%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT094+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 : n004.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 06:17:31 AM UTC 2026 % Result : Theorem 16.71s 3.01s % Output : Proof 22.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT094+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 : n004.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 14:25:00 UTC 2026 % 0.09/0.35 % CPUTime : % 0.09/0.37 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. % 0.54/0.69 ________ _____ % 0.54/0.69 ___ __ \_________(_)________________________________ % 0.54/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.54/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.54/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.54/0.69 % 0.54/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.54/0.69 (2023-06-19) % 0.54/0.69 % 0.54/0.69 (c) Philipp Rümmer, 2009-2023 % 0.54/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.54/0.69 Amanda Stjerna. % 0.54/0.69 Free software under BSD-3-Clause. % 0.54/0.69 % 0.54/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.54/0.69 % 0.54/0.69 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.71 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 % 5.78/1.51 Prover 4: Preprocessing ... % 5.78/1.52 Prover 2: Preprocessing ... % 5.78/1.52 Prover 6: Preprocessing ... % 5.78/1.52 Prover 3: Preprocessing ... % 5.78/1.52 Prover 0: Preprocessing ... % 5.78/1.52 Prover 5: Preprocessing ... % 5.78/1.53 Prover 1: Preprocessing ... % 13.55/2.54 Prover 5: Proving ... % 13.55/2.54 Prover 6: Proving ... % 13.55/2.55 Prover 2: Proving ... % 13.55/2.59 Prover 3: Constructing countermodel ... % 14.34/2.64 Prover 1: Constructing countermodel ... % 15.13/2.72 Prover 0: Proving ... % 15.13/2.76 Prover 4: Constructing countermodel ... % 16.71/3.00 Prover 6: proved (2274ms) % 16.71/3.00 % 16.71/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.71/3.01 % 16.71/3.01 Prover 5: stopped % 16.71/3.01 Prover 2: stopped % 16.71/3.01 Prover 3: stopped % 16.71/3.01 Prover 0: stopped % 16.71/3.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.71/3.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.71/3.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.71/3.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.71/3.02 Prover 1: Found proof (size 16) % 16.71/3.02 Prover 1: proved (2295ms) % 16.71/3.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.71/3.02 Prover 4: stopped % 17.93/3.16 Prover 8: Preprocessing ... % 18.70/3.19 Prover 7: Preprocessing ... % 18.97/3.27 Prover 13: Preprocessing ... % 18.97/3.27 Prover 10: Preprocessing ... % 18.97/3.27 Prover 7: stopped % 18.97/3.29 Prover 11: Preprocessing ... % 19.76/3.35 Prover 10: stopped % 20.52/3.44 Prover 11: stopped % 20.52/3.44 Prover 13: stopped % 21.10/3.52 Prover 8: Warning: ignoring some quantifiers % 21.10/3.54 Prover 8: Constructing countermodel ... % 21.10/3.58 Prover 8: stopped % 21.10/3.58 % 21.10/3.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.10/3.58 % 21.10/3.59 % SZS output start Proof for theBenchmark % 21.58/3.61 Assumptions after simplification: % 21.58/3.61 --------------------------------- % 21.58/3.61 % 21.58/3.61 (no_subs_hint) % 21.58/3.66 $i(v800) & $i(v600) & $i(v0) & ? [v0: int] : ( ~ (v0 = 0) & axis_subsumes(v0, % 21.58/3.66 v800, v0, v600) = v0) % 21.58/3.66 % 21.58/3.66 (odrl653) % 21.58/3.67 $i(v800) & $i(v600) & $i(v0) & $i(present) & $i(conflict) & ? [v0: $i] : ( ~ % 21.58/3.67 (v0 = conflict) & subs_verdict(v0, v800, present, v0, v600, present) = v0 & % 21.58/3.67 $i(v0)) % 21.58/3.67 % 21.58/3.67 (subs_present_no) % 21.58/3.67 $i(present) & $i(conflict) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 21.58/3.67 $i] : ! [v4: $i] : (v4 = conflict | ~ (subs_verdict(v0, v1, present, v2, % 21.58/3.67 v3, present) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.58/3.67 axis_subsumes(v0, v1, v2, v3) = 0) % 21.58/3.67 % 21.58/3.67 (function-axioms) % 22.05/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.05/3.70 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (subs_verdict(v7, v6, v5, % 22.05/3.70 v4, v3, v2) = v1) | ~ (subs_verdict(v7, v6, v5, v4, v3, v2) = v0)) & ! % 22.05/3.70 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 22.05/3.70 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_subsumes(v5, v4, v3, % 22.05/3.70 v2) = v1) | ~ (axis_subsumes(v5, v4, v3, v2) = v0)) & ! [v0: % 22.05/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.05/3.70 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_compatible(v5, v4, v3, v2) = % 22.05/3.70 v1) | ~ (axis_compatible(v5, v4, v3, v2) = v0)) & ! [v0: % 22.05/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.05/3.70 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_conflict(v5, v4, v3, v2) = % 22.05/3.70 v1) | ~ (axis_conflict(v5, v4, v3, v2) = v0)) & ! [v0: % 22.05/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.05/3.70 : ! [v4: $i] : (v1 = v0 | ~ (in_open(v4, v3, v2) = v1) | ~ (in_open(v4, v3, % 22.05/3.70 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 22.05/3.70 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_ropen(v4, v3, v2) = % 22.05/3.70 v1) | ~ (in_ropen(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 22.05/3.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 22.05/3.70 ~ (in_lopen(v4, v3, v2) = v1) | ~ (in_lopen(v4, v3, v2) = v0)) & ! [v0: % 22.05/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.05/3.70 : ! [v4: $i] : (v1 = v0 | ~ (in_closed(v4, v3, v2) = v1) | ~ (in_closed(v4, % 22.05/3.70 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 22.05/3.70 (v1 = v0 | ~ (box_subs(v3, v2) = v1) | ~ (box_subs(v3, v2) = v0)) & ! [v0: % 22.05/3.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.05/3.70 (box_verdict(v3, v2) = v1) | ~ (box_verdict(v3, v2) = v0)) & ! [v0: % 22.05/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.05/3.70 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 22.05/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.05/3.70 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 22.05/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 22.05/3.70 ~ (val(v2) = v1) | ~ (val(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.05/3.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_presence(v2) = v1) | ~ % 22.05/3.70 (is_presence(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.05/3.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_verdict(v2) = v1) | ~ % 22.05/3.70 (is_verdict(v2) = v0)) % 22.05/3.70 % 22.05/3.70 Further assumptions not needed in the proof: % 22.05/3.70 -------------------------------------------- % 22.05/3.70 absent_is_presence, axis_compatible_def, axis_conflict_def, axis_subsumes_def, % 22.05/3.70 box_compatible, box_conflict, box_subs_compat, box_subs_conflict, % 22.05/3.70 box_subs_total, box_subs_unknown, box_unknown, box_verdict_total, % 22.05/3.70 compatible_is_verdict, conflict_is_verdict, distinct, in_closed, in_lopen, % 22.05/3.70 in_open, in_ropen, irreflexive, leq_antisym, leq_def, leq_less_trans, leq_trans, % 22.05/3.70 less_implies_leq, less_leq_trans, ord_v0_v150, ord_v0_v16, ord_v0_v300, % 22.05/3.70 ord_v0_v32, ord_v0_v400, ord_v0_v600, ord_v0_v800, ord_v150_v300, ord_v150_v400, % 22.05/3.70 ord_v150_v600, ord_v150_v800, ord_v16_v150, ord_v16_v300, ord_v16_v32, % 22.05/3.70 ord_v16_v400, ord_v16_v600, ord_v16_v800, ord_v300_v400, ord_v300_v600, % 22.05/3.70 ord_v300_v800, ord_v32_v150, ord_v32_v300, ord_v32_v400, ord_v32_v600, % 22.05/3.70 ord_v32_v800, ord_v400_v600, ord_v400_v800, ord_v600_v800, presence_distinct, % 22.05/3.70 presence_enum, present_is_presence, subs_both_absent, subs_c1_absent, % 22.05/3.70 subs_c2_absent, subs_present_yes, subs_verdict_total, transitive, trichotomy, % 22.05/3.70 unknown_is_verdict, val_v0, val_v150, val_v16, val_v300, val_v32, val_v400, % 22.05/3.70 val_v600, val_v800, verdict_enum, verdicts_distinct_cf_cp, % 22.05/3.70 verdicts_distinct_cf_un, verdicts_distinct_cp_un % 22.05/3.70 % 22.05/3.70 Those formulas are unsatisfiable: % 22.05/3.70 --------------------------------- % 22.05/3.70 % 22.05/3.70 Begin of proof % 22.05/3.70 | % 22.05/3.71 | ALPHA: (subs_present_no) implies: % 22.05/3.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 22.05/3.71 | (v4 = conflict | ~ (subs_verdict(v0, v1, present, v2, v3, present) = % 22.05/3.71 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 22.05/3.71 | axis_subsumes(v0, v1, v2, v3) = 0) % 22.05/3.71 | % 22.05/3.71 | ALPHA: (no_subs_hint) implies: % 22.05/3.71 | (2) ? [v0: int] : ( ~ (v0 = 0) & axis_subsumes(v0, v800, v0, v600) = v0) % 22.05/3.71 | % 22.05/3.71 | ALPHA: (odrl653) implies: % 22.05/3.71 | (3) $i(v0) % 22.05/3.71 | (4) $i(v600) % 22.05/3.71 | (5) $i(v800) % 22.05/3.71 | (6) ? [v0: $i] : ( ~ (v0 = conflict) & subs_verdict(v0, v800, present, v0, % 22.05/3.71 | v600, present) = v0 & $i(v0)) % 22.05/3.71 | % 22.05/3.71 | ALPHA: (function-axioms) implies: % 22.05/3.72 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.05/3.72 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 22.05/3.72 | (axis_subsumes(v5, v4, v3, v2) = v1) | ~ (axis_subsumes(v5, v4, v3, % 22.05/3.72 | v2) = v0)) % 22.05/3.72 | % 22.05/3.72 | DELTA: instantiating (2) with fresh symbol all_36_0 gives: % 22.05/3.72 | (8) ~ (all_36_0 = 0) & axis_subsumes(v0, v800, v0, v600) = all_36_0 % 22.05/3.72 | % 22.05/3.72 | ALPHA: (8) implies: % 22.05/3.72 | (9) ~ (all_36_0 = 0) % 22.05/3.72 | (10) axis_subsumes(v0, v800, v0, v600) = all_36_0 % 22.05/3.72 | % 22.05/3.72 | DELTA: instantiating (6) with fresh symbol all_38_0 gives: % 22.05/3.72 | (11) ~ (all_38_0 = conflict) & subs_verdict(v0, v800, present, v0, v600, % 22.05/3.72 | present) = all_38_0 & $i(all_38_0) % 22.05/3.72 | % 22.05/3.72 | ALPHA: (11) implies: % 22.05/3.72 | (12) ~ (all_38_0 = conflict) % 22.05/3.72 | (13) subs_verdict(v0, v800, present, v0, v600, present) = all_38_0 % 22.05/3.72 | % 22.05/3.72 | GROUND_INST: instantiating (1) with v0, v800, v0, v600, all_38_0, simplifying % 22.05/3.72 | with (3), (4), (5), (13) gives: % 22.05/3.72 | (14) all_38_0 = conflict | axis_subsumes(v0, v800, v0, v600) = 0 % 22.05/3.72 | % 22.05/3.73 | BETA: splitting (14) gives: % 22.05/3.73 | % 22.05/3.73 | Case 1: % 22.05/3.73 | | % 22.05/3.73 | | (15) axis_subsumes(v0, v800, v0, v600) = 0 % 22.05/3.73 | | % 22.05/3.73 | | GROUND_INST: instantiating (7) with all_36_0, 0, v600, v0, v800, v0, % 22.05/3.73 | | simplifying with (10), (15) gives: % 22.05/3.73 | | (16) all_36_0 = 0 % 22.05/3.73 | | % 22.05/3.73 | | REDUCE: (9), (16) imply: % 22.05/3.73 | | (17) $false % 22.05/3.73 | | % 22.05/3.73 | | CLOSE: (17) is inconsistent. % 22.05/3.73 | | % 22.05/3.73 | Case 2: % 22.05/3.73 | | % 22.05/3.73 | | (18) all_38_0 = conflict % 22.05/3.73 | | % 22.05/3.73 | | REDUCE: (12), (18) imply: % 22.05/3.73 | | (19) $false % 22.05/3.73 | | % 22.05/3.73 | | CLOSE: (19) is inconsistent. % 22.05/3.73 | | % 22.05/3.73 | End of split % 22.05/3.73 | % 22.05/3.73 End of proof % 22.05/3.73 % SZS output end Proof for theBenchmark % 22.05/3.73 % 22.05/3.73 3038ms %------------------------------------------------------------------------------