%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT081+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 : n020.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 06:17:29 AM UTC 2026 % Result : Theorem 13.32s 2.50s % Output : Proof 16.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT081+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.37 % Computer : n020.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Mon Sep 7 14:17:13 UTC 2026 % 0.10/0.37 % CPUTime : % 0.14/0.39 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. % 0.67/0.73 ________ _____ % 0.67/0.73 ___ __ \_________(_)________________________________ % 0.67/0.73 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.73 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.73 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.73 % 0.67/0.74 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.74 (2023-06-19) % 0.67/0.74 % 0.67/0.74 (c) Philipp Rümmer, 2009-2023 % 0.67/0.74 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.74 Amanda Stjerna. % 0.67/0.74 Free software under BSD-3-Clause. % 0.67/0.74 % 0.67/0.74 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.74 % 0.67/0.74 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.76 Running up to 7 provers in parallel. % 0.67/0.77 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.77 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.77 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.77 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.88/1.34 Prover 4: Preprocessing ... % 3.88/1.35 Prover 1: Preprocessing ... % 4.66/1.42 Prover 2: Preprocessing ... % 4.66/1.42 Prover 6: Preprocessing ... % 4.66/1.42 Prover 0: Preprocessing ... % 4.66/1.42 Prover 3: Preprocessing ... % 4.66/1.42 Prover 5: Preprocessing ... % 9.76/2.06 Prover 5: Proving ... % 9.76/2.06 Prover 2: Proving ... % 9.76/2.09 Prover 6: Proving ... % 9.76/2.13 Prover 1: Constructing countermodel ... % 10.53/2.17 Prover 3: Constructing countermodel ... % 10.94/2.22 Prover 4: Constructing countermodel ... % 10.94/2.28 Prover 0: Proving ... % 12.53/2.49 Prover 3: proved (1714ms) % 12.53/2.50 % 13.32/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.32/2.50 % 13.32/2.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.32/2.50 Prover 0: stopped % 13.32/2.50 Prover 6: stopped % 13.32/2.51 Prover 5: stopped % 13.32/2.51 Prover 2: stopped % 13.32/2.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.32/2.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.32/2.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.32/2.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.32/2.52 Prover 1: Found proof (size 11) % 13.32/2.52 Prover 1: proved (1755ms) % 13.32/2.52 Prover 4: stopped % 14.10/2.63 Prover 7: Preprocessing ... % 14.10/2.65 Prover 8: Preprocessing ... % 14.10/2.65 Prover 11: Preprocessing ... % 14.10/2.66 Prover 13: Preprocessing ... % 14.10/2.68 Prover 7: stopped % 14.10/2.69 Prover 10: Preprocessing ... % 14.88/2.71 Prover 13: stopped % 14.88/2.72 Prover 10: stopped % 14.88/2.74 Prover 11: stopped % 15.45/2.90 Prover 8: Warning: ignoring some quantifiers % 15.95/2.91 Prover 8: Constructing countermodel ... % 15.95/2.94 Prover 8: stopped % 15.95/2.94 % 15.95/2.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.95/2.94 % 15.95/2.94 % SZS output start Proof for theBenchmark % 15.95/2.95 Assumptions after simplification: % 15.95/2.95 --------------------------------- % 15.95/2.95 % 15.95/2.95 (in_lopen) % 15.95/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.95/3.01 (in_lopen(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 15.95/3.01 any] : ? [v5: any] : (leq(v0, v2) = v5 & less(v1, v0) = v4 & ( ~ (v5 = 0) % 15.95/3.01 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.95/3.01 (in_lopen(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v0, % 15.95/3.01 v2) = 0 & less(v1, v0) = 0)) % 15.95/3.01 % 15.95/3.01 (irreflexive) % 15.95/3.01 ! [v0: $i] : ( ~ (less(v0, v0) = 0) | ~ $i(v0)) % 15.95/3.01 % 15.95/3.01 (less_leq_trans) % 15.95/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v1, v2) = 0) | ~ (less(v0, % 15.95/3.01 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v2) = 0) % 15.95/3.01 % 15.95/3.01 (odrl402) % 15.95/3.02 $i(v800) & $i(v600) & $i(v400) & $i(v200) & $i(v0) & ? [v0: $i] : ? [v1: $i] % 15.95/3.02 : (in_lopen(v1, v0, v600) = 0 & in_lopen(v0, v0, v400) = 0 & leq(v800, v0) = 0 % 15.95/3.02 & leq(v200, v1) = 0 & $i(v1) & $i(v0)) % 15.95/3.02 % 15.95/3.02 (ord_v400_v800) % 15.95/3.02 less(v400, v800) = 0 & $i(v800) & $i(v400) % 15.95/3.02 % 15.95/3.02 Further assumptions not needed in the proof: % 15.95/3.02 -------------------------------------------- % 15.95/3.02 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 15.95/3.02 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 15.95/3.02 conflict_is_verdict, distinct, in_closed, in_open, in_ropen, leq_antisym, % 15.95/3.02 leq_def, leq_less_trans, leq_trans, less_implies_leq, ord_v0_v200, ord_v0_v400, % 15.95/3.02 ord_v0_v600, ord_v0_v800, ord_v200_v400, ord_v200_v600, ord_v200_v800, % 15.95/3.02 ord_v400_v600, ord_v600_v800, transitive, trichotomy, unknown_is_verdict, % 15.95/3.02 val_v0, val_v200, val_v400, val_v600, val_v800, verdict_enum, % 15.95/3.02 verdicts_distinct_cf_cp, verdicts_distinct_cf_un, verdicts_distinct_cp_un % 15.95/3.02 % 15.95/3.02 Those formulas are unsatisfiable: % 15.95/3.02 --------------------------------- % 15.95/3.02 % 15.95/3.02 Begin of proof % 15.95/3.02 | % 15.95/3.02 | ALPHA: (in_lopen) implies: % 15.95/3.03 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (in_lopen(v0, v1, v2) = % 15.95/3.03 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v0, v2) = 0 & % 15.95/3.03 | less(v1, v0) = 0)) % 15.95/3.03 | % 15.95/3.03 | ALPHA: (ord_v400_v800) implies: % 15.95/3.03 | (2) less(v400, v800) = 0 % 15.95/3.03 | % 15.95/3.03 | ALPHA: (odrl402) implies: % 16.57/3.03 | (3) $i(v0) % 16.57/3.03 | (4) $i(v400) % 16.57/3.03 | (5) $i(v800) % 16.57/3.03 | (6) ? [v0: $i] : ? [v1: $i] : (in_lopen(v1, v0, v600) = 0 & in_lopen(v0, % 16.57/3.03 | v0, v400) = 0 & leq(v800, v0) = 0 & leq(v200, v1) = 0 & $i(v1) & % 16.57/3.03 | $i(v0)) % 16.57/3.03 | % 16.57/3.04 | DELTA: instantiating (6) with fresh symbols all_25_0, all_25_1 gives: % 16.57/3.04 | (7) in_lopen(all_25_0, v0, v600) = 0 & in_lopen(all_25_1, v0, v400) = 0 & % 16.57/3.04 | leq(v800, all_25_1) = 0 & leq(v200, all_25_0) = 0 & $i(all_25_0) & % 16.57/3.04 | $i(all_25_1) % 16.57/3.04 | % 16.57/3.04 | ALPHA: (7) implies: % 16.57/3.04 | (8) $i(all_25_1) % 16.57/3.04 | (9) leq(v800, all_25_1) = 0 % 16.57/3.04 | (10) in_lopen(all_25_1, v0, v400) = 0 % 16.57/3.04 | % 16.57/3.04 | GROUND_INST: instantiating (less_leq_trans) with v400, v800, all_25_1, % 16.57/3.04 | simplifying with (2), (4), (5), (8), (9) gives: % 16.57/3.04 | (11) less(v400, all_25_1) = 0 % 16.57/3.04 | % 16.57/3.04 | GROUND_INST: instantiating (1) with all_25_1, v0, v400, simplifying with (3), % 16.57/3.04 | (4), (8), (10) gives: % 16.57/3.04 | (12) leq(all_25_1, v400) = 0 & less(v0, all_25_1) = 0 % 16.57/3.04 | % 16.57/3.04 | ALPHA: (12) implies: % 16.57/3.04 | (13) leq(all_25_1, v400) = 0 % 16.57/3.04 | % 16.57/3.05 | GROUND_INST: instantiating (less_leq_trans) with v400, all_25_1, v400, % 16.57/3.05 | simplifying with (4), (8), (11), (13) gives: % 16.57/3.05 | (14) less(v400, v400) = 0 % 16.57/3.05 | % 16.57/3.05 | GROUND_INST: instantiating (irreflexive) with v400, simplifying with (4), (14) % 16.57/3.05 | gives: % 16.57/3.05 | (15) $false % 16.57/3.05 | % 16.57/3.05 | CLOSE: (15) is inconsistent. % 16.57/3.05 | % 16.57/3.05 End of proof % 16.57/3.05 % SZS output end Proof for theBenchmark % 16.57/3.05 % 16.57/3.05 2311ms %------------------------------------------------------------------------------