%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT012+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 06:17:19 AM UTC 2026 % Result : Theorem 6.63s 1.58s % Output : Proof 9.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT012+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.36 % Computer : n009.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 11:50:07 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. % 0.50/0.57 ________ _____ % 0.50/0.57 ___ __ \_________(_)________________________________ % 0.50/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.57 % 0.50/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.57 (2023-06-19) % 0.50/0.57 % 0.50/0.57 (c) Philipp Rümmer, 2009-2023 % 0.50/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.57 Amanda Stjerna. % 0.50/0.57 Free software under BSD-3-Clause. % 0.50/0.57 % 0.50/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.57 % 0.50/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.50/0.58 Running up to 7 provers in parallel. % 0.50/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.50/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.50/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.50/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.50/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.50/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.50/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.05/1.03 Prover 1: Preprocessing ... % 2.05/1.03 Prover 4: Preprocessing ... % 3.04/1.07 Prover 0: Preprocessing ... % 3.04/1.07 Prover 3: Preprocessing ... % 3.04/1.07 Prover 5: Preprocessing ... % 3.04/1.07 Prover 6: Preprocessing ... % 3.04/1.07 Prover 2: Preprocessing ... % 4.29/1.29 Prover 5: Constructing countermodel ... % 5.07/1.30 Prover 2: Constructing countermodel ... % 5.85/1.42 Prover 1: Constructing countermodel ... % 5.85/1.42 Prover 3: Constructing countermodel ... % 5.85/1.45 Prover 6: Constructing countermodel ... % 6.63/1.58 Prover 5: proved (984ms) % 6.63/1.58 % 6.63/1.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.63/1.58 % 6.63/1.58 Prover 3: stopped % 6.63/1.58 Prover 6: stopped % 6.63/1.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.63/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.63/1.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.63/1.59 Prover 2: stopped % 6.63/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.44/1.64 Prover 10: Preprocessing ... % 7.44/1.65 Prover 7: Preprocessing ... % 7.44/1.67 Prover 8: Preprocessing ... % 7.44/1.69 Prover 11: Preprocessing ... % 8.22/1.72 Prover 10: Constructing countermodel ... % 8.22/1.73 Prover 7: Constructing countermodel ... % 9.03/1.81 Prover 4: Constructing countermodel ... % 9.03/1.82 Prover 10: Found proof (size 21) % 9.03/1.84 Prover 10: proved (236ms) % 9.03/1.84 Prover 11: stopped % 9.03/1.84 Prover 4: stopped % 9.03/1.84 Prover 7: stopped % 9.03/1.85 Prover 1: stopped % 9.03/1.85 Prover 8: Warning: ignoring some quantifiers % 9.03/1.86 Prover 8: Constructing countermodel ... % 9.03/1.87 Prover 8: stopped % 9.03/1.88 Prover 0: Proving ... % 9.03/1.90 Prover 0: stopped % 9.66/1.90 % 9.66/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.66/1.90 % 9.66/1.91 % SZS output start Proof for theBenchmark % 9.66/1.91 Assumptions after simplification: % 9.66/1.91 --------------------------------- % 9.66/1.91 % 9.66/1.91 (a12_FOL) % 9.66/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 9.66/1.93 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ % 9.66/1.93 $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 9.66/1.93 $i(v0) | ~ complexity(v1, v4, v8) | ~ complexity(v0, v3, v7) | ~ % 9.66/1.93 class(v1, v2, v8) | ~ class(v0, v2, v7) | ~ greater(v4, v3) | ~ % 9.66/1.93 inertia(v1, v6, v8) | ~ inertia(v0, v5, v7) | ~ organization(v1, v8) | ~ % 9.66/1.93 organization(v0, v7) | greater(v6, v5)) % 9.66/1.93 % 9.66/1.93 (mp10) % 9.66/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 % 9.66/1.94 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 9.66/1.94 reorganization_free(v0, v1, v2) | ~ class(v0, v4, v2) | ~ class(v0, v3, % 9.66/1.94 v1) | ~ organization(v0, v2) | ~ organization(v0, v1)) % 9.66/1.94 % 9.66/1.94 (mp5) % 9.66/1.94 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ organization(v0, v1) | % 9.66/1.94 ? [v2: $i] : ($i(v2) & inertia(v0, v2, v1))) % 9.66/1.94 % 9.66/1.94 (mp6_2) % 9.66/1.94 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v1, v0) | ~ % 9.66/1.94 greater(v0, v1)) % 9.66/1.94 % 9.66/1.94 (mp9) % 9.66/1.94 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ organization(v0, v1) | % 9.66/1.94 ? [v2: $i] : ($i(v2) & class(v0, v2, v1))) % 9.66/1.94 % 9.66/1.94 (t12_FOL) % 9.66/1.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v4) % 9.66/1.95 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & complexity(v0, v2, v4) & % 9.66/1.95 complexity(v0, v1, v3) & reorganization_free(v0, v3, v4) & greater(v4, v3) & % 9.66/1.95 greater(v1, v2) & organization(v0, v4) & organization(v0, v3)) % 9.66/1.95 % 9.66/1.95 (t2_FOL) % 9.66/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 9.66/1.95 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 9.66/1.95 reorganization_free(v0, v3, v4) | ~ greater(v4, v3) | ~ inertia(v0, v2, % 9.66/1.95 v4) | ~ inertia(v0, v1, v3) | ~ organization(v0, v4) | ~ % 9.66/1.95 organization(v0, v3) | greater(v2, v1)) % 9.66/1.95 % 9.66/1.95 Further assumptions not needed in the proof: % 9.66/1.95 -------------------------------------------- % 9.66/1.95 mp6_1 % 9.66/1.95 % 9.66/1.95 Those formulas are unsatisfiable: % 9.66/1.95 --------------------------------- % 9.66/1.95 % 9.66/1.95 Begin of proof % 9.66/1.95 | % 9.66/1.96 | DELTA: instantiating (t12_FOL) with fresh symbols all_9_0, all_9_1, all_9_2, % 9.66/1.96 | all_9_3, all_9_4 gives: % 9.66/1.96 | (1) $i(all_9_0) & $i(all_9_1) & $i(all_9_2) & $i(all_9_3) & $i(all_9_4) & % 9.66/1.96 | complexity(all_9_4, all_9_2, all_9_0) & complexity(all_9_4, all_9_3, % 9.66/1.96 | all_9_1) & reorganization_free(all_9_4, all_9_1, all_9_0) & % 9.66/1.96 | greater(all_9_0, all_9_1) & greater(all_9_3, all_9_2) & % 9.66/1.96 | organization(all_9_4, all_9_0) & organization(all_9_4, all_9_1) % 9.66/1.96 | % 9.66/1.96 | ALPHA: (1) implies: % 9.66/1.97 | (2) organization(all_9_4, all_9_1) % 9.66/1.97 | (3) organization(all_9_4, all_9_0) % 9.66/1.97 | (4) greater(all_9_3, all_9_2) % 9.66/1.97 | (5) greater(all_9_0, all_9_1) % 9.66/1.97 | (6) reorganization_free(all_9_4, all_9_1, all_9_0) % 9.66/1.97 | (7) complexity(all_9_4, all_9_3, all_9_1) % 9.66/1.97 | (8) complexity(all_9_4, all_9_2, all_9_0) % 9.66/1.97 | (9) $i(all_9_4) % 9.66/1.97 | (10) $i(all_9_3) % 9.66/1.97 | (11) $i(all_9_2) % 9.66/1.97 | (12) $i(all_9_1) % 9.66/1.97 | (13) $i(all_9_0) % 9.66/1.97 | % 9.66/1.97 | GROUND_INST: instantiating (mp9) with all_9_4, all_9_1, simplifying with (2), % 9.66/1.97 | (9), (12) gives: % 9.66/1.97 | (14) ? [v0: $i] : ($i(v0) & class(all_9_4, v0, all_9_1)) % 9.66/1.97 | % 9.66/1.97 | GROUND_INST: instantiating (mp5) with all_9_4, all_9_1, simplifying with (2), % 9.66/1.97 | (9), (12) gives: % 9.66/1.97 | (15) ? [v0: $i] : ($i(v0) & inertia(all_9_4, v0, all_9_1)) % 9.66/1.97 | % 9.66/1.97 | GROUND_INST: instantiating (mp9) with all_9_4, all_9_0, simplifying with (3), % 9.66/1.97 | (9), (13) gives: % 9.66/1.98 | (16) ? [v0: $i] : ($i(v0) & class(all_9_4, v0, all_9_0)) % 9.66/1.98 | % 9.66/1.98 | GROUND_INST: instantiating (mp5) with all_9_4, all_9_0, simplifying with (3), % 9.66/1.98 | (9), (13) gives: % 9.66/1.98 | (17) ? [v0: $i] : ($i(v0) & inertia(all_9_4, v0, all_9_0)) % 9.66/1.98 | % 9.66/1.98 | DELTA: instantiating (17) with fresh symbol all_16_0 gives: % 9.66/1.98 | (18) $i(all_16_0) & inertia(all_9_4, all_16_0, all_9_0) % 9.66/1.98 | % 9.66/1.98 | ALPHA: (18) implies: % 9.66/1.98 | (19) inertia(all_9_4, all_16_0, all_9_0) % 9.66/1.98 | (20) $i(all_16_0) % 9.66/1.98 | % 9.66/1.98 | DELTA: instantiating (15) with fresh symbol all_18_0 gives: % 9.66/1.98 | (21) $i(all_18_0) & inertia(all_9_4, all_18_0, all_9_1) % 9.66/1.98 | % 9.66/1.98 | ALPHA: (21) implies: % 9.66/1.98 | (22) inertia(all_9_4, all_18_0, all_9_1) % 9.66/1.98 | (23) $i(all_18_0) % 9.66/1.98 | % 9.66/1.98 | DELTA: instantiating (14) with fresh symbol all_20_0 gives: % 9.66/1.98 | (24) $i(all_20_0) & class(all_9_4, all_20_0, all_9_1) % 9.66/1.98 | % 9.66/1.98 | ALPHA: (24) implies: % 9.66/1.98 | (25) class(all_9_4, all_20_0, all_9_1) % 9.66/1.98 | (26) $i(all_20_0) % 9.66/1.98 | % 9.66/1.98 | DELTA: instantiating (16) with fresh symbol all_22_0 gives: % 9.66/1.98 | (27) $i(all_22_0) & class(all_9_4, all_22_0, all_9_0) % 9.66/1.98 | % 9.66/1.98 | ALPHA: (27) implies: % 9.66/1.98 | (28) class(all_9_4, all_22_0, all_9_0) % 9.66/1.98 | (29) $i(all_22_0) % 9.66/1.98 | % 9.66/1.99 | GROUND_INST: instantiating (t2_FOL) with all_9_4, all_18_0, all_16_0, all_9_1, % 9.66/1.99 | all_9_0, simplifying with (2), (3), (5), (6), (9), (12), (13), % 9.66/1.99 | (19), (20), (22), (23) gives: % 9.66/1.99 | (30) greater(all_16_0, all_18_0) % 9.66/1.99 | % 9.66/1.99 | GROUND_INST: instantiating (mp10) with all_9_4, all_9_1, all_9_0, all_20_0, % 9.66/1.99 | all_22_0, simplifying with (2), (3), (6), (9), (12), (13), (25), % 9.66/1.99 | (26), (28), (29) gives: % 9.66/1.99 | (31) all_22_0 = all_20_0 % 9.66/1.99 | % 9.66/1.99 | REDUCE: (28), (31) imply: % 9.66/1.99 | (32) class(all_9_4, all_20_0, all_9_0) % 9.66/1.99 | % 9.66/1.99 | GROUND_INST: instantiating (a12_FOL) with all_9_4, all_9_4, all_20_0, all_9_2, % 9.66/1.99 | all_9_3, all_16_0, all_18_0, all_9_0, all_9_1, simplifying with % 9.66/1.99 | (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (19), (20), % 9.66/1.99 | (22), (23), (25), (26), (32) gives: % 9.66/1.99 | (33) greater(all_18_0, all_16_0) % 9.66/1.99 | % 9.66/1.99 | GROUND_INST: instantiating (mp6_2) with all_16_0, all_18_0, simplifying with % 9.66/1.99 | (20), (23), (30), (33) gives: % 9.66/1.99 | (34) $false % 9.66/2.00 | % 9.66/2.00 | CLOSE: (34) is inconsistent. % 9.66/2.00 | % 9.66/2.00 End of proof % 9.66/2.00 % SZS output end Proof for theBenchmark % 9.66/2.00 % 9.66/2.00 1422ms %------------------------------------------------------------------------------