%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT041+2 : TPTP v9.3.0. Released v2.0.0. % 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 06:17:25 AM UTC 2026 % Result : Theorem 4.87s 1.47s % Output : Proof 7.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT041+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.36 % Computer : n002.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Mon Sep 7 13:04:52 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.38 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. % 0.34/0.57 ________ _____ % 0.34/0.57 ___ __ \_________(_)________________________________ % 0.34/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.34/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.34/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.34/0.57 % 0.34/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.34/0.57 (2023-06-19) % 0.34/0.57 % 0.34/0.57 (c) Philipp Rümmer, 2009-2023 % 0.34/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.34/0.57 Amanda Stjerna. % 0.34/0.57 Free software under BSD-3-Clause. % 0.34/0.57 % 0.34/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.34/0.57 % 0.34/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.34/0.58 Running up to 7 provers in parallel. % 0.34/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.34/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.34/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.34/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.34/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.34/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.34/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.03/1.07 Prover 1: Preprocessing ... % 2.03/1.07 Prover 4: Preprocessing ... % 2.03/1.11 Prover 2: Preprocessing ... % 2.03/1.11 Prover 5: Preprocessing ... % 2.03/1.11 Prover 3: Preprocessing ... % 2.03/1.11 Prover 6: Preprocessing ... % 2.03/1.11 Prover 0: Preprocessing ... % 3.29/1.27 Prover 5: Constructing countermodel ... % 3.29/1.28 Prover 2: Constructing countermodel ... % 4.11/1.31 Prover 3: Constructing countermodel ... % 4.11/1.32 Prover 1: Constructing countermodel ... % 4.11/1.33 Prover 6: Proving ... % 4.11/1.39 Prover 4: Constructing countermodel ... % 4.87/1.45 Prover 0: Proving ... % 4.87/1.46 Prover 2: proved (876ms) % 4.87/1.47 % 4.87/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.87/1.47 % 4.87/1.47 Prover 5: proved (875ms) % 4.87/1.47 % 4.87/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.87/1.47 % 4.87/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.87/1.47 Prover 3: stopped % 4.87/1.48 Prover 6: stopped % 4.87/1.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.87/1.48 Prover 0: stopped % 4.87/1.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.87/1.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.87/1.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.64/1.53 Prover 10: Preprocessing ... % 5.64/1.53 Prover 13: Preprocessing ... % 5.64/1.54 Prover 8: Preprocessing ... % 5.64/1.55 Prover 7: Preprocessing ... % 5.64/1.56 Prover 11: Preprocessing ... % 5.64/1.57 Prover 10: Constructing countermodel ... % 5.64/1.58 Prover 7: Constructing countermodel ... % 6.41/1.60 Prover 13: Constructing countermodel ... % 6.41/1.63 Prover 10: Found proof (size 12) % 6.41/1.63 Prover 8: Warning: ignoring some quantifiers % 6.41/1.63 Prover 10: proved (151ms) % 6.41/1.63 Prover 1: gave up % 6.41/1.63 Prover 7: stopped % 6.41/1.63 Prover 4: stopped % 6.41/1.63 Prover 13: stopped % 6.41/1.64 Prover 8: Constructing countermodel ... % 6.41/1.65 Prover 8: stopped % 7.02/1.70 Prover 11: Constructing countermodel ... % 7.02/1.71 Prover 11: stopped % 7.02/1.71 % 7.02/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.02/1.71 % 7.02/1.72 % SZS output start Proof for theBenchmark % 7.02/1.72 Assumptions after simplification: % 7.02/1.72 --------------------------------- % 7.02/1.72 % 7.02/1.72 (a14) % 7.02/1.73 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ founding_time(v0, v1) % 7.02/1.73 | ~ efficient_producer(v0) | ~ organisation_at_time(v0, v1) | % 7.02/1.73 has_elaborated_routines(v0, v1)) % 7.02/1.73 % 7.02/1.73 (a15) % 7.02/1.74 $i(low) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 7.02/1.74 first_mover(v0) | ~ founding_time(v0, v1) | ~ organisation_at_time(v0, v1) % 7.02/1.74 | number_of_routines(v0, v1, low)) % 7.02/1.74 % 7.02/1.74 (a16) % 7.02/1.74 $i(high) & ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & founding_time(v0, % 7.02/1.74 v1) & organisation_at_time(v0, v1) & number_of_routines(v0, v1, high) & ~ % 7.02/1.74 has_elaborated_routines(v0, v1)) % 7.02/1.74 % 7.02/1.74 (mp_not_high_and_low) % 7.02/1.74 $i(high) & $i(low) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 7.02/1.74 number_of_routines(v0, v1, high) | ~ number_of_routines(v0, v1, low)) % 7.02/1.74 % 7.02/1.75 (prove_t10) % 7.02/1.75 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 7.02/1.75 organisation_at_time(v0, v1) | first_mover(v0) | efficient_producer(v0)) % 7.02/1.75 % 7.02/1.75 Those formulas are unsatisfiable: % 7.02/1.75 --------------------------------- % 7.02/1.75 % 7.02/1.75 Begin of proof % 7.02/1.75 | % 7.02/1.75 | ALPHA: (a16) implies: % 7.02/1.75 | (1) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & founding_time(v0, v1) & % 7.02/1.75 | organisation_at_time(v0, v1) & number_of_routines(v0, v1, high) & ~ % 7.02/1.75 | has_elaborated_routines(v0, v1)) % 7.02/1.75 | % 7.02/1.75 | ALPHA: (a15) implies: % 7.02/1.76 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ first_mover(v0) % 7.02/1.76 | | ~ founding_time(v0, v1) | ~ organisation_at_time(v0, v1) | % 7.02/1.76 | number_of_routines(v0, v1, low)) % 7.02/1.76 | % 7.02/1.76 | ALPHA: (mp_not_high_and_low) implies: % 7.02/1.76 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 7.02/1.76 | number_of_routines(v0, v1, high) | ~ number_of_routines(v0, v1, % 7.02/1.76 | low)) % 7.02/1.76 | % 7.02/1.76 | DELTA: instantiating (1) with fresh symbols all_7_0, all_7_1 gives: % 7.02/1.76 | (4) $i(all_7_0) & $i(all_7_1) & founding_time(all_7_1, all_7_0) & % 7.02/1.76 | organisation_at_time(all_7_1, all_7_0) & number_of_routines(all_7_1, % 7.02/1.76 | all_7_0, high) & ~ has_elaborated_routines(all_7_1, all_7_0) % 7.02/1.76 | % 7.02/1.76 | ALPHA: (4) implies: % 7.02/1.76 | (5) ~ has_elaborated_routines(all_7_1, all_7_0) % 7.02/1.77 | (6) number_of_routines(all_7_1, all_7_0, high) % 7.02/1.77 | (7) organisation_at_time(all_7_1, all_7_0) % 7.02/1.77 | (8) founding_time(all_7_1, all_7_0) % 7.02/1.77 | (9) $i(all_7_1) % 7.02/1.77 | (10) $i(all_7_0) % 7.02/1.77 | % 7.02/1.77 | GROUND_INST: instantiating (prove_t10) with all_7_1, all_7_0, simplifying with % 7.02/1.77 | (7), (9), (10) gives: % 7.02/1.77 | (11) first_mover(all_7_1) | efficient_producer(all_7_1) % 7.02/1.77 | % 7.02/1.77 | BETA: splitting (11) gives: % 7.02/1.77 | % 7.02/1.77 | Case 1: % 7.02/1.77 | | % 7.02/1.77 | | (12) first_mover(all_7_1) % 7.02/1.77 | | % 7.02/1.77 | | GROUND_INST: instantiating (2) with all_7_1, all_7_0, simplifying with (7), % 7.02/1.77 | | (8), (9), (10), (12) gives: % 7.02/1.77 | | (13) number_of_routines(all_7_1, all_7_0, low) % 7.02/1.77 | | % 7.02/1.77 | | GROUND_INST: instantiating (3) with all_7_1, all_7_0, simplifying with (6), % 7.02/1.77 | | (9), (10), (13) gives: % 7.02/1.77 | | (14) $false % 7.02/1.78 | | % 7.02/1.78 | | CLOSE: (14) is inconsistent. % 7.02/1.78 | | % 7.02/1.78 | Case 2: % 7.02/1.78 | | % 7.02/1.78 | | (15) efficient_producer(all_7_1) % 7.02/1.78 | | % 7.02/1.78 | | GROUND_INST: instantiating (a14) with all_7_1, all_7_0, simplifying with % 7.02/1.78 | | (5), (7), (8), (9), (10), (15) gives: % 7.02/1.78 | | (16) $false % 7.02/1.78 | | % 7.02/1.78 | | CLOSE: (16) is inconsistent. % 7.02/1.78 | | % 7.02/1.78 | End of split % 7.02/1.78 | % 7.02/1.78 End of proof % 7.02/1.78 % SZS output end Proof for theBenchmark % 7.02/1.78 % 7.02/1.78 1210ms %------------------------------------------------------------------------------