%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT084+1 : TPTP v9.3.1. Bugfixed v9.3.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:17:30 AM UTC 2026 % Result : Theorem 13.56s 2.51s % Output : Proof 16.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT084+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.35 % Computer : n001.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Mon Sep 7 14:23:52 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.37 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.67/0.70 ________ _____ % 0.67/0.70 ___ __ \_________(_)________________________________ % 0.67/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.70 % 0.67/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.70 (2023-06-19) % 0.67/0.70 % 0.67/0.70 (c) Philipp Rümmer, 2009-2023 % 0.67/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.70 Amanda Stjerna. % 0.67/0.70 Free software under BSD-3-Clause. % 0.67/0.70 % 0.67/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.70 % 0.67/0.70 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.72 Running up to 7 provers in parallel. % 0.67/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.17/1.33 Prover 1: Preprocessing ... % 4.17/1.34 Prover 4: Preprocessing ... % 4.88/1.40 Prover 5: Preprocessing ... % 4.88/1.40 Prover 6: Preprocessing ... % 4.88/1.40 Prover 0: Preprocessing ... % 4.88/1.40 Prover 2: Preprocessing ... % 4.88/1.40 Prover 3: Preprocessing ... % 9.89/2.05 Prover 5: Proving ... % 9.89/2.08 Prover 2: Proving ... % 9.89/2.11 Prover 6: Proving ... % 10.72/2.16 Prover 3: Constructing countermodel ... % 10.72/2.17 Prover 4: Constructing countermodel ... % 10.72/2.19 Prover 1: Constructing countermodel ... % 11.17/2.29 Prover 0: Proving ... % 13.56/2.51 Prover 3: proved (1775ms) % 13.56/2.51 % 13.56/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.56/2.51 % 13.56/2.51 Prover 2: stopped % 13.56/2.51 Prover 0: stopped % 13.56/2.52 Prover 5: stopped % 13.56/2.52 Prover 6: proved (1780ms) % 13.56/2.52 % 13.56/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.56/2.52 % 13.56/2.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.56/2.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.56/2.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.56/2.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.56/2.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.37/2.63 Prover 10: Preprocessing ... % 14.37/2.65 Prover 13: Preprocessing ... % 14.37/2.66 Prover 7: Preprocessing ... % 14.37/2.69 Prover 11: Preprocessing ... % 14.37/2.69 Prover 8: Preprocessing ... % 15.12/2.70 Prover 1: Found proof (size 10) % 15.12/2.70 Prover 1: proved (1974ms) % 15.12/2.71 Prover 4: stopped % 15.12/2.71 Prover 10: stopped % 15.12/2.72 Prover 7: stopped % 15.12/2.74 Prover 13: stopped % 15.12/2.78 Prover 11: stopped % 16.26/2.92 Prover 8: Warning: ignoring some quantifiers % 16.26/2.94 Prover 8: Constructing countermodel ... % 16.26/2.96 Prover 8: stopped % 16.26/2.96 % 16.26/2.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.26/2.96 % 16.26/2.96 % SZS output start Proof for theBenchmark % 16.26/2.97 Assumptions after simplification: % 16.26/2.97 --------------------------------- % 16.26/2.97 % 16.26/2.97 (in_lopen) % 16.26/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.26/3.02 (in_lopen(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 16.26/3.02 any] : ? [v5: any] : (leq(v0, v2) = v5 & less(v1, v0) = v4 & ( ~ (v5 = 0) % 16.26/3.02 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 16.26/3.02 (in_lopen(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v0, % 16.26/3.03 v2) = 0 & less(v1, v0) = 0)) % 16.26/3.03 % 16.26/3.03 (irreflexive) % 16.26/3.03 ! [v0: $i] : ( ~ (less(v0, v0) = 0) | ~ $i(v0)) % 16.26/3.03 % 16.26/3.03 (less_leq_trans) % 16.88/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v1, v2) = 0) | ~ (less(v0, % 16.88/3.03 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v2) = 0) % 16.88/3.03 % 16.88/3.03 (odrl432) % 16.88/3.04 $i(v600) & $i(v400) & $i(v200) & $i(v0) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 16.88/3.04 $i] : (in_lopen(v2, v0, v200) = 0 & in_lopen(v1, v0, v400) = 0 & % 16.88/3.04 in_lopen(v0, v0, v600) = 0 & leq(v600, v0) = 0 & leq(v200, v2) = 0 & % 16.88/3.04 less(v400, v1) = 0 & $i(v2) & $i(v1) & $i(v0)) % 16.88/3.04 % 16.88/3.04 Further assumptions not needed in the proof: % 16.88/3.04 -------------------------------------------- % 16.88/3.04 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 16.88/3.04 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 16.88/3.04 conflict_is_verdict, distinct, in_closed, in_open, in_ropen, leq_antisym, % 16.88/3.04 leq_def, leq_less_trans, leq_trans, less_implies_leq, ord_v0_v200, ord_v0_v400, % 16.88/3.04 ord_v0_v600, ord_v200_v400, ord_v200_v600, ord_v400_v600, transitive, % 16.88/3.04 trichotomy, unknown_is_verdict, val_v0, val_v200, val_v400, val_v600, % 16.88/3.04 verdict_enum, verdicts_distinct_cf_cp, verdicts_distinct_cf_un, % 16.88/3.04 verdicts_distinct_cp_un % 16.88/3.04 % 16.88/3.04 Those formulas are unsatisfiable: % 16.88/3.04 --------------------------------- % 16.88/3.04 % 16.88/3.04 Begin of proof % 16.88/3.04 | % 16.88/3.04 | ALPHA: (in_lopen) implies: % 16.88/3.04 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (in_lopen(v0, v1, v2) = % 16.88/3.04 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v0, v2) = 0 & % 16.88/3.04 | less(v1, v0) = 0)) % 16.88/3.04 | % 16.88/3.04 | ALPHA: (odrl432) implies: % 16.88/3.05 | (2) $i(v0) % 16.88/3.05 | (3) $i(v400) % 16.88/3.05 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (in_lopen(v2, v0, v200) = 0 & % 16.88/3.05 | in_lopen(v1, v0, v400) = 0 & in_lopen(v0, v0, v600) = 0 & leq(v600, % 16.88/3.05 | v0) = 0 & leq(v200, v2) = 0 & less(v400, v1) = 0 & $i(v2) & $i(v1) % 16.88/3.05 | & $i(v0)) % 16.88/3.05 | % 16.88/3.05 | DELTA: instantiating (4) with fresh symbols all_25_0, all_25_1, all_25_2 % 16.88/3.05 | gives: % 16.88/3.05 | (5) in_lopen(all_25_0, v0, v200) = 0 & in_lopen(all_25_1, v0, v400) = 0 & % 16.88/3.05 | in_lopen(all_25_2, v0, v600) = 0 & leq(v600, all_25_2) = 0 & leq(v200, % 16.88/3.05 | all_25_0) = 0 & less(v400, all_25_1) = 0 & $i(all_25_0) & % 16.88/3.05 | $i(all_25_1) & $i(all_25_2) % 16.88/3.05 | % 16.88/3.06 | ALPHA: (5) implies: % 16.88/3.06 | (6) $i(all_25_1) % 16.88/3.06 | (7) less(v400, all_25_1) = 0 % 16.88/3.06 | (8) in_lopen(all_25_1, v0, v400) = 0 % 16.88/3.06 | % 16.88/3.06 | GROUND_INST: instantiating (1) with all_25_1, v0, v400, simplifying with (2), % 16.88/3.06 | (3), (6), (8) gives: % 16.88/3.06 | (9) leq(all_25_1, v400) = 0 & less(v0, all_25_1) = 0 % 16.88/3.06 | % 16.88/3.06 | ALPHA: (9) implies: % 16.88/3.06 | (10) leq(all_25_1, v400) = 0 % 16.88/3.06 | % 16.88/3.06 | GROUND_INST: instantiating (less_leq_trans) with v400, all_25_1, v400, % 16.88/3.06 | simplifying with (3), (6), (7), (10) gives: % 16.88/3.06 | (11) less(v400, v400) = 0 % 16.88/3.06 | % 16.88/3.06 | GROUND_INST: instantiating (irreflexive) with v400, simplifying with (3), (11) % 16.88/3.06 | gives: % 16.88/3.06 | (12) $false % 16.88/3.07 | % 16.88/3.07 | CLOSE: (12) is inconsistent. % 16.88/3.07 | % 16.88/3.07 End of proof % 16.88/3.07 % SZS output end Proof for theBenchmark % 16.88/3.07 % 16.88/3.07 2364ms %------------------------------------------------------------------------------