%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT093+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 13.86s 2.44s % Output : Proof 18.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT093+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.34 % Computer : n002.cluster.edu % 0.08/0.34 % Model : x86_64 x86_64 % 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.34 % Memory : 8046.5625MB % 0.08/0.34 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Mon Sep 7 14:03:37 UTC 2026 % 0.08/0.35 % CPUTime : % 0.08/0.36 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. % 0.53/0.56 ________ _____ % 0.53/0.56 ___ __ \_________(_)________________________________ % 0.53/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.53/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.53/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.53/0.56 % 0.53/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.53/0.56 (2023-06-19) % 0.53/0.56 % 0.53/0.56 (c) Philipp Rümmer, 2009-2023 % 0.53/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.53/0.56 Amanda Stjerna. % 0.53/0.56 Free software under BSD-3-Clause. % 0.53/0.56 % 0.53/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.53/0.56 % 0.53/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.53/0.58 Running up to 7 provers in parallel. % 0.53/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.53/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.53/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.53/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.53/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.53/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.53/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.99/1.41 Prover 4: Preprocessing ... % 5.99/1.43 Prover 1: Preprocessing ... % 6.78/1.51 Prover 3: Preprocessing ... % 6.78/1.51 Prover 0: Preprocessing ... % 6.78/1.51 Prover 2: Preprocessing ... % 6.78/1.51 Prover 6: Preprocessing ... % 6.78/1.51 Prover 5: Preprocessing ... % 12.32/2.25 Prover 5: Proving ... % 13.08/2.31 Prover 6: Proving ... % 13.08/2.31 Prover 1: Constructing countermodel ... % 13.08/2.37 Prover 2: Proving ... % 13.86/2.40 Prover 3: Constructing countermodel ... % 13.86/2.43 Prover 5: proved (1841ms) % 13.86/2.43 % 13.86/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.86/2.44 % 13.86/2.44 Prover 2: proved (1849ms) % 13.86/2.44 % 13.86/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.86/2.44 % 13.86/2.44 Prover 3: stopped % 13.86/2.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.86/2.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.86/2.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.86/2.46 Prover 6: stopped % 13.86/2.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.45/2.60 Prover 4: Constructing countermodel ... % 15.45/2.63 Prover 8: Preprocessing ... % 15.45/2.65 Prover 10: Preprocessing ... % 15.45/2.68 Prover 11: Preprocessing ... % 15.45/2.70 Prover 1: Found proof (size 20) % 16.25/2.70 Prover 1: proved (2115ms) % 16.25/2.70 Prover 4: stopped % 16.25/2.70 Prover 7: Preprocessing ... % 16.25/2.72 Prover 0: Proving ... % 16.25/2.72 Prover 0: stopped % 16.25/2.74 Prover 10: stopped % 16.25/2.76 Prover 7: stopped % 16.89/2.82 Prover 11: stopped % 17.40/2.96 Prover 8: Warning: ignoring some quantifiers % 17.40/2.98 Prover 8: Constructing countermodel ... % 17.40/3.01 Prover 8: stopped % 17.40/3.01 % 17.40/3.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.40/3.01 % 17.40/3.02 % SZS output start Proof for theBenchmark % 17.40/3.02 Assumptions after simplification: % 17.40/3.02 --------------------------------- % 17.40/3.03 % 17.40/3.03 (compatible_is_verdict) % 18.05/3.07 is_verdict(compatible) = 0 & $i(compatible) % 18.05/3.07 % 18.05/3.07 (conflict_is_verdict) % 18.05/3.07 is_verdict(conflict) = 0 & $i(conflict) % 18.05/3.07 % 18.05/3.07 (odrl644) % 18.05/3.07 $i(conflict) & $i(compatible) & ? [v0: $i] : ( ~ (v0 = compatible) & % 18.05/3.07 xone_verdict(compatible, conflict) = v0 & $i(v0)) % 18.05/3.07 % 18.05/3.07 (xone_compat) % 18.05/3.08 $i(conflict) & $i(compatible) & ! [v0: $i] : (v0 = compatible | ~ % 18.05/3.08 (xone_verdict(compatible, conflict) = v0) | ? [v1: any] : ? [v2: any] : % 18.05/3.08 (is_verdict(conflict) = v2 & is_verdict(compatible) = v1 & ( ~ (v2 = 0) | ~ % 18.05/3.08 (v1 = 0)))) % 18.05/3.08 % 18.05/3.08 (function-axioms) % 18.05/3.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 18.05/3.10 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_subsumes(v5, v4, % 18.05/3.10 v3, v2) = v1) | ~ (axis_subsumes(v5, v4, v3, v2) = v0)) & ! [v0: % 18.05/3.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.05/3.10 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_compatible(v5, v4, v3, v2) = % 18.05/3.10 v1) | ~ (axis_compatible(v5, v4, v3, v2) = v0)) & ! [v0: % 18.05/3.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.05/3.10 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_conflict(v5, v4, v3, v2) = % 18.05/3.10 v1) | ~ (axis_conflict(v5, v4, v3, v2) = v0)) & ! [v0: % 18.05/3.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.05/3.10 : ! [v4: $i] : (v1 = v0 | ~ (in_open(v4, v3, v2) = v1) | ~ (in_open(v4, v3, % 18.05/3.10 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 18.05/3.10 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_ropen(v4, v3, v2) = % 18.05/3.10 v1) | ~ (in_ropen(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 18.05/3.10 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 18.05/3.10 ~ (in_lopen(v4, v3, v2) = v1) | ~ (in_lopen(v4, v3, v2) = v0)) & ! [v0: % 18.05/3.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.05/3.11 : ! [v4: $i] : (v1 = v0 | ~ (in_closed(v4, v3, v2) = v1) | ~ (in_closed(v4, % 18.05/3.11 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 18.05/3.11 (v1 = v0 | ~ (box_verdict(v3, v2) = v1) | ~ (box_verdict(v3, v2) = v0)) & ! % 18.05/3.11 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.05/3.11 (xone_verdict(v3, v2) = v1) | ~ (xone_verdict(v3, v2) = v0)) & ! [v0: $i] % 18.05/3.11 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or_verdict(v3, v2) % 18.05/3.11 = v1) | ~ (or_verdict(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 18.05/3.11 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, % 18.05/3.11 v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 18.05/3.11 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, % 18.05/3.11 v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 18.05/3.11 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_verdict(v2) = v1) | % 18.05/3.11 ~ (is_verdict(v2) = v0)) % 18.05/3.11 % 18.05/3.11 Further assumptions not needed in the proof: % 18.05/3.11 -------------------------------------------- % 18.05/3.11 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 18.05/3.11 box_conflict, box_unknown, box_verdict_total, in_closed, in_lopen, in_open, % 18.05/3.11 in_ropen, irreflexive, leq_antisym, leq_def, leq_less_trans, leq_trans, % 18.05/3.11 less_implies_leq, less_leq_trans, or_compat, or_conflict, or_sound_2branch, % 18.05/3.11 or_unknown, or_verdict_total, transitive, trichotomy, unknown_is_verdict, % 18.05/3.11 verdict_enum, verdicts_distinct_cf_cp, verdicts_distinct_cf_un, % 18.05/3.11 verdicts_distinct_cp_un, xone_conflict, xone_unknown, xone_verdict_total % 18.05/3.11 % 18.05/3.11 Those formulas are unsatisfiable: % 18.05/3.11 --------------------------------- % 18.05/3.11 % 18.05/3.11 Begin of proof % 18.05/3.11 | % 18.05/3.11 | ALPHA: (xone_compat) implies: % 18.05/3.12 | (1) ! [v0: $i] : (v0 = compatible | ~ (xone_verdict(compatible, conflict) % 18.05/3.12 | = v0) | ? [v1: any] : ? [v2: any] : (is_verdict(conflict) = v2 & % 18.05/3.12 | is_verdict(compatible) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 18.05/3.12 | % 18.05/3.12 | ALPHA: (conflict_is_verdict) implies: % 18.05/3.12 | (2) is_verdict(conflict) = 0 % 18.05/3.12 | % 18.05/3.12 | ALPHA: (compatible_is_verdict) implies: % 18.05/3.12 | (3) is_verdict(compatible) = 0 % 18.05/3.12 | % 18.05/3.12 | ALPHA: (odrl644) implies: % 18.05/3.12 | (4) ? [v0: $i] : ( ~ (v0 = compatible) & xone_verdict(compatible, % 18.05/3.12 | conflict) = v0 & $i(v0)) % 18.05/3.12 | % 18.05/3.12 | ALPHA: (function-axioms) implies: % 18.05/3.13 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.05/3.13 | (v1 = v0 | ~ (is_verdict(v2) = v1) | ~ (is_verdict(v2) = v0)) % 18.05/3.13 | % 18.05/3.13 | DELTA: instantiating (4) with fresh symbol all_34_0 gives: % 18.05/3.13 | (6) ~ (all_34_0 = compatible) & xone_verdict(compatible, conflict) = % 18.05/3.13 | all_34_0 & $i(all_34_0) % 18.05/3.13 | % 18.05/3.13 | ALPHA: (6) implies: % 18.52/3.13 | (7) ~ (all_34_0 = compatible) % 18.52/3.13 | (8) xone_verdict(compatible, conflict) = all_34_0 % 18.52/3.13 | % 18.52/3.13 | GROUND_INST: instantiating (1) with all_34_0, simplifying with (8) gives: % 18.52/3.13 | (9) all_34_0 = compatible | ? [v0: any] : ? [v1: any] : % 18.52/3.13 | (is_verdict(conflict) = v1 & is_verdict(compatible) = v0 & ( ~ (v1 = 0) % 18.52/3.13 | | ~ (v0 = 0))) % 18.52/3.13 | % 18.52/3.13 | BETA: splitting (9) gives: % 18.52/3.13 | % 18.52/3.13 | Case 1: % 18.52/3.13 | | % 18.52/3.14 | | (10) all_34_0 = compatible % 18.52/3.14 | | % 18.52/3.14 | | REDUCE: (7), (10) imply: % 18.52/3.14 | | (11) $false % 18.52/3.14 | | % 18.52/3.14 | | CLOSE: (11) is inconsistent. % 18.52/3.14 | | % 18.52/3.14 | Case 2: % 18.52/3.14 | | % 18.52/3.14 | | (12) ? [v0: any] : ? [v1: any] : (is_verdict(conflict) = v1 & % 18.52/3.14 | | is_verdict(compatible) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 18.52/3.14 | | % 18.52/3.14 | | DELTA: instantiating (12) with fresh symbols all_43_0, all_43_1 gives: % 18.52/3.14 | | (13) is_verdict(conflict) = all_43_0 & is_verdict(compatible) = all_43_1 % 18.52/3.14 | | & ( ~ (all_43_0 = 0) | ~ (all_43_1 = 0)) % 18.52/3.14 | | % 18.52/3.14 | | ALPHA: (13) implies: % 18.52/3.14 | | (14) is_verdict(compatible) = all_43_1 % 18.52/3.14 | | (15) is_verdict(conflict) = all_43_0 % 18.52/3.14 | | (16) ~ (all_43_0 = 0) | ~ (all_43_1 = 0) % 18.52/3.14 | | % 18.52/3.14 | | GROUND_INST: instantiating (5) with 0, all_43_1, compatible, simplifying % 18.52/3.14 | | with (3), (14) gives: % 18.52/3.14 | | (17) all_43_1 = 0 % 18.52/3.14 | | % 18.52/3.15 | | GROUND_INST: instantiating (5) with 0, all_43_0, conflict, simplifying with % 18.52/3.15 | | (2), (15) gives: % 18.52/3.15 | | (18) all_43_0 = 0 % 18.52/3.15 | | % 18.52/3.15 | | BETA: splitting (16) gives: % 18.52/3.15 | | % 18.52/3.15 | | Case 1: % 18.52/3.15 | | | % 18.52/3.15 | | | (19) ~ (all_43_0 = 0) % 18.52/3.15 | | | % 18.52/3.15 | | | REDUCE: (18), (19) imply: % 18.52/3.15 | | | (20) $false % 18.52/3.15 | | | % 18.52/3.15 | | | CLOSE: (20) is inconsistent. % 18.52/3.15 | | | % 18.52/3.15 | | Case 2: % 18.52/3.15 | | | % 18.52/3.15 | | | (21) ~ (all_43_1 = 0) % 18.52/3.15 | | | % 18.52/3.15 | | | REDUCE: (17), (21) imply: % 18.52/3.15 | | | (22) $false % 18.52/3.15 | | | % 18.52/3.15 | | | CLOSE: (22) is inconsistent. % 18.52/3.15 | | | % 18.52/3.15 | | End of split % 18.52/3.15 | | % 18.52/3.15 | End of split % 18.52/3.15 | % 18.52/3.15 End of proof % 18.52/3.15 % SZS output end Proof for theBenchmark % 18.52/3.15 % 18.52/3.15 2584ms %------------------------------------------------------------------------------