%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT059+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 06:17:27 AM UTC 2026 % Result : Theorem 6.97s 1.85s % Output : Proof 11.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT059+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.35 % Computer : n026.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Mon Sep 7 13:35:42 UTC 2026 % 0.08/0.36 % 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. % 0.66/0.71 ________ _____ % 0.66/0.71 ___ __ \_________(_)________________________________ % 0.66/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.71 % 0.66/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.71 (2023-06-19) % 0.66/0.71 % 0.66/0.71 (c) Philipp Rümmer, 2009-2023 % 0.66/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.71 Amanda Stjerna. % 0.66/0.71 Free software under BSD-3-Clause. % 0.66/0.71 % 0.66/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.71 % 0.66/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.73 Running up to 7 provers in parallel. % 0.66/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.10/1.31 Prover 1: Preprocessing ... % 3.10/1.33 Prover 4: Preprocessing ... % 3.10/1.39 Prover 3: Preprocessing ... % 3.10/1.39 Prover 0: Preprocessing ... % 3.10/1.39 Prover 6: Preprocessing ... % 3.10/1.39 Prover 5: Preprocessing ... % 3.10/1.39 Prover 2: Preprocessing ... % 5.42/1.67 Prover 2: Proving ... % 5.42/1.67 Prover 5: Proving ... % 5.42/1.69 Prover 1: Constructing countermodel ... % 5.42/1.70 Prover 3: Constructing countermodel ... % 6.19/1.71 Prover 6: Constructing countermodel ... % 6.19/1.79 Prover 4: Constructing countermodel ... % 6.97/1.83 Prover 6: gave up % 6.97/1.83 Prover 1: gave up % 6.97/1.83 Prover 3: gave up % 6.97/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.97/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.97/1.84 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.97/1.85 Prover 5: proved (1106ms) % 6.97/1.85 % 6.97/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.97/1.85 % 6.97/1.86 Prover 2: proved (1108ms) % 6.97/1.86 % 6.97/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.97/1.86 % 6.97/1.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.97/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.76/1.92 Prover 7: Preprocessing ... % 7.76/1.92 Prover 8: Preprocessing ... % 7.76/1.94 Prover 9: Preprocessing ... % 7.76/1.95 Prover 11: Preprocessing ... % 7.76/1.95 Prover 0: Proving ... % 7.76/1.95 Prover 10: Preprocessing ... % 7.76/1.97 Prover 0: stopped % 7.76/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.76/2.00 Prover 13: Preprocessing ... % 7.76/2.03 Prover 7: Warning: ignoring some quantifiers % 7.76/2.05 Prover 7: Constructing countermodel ... % 8.90/2.07 Prover 10: Warning: ignoring some quantifiers % 8.90/2.09 Prover 10: Constructing countermodel ... % 8.90/2.09 Prover 8: Warning: ignoring some quantifiers % 8.90/2.11 Prover 8: Constructing countermodel ... % 8.90/2.14 Prover 7: Found proof (size 7) % 8.90/2.14 Prover 13: Warning: ignoring some quantifiers % 8.90/2.14 Prover 7: proved (301ms) % 8.90/2.14 Prover 10: stopped % 8.90/2.14 Prover 4: Found proof (size 41) % 8.90/2.14 Prover 4: proved (1394ms) % 8.90/2.14 Prover 13: Constructing countermodel ... % 8.90/2.14 Prover 8: stopped % 9.69/2.15 Prover 13: stopped % 10.01/2.24 Prover 9: Constructing countermodel ... % 10.01/2.25 Prover 9: stopped % 10.01/2.28 Prover 11: Constructing countermodel ... % 10.01/2.30 Prover 11: stopped % 10.54/2.30 % 10.54/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.54/2.30 % 10.54/2.30 % SZS output start Proof for theBenchmark % 10.54/2.31 Assumptions after simplification: % 10.54/2.31 --------------------------------- % 10.54/2.31 % 10.54/2.31 (assumption_17) % 10.54/2.38 $i(high) & $i(mod2) & $i(mod1) & $i(low) & $i(very_low) & ! [v0: $i] : ! % 10.54/2.38 [v1: $i] : ! [v2: $i] : (v2 = high | ~ (hazard_of_mortality(v0, v1) = v2) | % 10.54/2.38 ~ $i(v1) | ~ $i(v0) | ~ organization(v0) | positional_advantage(v0, v1) | % 10.54/2.38 is_aligned(v0, v1) | has_immunity(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! % 10.54/2.38 [v2: $i] : (v2 = mod2 | ~ (hazard_of_mortality(v0, v1) = v2) | ~ $i(v1) | ~ % 10.54/2.38 $i(v0) | ~ is_aligned(v0, v1) | ~ organization(v0) | % 10.54/2.38 positional_advantage(v0, v1) | has_immunity(v0, v1)) & ! [v0: $i] : ! [v1: % 10.54/2.38 $i] : ! [v2: $i] : (v2 = mod1 | ~ (hazard_of_mortality(v0, v1) = v2) | ~ % 10.54/2.38 $i(v1) | ~ $i(v0) | ~ positional_advantage(v0, v1) | ~ organization(v0) | % 10.54/2.38 is_aligned(v0, v1) | has_immunity(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! % 10.54/2.38 [v2: $i] : (v2 = low | ~ (hazard_of_mortality(v0, v1) = v2) | ~ $i(v1) | ~ % 10.54/2.38 $i(v0) | ~ positional_advantage(v0, v1) | ~ is_aligned(v0, v1) | ~ % 10.54/2.38 organization(v0) | has_immunity(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! % 10.54/2.38 [v2: $i] : (v2 = very_low | ~ (hazard_of_mortality(v0, v1) = v2) | ~ $i(v1) % 10.54/2.38 | ~ $i(v0) | ~ has_immunity(v0, v1) | ~ organization(v0)) % 10.54/2.38 % 10.54/2.38 (assumption_2) % 10.54/2.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 % 10.54/2.39 = v3) & hazard_of_mortality(v0, v2) = v4 & hazard_of_mortality(v0, v1) = % 10.54/2.39 v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & has_immunity(v0, v2) & % 10.54/2.39 has_immunity(v0, v1) & organization(v0)) % 10.54/2.39 % 10.54/2.39 Further assumptions not needed in the proof: % 10.54/2.39 -------------------------------------------- % 10.54/2.39 definition_greater_or_equal, definition_smaller, definition_smaller_or_equal, % 10.54/2.39 meaning_postulate_greater_comparable, meaning_postulate_greater_strict, % 10.54/2.39 meaning_postulate_greater_transitive % 10.54/2.39 % 10.54/2.39 Those formulas are unsatisfiable: % 10.54/2.39 --------------------------------- % 10.54/2.39 % 10.54/2.39 Begin of proof % 10.54/2.39 | % 10.54/2.39 | ALPHA: (assumption_17) implies: % 10.54/2.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = very_low | ~ % 10.54/2.40 | (hazard_of_mortality(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 10.54/2.40 | has_immunity(v0, v1) | ~ organization(v0)) % 10.54/2.40 | % 11.04/2.40 | DELTA: instantiating (assumption_2) with fresh symbols all_13_0, all_13_1, % 11.04/2.40 | all_13_2, all_13_3, all_13_4 gives: % 11.04/2.40 | (2) ~ (all_13_0 = all_13_1) & hazard_of_mortality(all_13_4, all_13_2) = % 11.04/2.40 | all_13_0 & hazard_of_mortality(all_13_4, all_13_3) = all_13_1 & % 11.04/2.40 | $i(all_13_0) & $i(all_13_1) & $i(all_13_2) & $i(all_13_3) & % 11.04/2.40 | $i(all_13_4) & has_immunity(all_13_4, all_13_2) & % 11.04/2.40 | has_immunity(all_13_4, all_13_3) & organization(all_13_4) % 11.04/2.40 | % 11.04/2.40 | ALPHA: (2) implies: % 11.04/2.40 | (3) ~ (all_13_0 = all_13_1) % 11.04/2.41 | (4) organization(all_13_4) % 11.04/2.41 | (5) has_immunity(all_13_4, all_13_3) % 11.04/2.41 | (6) has_immunity(all_13_4, all_13_2) % 11.04/2.41 | (7) $i(all_13_4) % 11.04/2.41 | (8) $i(all_13_3) % 11.04/2.41 | (9) $i(all_13_2) % 11.04/2.41 | (10) hazard_of_mortality(all_13_4, all_13_3) = all_13_1 % 11.04/2.41 | (11) hazard_of_mortality(all_13_4, all_13_2) = all_13_0 % 11.04/2.41 | % 11.04/2.41 | GROUND_INST: instantiating (1) with all_13_4, all_13_3, all_13_1, simplifying % 11.04/2.41 | with (4), (5), (7), (8), (10) gives: % 11.04/2.41 | (12) all_13_1 = very_low % 11.04/2.41 | % 11.04/2.41 | GROUND_INST: instantiating (1) with all_13_4, all_13_2, all_13_0, simplifying % 11.04/2.41 | with (4), (6), (7), (9), (11) gives: % 11.04/2.41 | (13) all_13_0 = very_low % 11.04/2.41 | % 11.04/2.42 | REDUCE: (3), (12), (13) imply: % 11.04/2.42 | (14) $false % 11.04/2.42 | % 11.04/2.42 | CLOSE: (14) is inconsistent. % 11.04/2.42 | % 11.04/2.42 End of proof % 11.04/2.42 % SZS output end Proof for theBenchmark % 11.04/2.42 % 11.04/2.42 1704ms %------------------------------------------------------------------------------