % 81.32/11.66 | ALPHA: (ax5) implies: % 81.32/11.66 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 81.32/11.66 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 81.32/11.67 | v0 & $i(v2) & ssList(v2))) % 81.32/11.67 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ % 81.32/11.67 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ % 81.32/11.67 | ssList(v0) | frontsegP(v0, v1)) % 81.32/11.67 | % 81.32/11.67 | ALPHA: (ax15) implies: % 81.32/11.67 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 81.32/11.67 | ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 81.32/11.67 | % 81.32/11.67 | ALPHA: (ax17) implies: % 81.32/11.67 | (4) ssList(nil) % 81.32/11.67 | % 81.32/11.67 | ALPHA: (ax28) implies: % 81.32/11.67 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 81.32/11.67 | $i(v0) | ~ ssList(v0)) % 81.32/11.67 | % 81.32/11.67 | ALPHA: (ax46) implies: % 81.32/11.67 | (6) ~ ssList(nil) | frontsegP(nil, nil) % 81.32/11.67 | % 81.32/11.67 | ALPHA: (co1) implies: % 81.32/11.67 | (7) $i(nil) % 81.32/11.67 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) & % 81.32/11.67 | $i(v1) & $i(v0) & equalelemsP(v0) & ssList(v2) & ssList(v1) & % 81.32/11.67 | ssList(v0) & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 81.32/11.67 | ! [v6: $i] : ( ~ (cons(v3, nil) = v4) | ~ (app(v6, v4) = v0) | ~ % 81.32/11.67 | (app(v4, v5) = v2) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~ % 81.32/11.67 | ssList(v6) | ~ ssList(v5) | ~ ssItem(v3)) & ! [v3: $i] : ( ~ % 81.32/11.67 | $i(v3) | ~ frontsegP(v1, v3) | ~ frontsegP(v0, v3) | ~ % 81.32/11.67 | ssList(v3) | ~ neq(v3, nil)) & ( ~ (v0 = nil) | v1 = nil)) % 81.32/11.67 | % 81.32/11.67 | DELTA: instantiating (8) with fresh symbols all_91_0, all_91_1, all_91_2 % 81.32/11.67 | gives: % 81.32/11.68 | (9) app(all_91_2, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) & % 81.32/11.68 | $i(all_91_2) & equalelemsP(all_91_2) & ssList(all_91_0) & % 81.32/11.68 | ssList(all_91_1) & ssList(all_91_2) & neq(all_91_1, nil) & ! [v0: $i] % 81.32/11.68 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, nil) = v1) | % 81.32/11.68 | ~ (app(v3, v1) = all_91_2) | ~ (app(v1, v2) = all_91_0) | ~ $i(v3) % 81.32/11.68 | | ~ $i(v2) | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v2) | ~ % 81.32/11.68 | ssItem(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ frontsegP(all_91_1, v0) | % 81.32/11.68 | ~ frontsegP(all_91_2, v0) | ~ ssList(v0) | ~ neq(v0, nil)) & ( ~ % 81.32/11.68 | (all_91_2 = nil) | all_91_1 = nil) % 81.32/11.68 | % 81.32/11.68 | ALPHA: (9) implies: % 81.32/11.68 | (10) neq(all_91_1, nil) % 81.32/11.68 | (11) ssList(all_91_2) % 81.32/11.68 | (12) ssList(all_91_1) % 81.32/11.68 | (13) ssList(all_91_0) % 81.32/11.68 | (14) $i(all_91_2) % 81.32/11.68 | (15) $i(all_91_1) % 81.32/11.68 | (16) $i(all_91_0) % 81.32/11.68 | (17) app(all_91_2, all_91_0) = all_91_1 % 81.32/11.68 | (18) ~ (all_91_2 = nil) | all_91_1 = nil % 81.32/11.68 | (19) ! [v0: $i] : ( ~ $i(v0) | ~ frontsegP(all_91_1, v0) | ~ % 81.32/11.68 | frontsegP(all_91_2, v0) | ~ ssList(v0) | ~ neq(v0, nil)) % 81.32/11.68 | % 81.32/11.68 | BETA: splitting (6) gives: % 81.32/11.68 | % 81.32/11.68 | Case 1: % 81.32/11.68 | | % 81.32/11.68 | | (20) ~ ssList(nil) % 81.32/11.68 | | % 81.32/11.68 | | PRED_UNIFY: (4), (20) imply: % 81.32/11.68 | | (21) $false % 81.32/11.68 | | % 81.32/11.68 | | CLOSE: (21) is inconsistent. % 81.32/11.68 | | % 81.32/11.68 | Case 2: % 81.32/11.68 | | % 81.32/11.68 | | (22) frontsegP(nil, nil) % 81.32/11.68 | | % 81.32/11.68 | | GROUND_INST: instantiating (ax42) with all_91_2, simplifying with (11), (14) % 81.32/11.68 | | gives: % 81.32/11.68 | | (23) frontsegP(all_91_2, all_91_2) % 81.32/11.68 | | % 81.32/11.68 | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (4), (7), % 81.32/11.68 | | (22) gives: % 81.32/11.68 | | (24) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 81.32/11.68 | | % 81.32/11.68 | | GROUND_INST: instantiating (2) with all_91_1, all_91_2, all_91_0, % 81.32/11.68 | | simplifying with (11), (12), (13), (14), (15), (16), (17) % 81.32/11.68 | | gives: % 81.32/11.68 | | (25) frontsegP(all_91_1, all_91_2) % 81.32/11.68 | | % 81.32/11.68 | | DELTA: instantiating (24) with fresh symbol all_114_0 gives: % 81.32/11.68 | | (26) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0) % 81.32/11.68 | | % 81.32/11.68 | | ALPHA: (26) implies: % 81.32/11.68 | | (27) ssList(all_114_0) % 81.32/11.68 | | (28) $i(all_114_0) % 81.32/11.68 | | (29) app(nil, all_114_0) = nil % 81.32/11.68 | | % 81.32/11.68 | | GROUND_INST: instantiating (3) with all_91_2, all_114_0, simplifying with % 81.32/11.68 | | (11), (14), (27), (28) gives: % 81.32/11.69 | | (30) all_114_0 = all_91_2 | neq(all_91_2, all_114_0) % 81.32/11.69 | | % 81.32/11.69 | | GROUND_INST: instantiating (19) with all_91_2, simplifying with (11), (14), % 81.32/11.69 | | (23), (25) gives: % 81.61/11.69 | | (31) ~ neq(all_91_2, nil) % 81.61/11.69 | | % 81.61/11.69 | | GROUND_INST: instantiating (5) with all_114_0, nil, simplifying with (27), % 81.61/11.69 | | (28), (29) gives: % 81.61/11.69 | | (32) all_114_0 = nil % 81.61/11.69 | | % 81.61/11.69 | | BETA: splitting (30) gives: % 81.61/11.69 | | % 81.61/11.69 | | Case 1: % 81.61/11.69 | | | % 81.61/11.69 | | | (33) neq(all_91_2, all_114_0) % 81.61/11.69 | | | % 81.61/11.69 | | | REDUCE: (32), (33) imply: % 81.61/11.69 | | | (34) neq(all_91_2, nil) % 81.61/11.69 | | | % 81.61/11.69 | | | PRED_UNIFY: (31), (34) imply: % 81.61/11.69 | | | (35) $false % 81.61/11.69 | | | % 81.61/11.69 | | | CLOSE: (35) is inconsistent. % 81.61/11.69 | | | % 81.61/11.69 | | Case 2: % 81.61/11.69 | | | % 81.61/11.69 | | | (36) all_114_0 = all_91_2 % 81.61/11.69 | | | % 81.61/11.69 | | | COMBINE_EQS: (32), (36) imply: % 81.61/11.69 | | | (37) all_91_2 = nil % 81.61/11.69 | | | % 81.61/11.69 | | | REDUCE: (31), (37) imply: % 81.61/11.69 | | | (38) ~ neq(nil, nil) % 81.61/11.69 | | | % 81.61/11.69 | | | BETA: splitting (18) gives: % 81.61/11.69 | | | % 81.61/11.69 | | | Case 1: % 81.61/11.69 | | | | % 81.61/11.69 | | | | (39) ~ (all_91_2 = nil) % 81.61/11.69 | | | | % 81.61/11.69 | | | | REDUCE: (37), (39) imply: % 81.61/11.69 | | | | (40) $false % 81.61/11.69 | | | | % 81.61/11.69 | | | | CLOSE: (40) is inconsistent. % 81.61/11.69 | | | | % 81.61/11.69 | | | Case 2: % 81.61/11.69 | | | | % 81.61/11.69 | | | | (41) all_91_1 = nil % 81.61/11.69 | | | | % 81.61/11.69 | | | | REDUCE: (10), (41) imply: % 81.61/11.69 | | | | (42) neq(nil, nil) % 81.61/11.69 | | | | % 81.61/11.69 | | | | PRED_UNIFY: (38), (42) imply: % 81.61/11.69 | | | | (43) $false % 81.61/11.69 | | | | % 81.61/11.69 | | | | CLOSE: (43) is inconsistent. % 81.61/11.69 | | | | % 81.61/11.69 | | | End of split % 81.61/11.69 | | | % 81.61/11.69 | | End of split % 81.61/11.69 | | % 81.61/11.69 | End of split % 81.61/11.69 | % 81.61/11.69 End of proof % 81.61/11.69 % SZS output end Proof for theBenchmark % 81.61/11.69 % 81.61/11.69 10999ms %------------------------------------------------------------------------------