%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT076+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 11.92s 2.37s % Output : Proof 15.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT076+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.36 % Computer : n020.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Mon Sep 7 14:12:43 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.38 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. % 0.72/0.70 ________ _____ % 0.72/0.70 ___ __ \_________(_)________________________________ % 0.72/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.72/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.72/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.72/0.70 % 0.72/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.72/0.70 (2023-06-19) % 0.72/0.70 % 0.72/0.70 (c) Philipp Rümmer, 2009-2023 % 0.72/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.72/0.70 Amanda Stjerna. % 0.72/0.70 Free software under BSD-3-Clause. % 0.72/0.70 % 0.72/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.72/0.70 % 0.72/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.73 Running up to 7 provers in parallel. % 0.72/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.12/1.33 Prover 4: Preprocessing ... % 4.12/1.33 Prover 1: Preprocessing ... % 4.12/1.39 Prover 2: Preprocessing ... % 4.12/1.39 Prover 3: Preprocessing ... % 4.12/1.39 Prover 6: Preprocessing ... % 4.12/1.39 Prover 5: Preprocessing ... % 4.12/1.39 Prover 0: Preprocessing ... % 9.83/2.04 Prover 5: Proving ... % 9.83/2.12 Prover 2: Proving ... % 10.63/2.16 Prover 1: Constructing countermodel ... % 10.63/2.19 Prover 0: Proving ... % 11.14/2.24 Prover 6: Proving ... % 11.14/2.25 Prover 3: Constructing countermodel ... % 11.92/2.37 Prover 6: proved (1631ms) % 11.92/2.37 % 11.92/2.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.92/2.37 % 11.92/2.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.92/2.38 Prover 0: stopped % 11.92/2.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.92/2.38 Prover 3: stopped % 11.92/2.38 Prover 2: stopped % 11.92/2.38 Prover 4: Constructing countermodel ... % 11.92/2.38 Prover 5: stopped % 11.92/2.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.92/2.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.92/2.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.72/2.49 Prover 1: Found proof (size 17) % 12.72/2.49 Prover 1: proved (1759ms) % 12.72/2.50 Prover 4: stopped % 13.54/2.51 Prover 7: Preprocessing ... % 13.54/2.52 Prover 10: Preprocessing ... % 13.54/2.53 Prover 8: Preprocessing ... % 13.54/2.55 Prover 7: stopped % 13.54/2.55 Prover 10: stopped % 13.54/2.57 Prover 11: Preprocessing ... % 13.54/2.57 Prover 13: Preprocessing ... % 14.26/2.61 Prover 13: stopped % 14.26/2.68 Prover 11: stopped % 14.86/2.77 Prover 8: Warning: ignoring some quantifiers % 14.86/2.79 Prover 8: Constructing countermodel ... % 15.36/2.82 Prover 8: stopped % 15.36/2.82 % 15.36/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.36/2.82 % 15.36/2.83 % SZS output start Proof for theBenchmark % 15.36/2.85 Assumptions after simplification: % 15.36/2.85 --------------------------------- % 15.36/2.85 % 15.36/2.85 (leq_def) % 15.83/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = v2) | % 15.83/2.91 ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ (v3 = 0) & % 15.83/2.91 less(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 15.83/2.91 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0) % 15.83/2.91 % 15.83/2.91 (less_leq_trans) % 15.83/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v1, v2) = 0) | ~ (less(v0, % 15.83/2.91 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v2) = 0) % 15.83/2.91 % 15.83/2.91 (odrl311) % 15.83/2.92 $i(v800) & $i(v400) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & leq(v800, % 15.83/2.92 v0) = 0 & leq(v400, v0) = v1 & $i(v0)) % 15.83/2.92 % 15.83/2.92 (ord_v400_v800) % 15.83/2.92 less(v400, v800) = 0 & $i(v800) & $i(v400) % 15.83/2.92 % 15.83/2.92 (function-axioms) % 15.83/2.94 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.83/2.94 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_subsumes(v5, v4, % 15.83/2.94 v3, v2) = v1) | ~ (axis_subsumes(v5, v4, v3, v2) = v0)) & ! [v0: % 15.83/2.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.94 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_compatible(v5, v4, v3, v2) = % 15.83/2.94 v1) | ~ (axis_compatible(v5, v4, v3, v2) = v0)) & ! [v0: % 15.83/2.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.94 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_conflict(v5, v4, v3, v2) = % 15.83/2.94 v1) | ~ (axis_conflict(v5, v4, v3, v2) = v0)) & ! [v0: % 15.83/2.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.94 : ! [v4: $i] : (v1 = v0 | ~ (in_open(v4, v3, v2) = v1) | ~ (in_open(v4, v3, % 15.83/2.94 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 15.83/2.94 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_ropen(v4, v3, v2) = % 15.83/2.94 v1) | ~ (in_ropen(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.83/2.94 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 15.83/2.94 ~ (in_lopen(v4, v3, v2) = v1) | ~ (in_lopen(v4, v3, v2) = v0)) & ! [v0: % 15.83/2.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.94 : ! [v4: $i] : (v1 = v0 | ~ (in_closed(v4, v3, v2) = v1) | ~ (in_closed(v4, % 15.83/2.94 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 15.83/2.94 (v1 = v0 | ~ (box_verdict(v3, v2) = v1) | ~ (box_verdict(v3, v2) = v0)) & ! % 15.83/2.94 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.83/2.94 $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 15.83/2.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.83/2.94 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 15.83/2.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.83/2.94 ~ (val(v2) = v1) | ~ (val(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.83/2.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_verdict(v2) = v1) | ~ % 15.83/2.94 (is_verdict(v2) = v0)) % 15.83/2.94 % 15.83/2.94 Further assumptions not needed in the proof: % 15.83/2.94 -------------------------------------------- % 15.83/2.94 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 15.83/2.94 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 15.83/2.94 conflict_is_verdict, distinct, in_closed, in_lopen, in_open, in_ropen, % 15.83/2.94 irreflexive, leq_antisym, leq_less_trans, leq_trans, less_implies_leq, % 15.83/2.94 ord_v0_v400, ord_v0_v800, transitive, trichotomy, unknown_is_verdict, val_v0, % 15.83/2.94 val_v400, val_v800, verdict_enum, verdicts_distinct_cf_cp, % 15.83/2.94 verdicts_distinct_cf_un, verdicts_distinct_cp_un % 15.83/2.94 % 15.83/2.94 Those formulas are unsatisfiable: % 15.83/2.94 --------------------------------- % 15.83/2.94 % 15.83/2.94 Begin of proof % 15.83/2.94 | % 15.83/2.94 | ALPHA: (leq_def) implies: % 15.83/2.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = % 15.83/2.95 | v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ % 15.83/2.95 | (v3 = 0) & less(v0, v1) = v3))) % 15.83/2.95 | % 15.83/2.95 | ALPHA: (ord_v400_v800) implies: % 15.83/2.95 | (2) less(v400, v800) = 0 % 15.83/2.95 | % 15.83/2.95 | ALPHA: (odrl311) implies: % 15.83/2.95 | (3) $i(v400) % 15.83/2.95 | (4) $i(v800) % 15.83/2.95 | (5) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & leq(v800, v0) = 0 & % 15.83/2.95 | leq(v400, v0) = v1 & $i(v0)) % 15.83/2.95 | % 15.83/2.95 | ALPHA: (function-axioms) implies: % 15.83/2.95 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.83/2.95 | ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = % 15.83/2.96 | v0)) % 15.83/2.96 | % 15.83/2.96 | DELTA: instantiating (5) with fresh symbols all_25_0, all_25_1 gives: % 15.83/2.96 | (7) ~ (all_25_0 = 0) & leq(v800, all_25_1) = 0 & leq(v400, all_25_1) = % 15.83/2.96 | all_25_0 & $i(all_25_1) % 15.83/2.96 | % 15.83/2.96 | ALPHA: (7) implies: % 15.83/2.96 | (8) ~ (all_25_0 = 0) % 15.83/2.96 | (9) $i(all_25_1) % 15.83/2.96 | (10) leq(v400, all_25_1) = all_25_0 % 15.83/2.96 | (11) leq(v800, all_25_1) = 0 % 15.83/2.96 | % 15.83/2.96 | GROUND_INST: instantiating (1) with v400, all_25_1, all_25_0, simplifying with % 15.83/2.96 | (3), (9), (10) gives: % 15.83/2.96 | (12) all_25_0 = 0 | ( ~ (all_25_1 = v400) & ? [v0: int] : ( ~ (v0 = 0) & % 15.83/2.96 | less(v400, all_25_1) = v0)) % 15.83/2.96 | % 15.83/2.96 | GROUND_INST: instantiating (less_leq_trans) with v400, v800, all_25_1, % 15.83/2.96 | simplifying with (2), (3), (4), (9), (11) gives: % 15.83/2.96 | (13) less(v400, all_25_1) = 0 % 15.83/2.96 | % 15.83/2.96 | BETA: splitting (12) gives: % 15.83/2.96 | % 15.83/2.96 | Case 1: % 15.83/2.96 | | % 15.83/2.96 | | (14) all_25_0 = 0 % 15.83/2.97 | | % 15.83/2.97 | | REDUCE: (8), (14) imply: % 15.83/2.97 | | (15) $false % 15.83/2.97 | | % 15.83/2.97 | | CLOSE: (15) is inconsistent. % 15.83/2.97 | | % 15.83/2.97 | Case 2: % 15.83/2.97 | | % 15.83/2.97 | | (16) ~ (all_25_1 = v400) & ? [v0: int] : ( ~ (v0 = 0) & less(v400, % 15.83/2.97 | | all_25_1) = v0) % 15.83/2.97 | | % 15.83/2.97 | | ALPHA: (16) implies: % 15.83/2.97 | | (17) ? [v0: int] : ( ~ (v0 = 0) & less(v400, all_25_1) = v0) % 15.83/2.97 | | % 15.83/2.97 | | DELTA: instantiating (17) with fresh symbol all_37_0 gives: % 15.83/2.97 | | (18) ~ (all_37_0 = 0) & less(v400, all_25_1) = all_37_0 % 15.83/2.97 | | % 15.83/2.97 | | ALPHA: (18) implies: % 15.83/2.97 | | (19) ~ (all_37_0 = 0) % 15.83/2.97 | | (20) less(v400, all_25_1) = all_37_0 % 15.83/2.97 | | % 15.83/2.97 | | GROUND_INST: instantiating (6) with 0, all_37_0, all_25_1, v400, simplifying % 15.83/2.97 | | with (13), (20) gives: % 15.83/2.97 | | (21) all_37_0 = 0 % 15.83/2.97 | | % 15.83/2.97 | | REDUCE: (19), (21) imply: % 15.83/2.97 | | (22) $false % 15.83/2.97 | | % 15.83/2.97 | | CLOSE: (22) is inconsistent. % 15.83/2.97 | | % 15.83/2.97 | End of split % 15.83/2.97 | % 15.83/2.97 End of proof % 15.83/2.97 % SZS output end Proof for theBenchmark % 15.83/2.97 % 15.83/2.97 2267ms %------------------------------------------------------------------------------