%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 06:17:23 AM UTC 2026 % Result : Theorem 6.30s 1.61s % Output : Proof 8.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.35 % Computer : n008.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 % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Mon Sep 7 12:42:53 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. % 0.70/0.71 ________ _____ % 0.70/0.71 ___ __ \_________(_)________________________________ % 0.70/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.70/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.70/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.70/0.71 % 0.70/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.70/0.71 (2023-06-19) % 0.70/0.71 % 0.70/0.71 (c) Philipp Rümmer, 2009-2023 % 0.70/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.70/0.71 Amanda Stjerna. % 0.70/0.71 Free software under BSD-3-Clause. % 0.70/0.71 % 0.70/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.70/0.71 % 0.70/0.72 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.74 Running up to 7 provers in parallel. % 0.70/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.04/1.10 Prover 1: Preprocessing ... % 2.04/1.10 Prover 4: Preprocessing ... % 2.76/1.16 Prover 2: Preprocessing ... % 2.76/1.16 Prover 6: Preprocessing ... % 2.76/1.16 Prover 3: Preprocessing ... % 2.76/1.16 Prover 5: Preprocessing ... % 2.76/1.16 Prover 0: Preprocessing ... % 3.98/1.38 Prover 5: Constructing countermodel ... % 3.98/1.38 Prover 4: Constructing countermodel ... % 3.98/1.38 Prover 3: Constructing countermodel ... % 3.98/1.39 Prover 0: Proving ... % 3.98/1.39 Prover 2: Proving ... % 4.72/1.40 Prover 1: Constructing countermodel ... % 4.72/1.40 Prover 6: Proving ... % 5.50/1.55 Prover 3: gave up % 5.50/1.55 Prover 1: gave up % 5.50/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.50/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.50/1.58 Prover 8: Preprocessing ... % 6.30/1.61 Prover 2: proved (862ms) % 6.30/1.61 % 6.30/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.30/1.61 % 6.30/1.62 Prover 5: stopped % 6.30/1.62 Prover 6: stopped % 6.30/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.30/1.62 Prover 0: stopped % 6.30/1.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.30/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.30/1.63 Prover 7: Preprocessing ... % 6.30/1.63 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.30/1.65 Prover 11: Preprocessing ... % 6.30/1.66 Prover 8: Warning: ignoring some quantifiers % 6.30/1.66 Prover 10: Preprocessing ... % 6.30/1.67 Prover 8: Constructing countermodel ... % 6.30/1.68 Prover 13: Preprocessing ... % 6.30/1.69 Prover 7: Constructing countermodel ... % 6.30/1.69 Prover 16: Preprocessing ... % 7.05/1.72 Prover 11: Constructing countermodel ... % 7.05/1.76 Prover 10: Constructing countermodel ... % 7.05/1.78 Prover 16: Constructing countermodel ... % 7.05/1.79 Prover 13: Constructing countermodel ... % 7.83/1.81 Prover 8: gave up % 7.83/1.81 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.83/1.83 Prover 19: Preprocessing ... % 7.83/1.83 Prover 7: Found proof (size 9) % 7.83/1.84 Prover 7: proved (270ms) % 7.83/1.84 Prover 4: stopped % 7.83/1.84 Prover 16: stopped % 7.83/1.84 Prover 11: stopped % 7.83/1.84 Prover 10: stopped % 7.83/1.84 Prover 13: stopped % 8.47/1.90 Prover 19: Warning: ignoring some quantifiers % 8.47/1.91 Prover 19: Constructing countermodel ... % 8.47/1.92 Prover 19: stopped % 8.47/1.92 % 8.47/1.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.47/1.92 % 8.47/1.92 % SZS output start Proof for theBenchmark % 8.47/1.93 Assumptions after simplification: % 8.47/1.93 --------------------------------- % 8.47/1.93 % 8.47/1.93 (a13_star) % 8.47/2.00 $i(efficient_producers) & $i(first_movers) & $i(zero) & ? [v0: $i] : ? [v1: % 8.47/2.00 $i] : ? [v2: $i] : ? [v3: $i] : (growth_rate(efficient_producers, v1) = v3 % 8.47/2.00 & growth_rate(first_movers, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 8.47/2.00 greater(zero, v3) & greater_or_equal(v2, zero) & % 8.47/2.00 subpopulations(first_movers, efficient_producers, v0, v1) & environment(v0)) % 8.47/2.00 % 8.47/2.01 (d2) % 8.47/2.02 $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 8.47/2.02 : ! [v5: $i] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5) % 8.47/2.02 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ outcompetes(v2, v1, v3) % 8.47/2.02 | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | greater(zero, % 8.47/2.02 v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 8.47/2.02 : ! [v5: $i] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5) % 8.47/2.02 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ outcompetes(v2, v1, v3) % 8.47/2.02 | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | % 8.47/2.02 greater_or_equal(v4, zero)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 8.47/2.02 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (growth_rate(v2, v3) = v4) | ~ % 8.47/2.02 (growth_rate(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.47/2.02 ~ greater(zero, v5) | ~ greater_or_equal(v4, zero) | ~ subpopulations(v1, % 8.47/2.03 v2, v0, v3) | ~ environment(v0) | outcompetes(v2, v1, v3)) % 8.47/2.03 % 8.47/2.03 (mp_symmetry_of_subpopulations) % 8.47/2.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 8.47/2.03 | ~ $i(v1) | ~ $i(v0) | ~ subpopulations(v1, v2, v0, v3) | ~ % 8.47/2.03 environment(v0) | subpopulations(v2, v1, v0, v3)) % 8.47/2.03 % 8.47/2.03 (prove_t5_star) % 8.47/2.03 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : ( ~ % 8.47/2.03 $i(v1) | ~ $i(v0) | ~ outcompetes(first_movers, efficient_producers, v1) | % 8.47/2.03 ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ % 8.47/2.03 environment(v0)) % 8.47/2.03 % 8.47/2.03 Those formulas are unsatisfiable: % 8.47/2.03 --------------------------------- % 8.47/2.03 % 8.47/2.03 Begin of proof % 8.47/2.03 | % 8.47/2.03 | ALPHA: (d2) implies: % 8.47/2.04 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 8.47/2.04 | ! [v5: $i] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = % 8.47/2.04 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 8.47/2.04 | greater(zero, v5) | ~ greater_or_equal(v4, zero) | ~ % 8.47/2.04 | subpopulations(v1, v2, v0, v3) | ~ environment(v0) | outcompetes(v2, % 8.47/2.04 | v1, v3)) % 8.47/2.04 | % 8.47/2.04 | ALPHA: (a13_star) implies: % 8.47/2.04 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 8.47/2.04 | (growth_rate(efficient_producers, v1) = v3 & growth_rate(first_movers, % 8.47/2.04 | v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & greater(zero, v3) & % 8.47/2.04 | greater_or_equal(v2, zero) & subpopulations(first_movers, % 8.47/2.04 | efficient_producers, v0, v1) & environment(v0)) % 8.47/2.04 | % 8.47/2.04 | ALPHA: (prove_t5_star) implies: % 8.47/2.04 | (3) $i(first_movers) % 8.47/2.04 | (4) $i(efficient_producers) % 8.47/2.04 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 8.47/2.04 | outcompetes(first_movers, efficient_producers, v1) | ~ % 8.47/2.04 | subpopulations(first_movers, efficient_producers, v0, v1) | ~ % 8.47/2.04 | environment(v0)) % 8.47/2.04 | % 8.47/2.05 | DELTA: instantiating (2) with fresh symbols all_7_0, all_7_1, all_7_2, all_7_3 % 8.47/2.05 | gives: % 8.47/2.05 | (6) growth_rate(efficient_producers, all_7_2) = all_7_0 & % 8.47/2.05 | growth_rate(first_movers, all_7_2) = all_7_1 & $i(all_7_0) & % 8.47/2.05 | $i(all_7_1) & $i(all_7_2) & $i(all_7_3) & greater(zero, all_7_0) & % 8.47/2.05 | greater_or_equal(all_7_1, zero) & subpopulations(first_movers, % 8.47/2.05 | efficient_producers, all_7_3, all_7_2) & environment(all_7_3) % 8.47/2.05 | % 8.47/2.05 | ALPHA: (6) implies: % 8.47/2.05 | (7) environment(all_7_3) % 8.47/2.05 | (8) subpopulations(first_movers, efficient_producers, all_7_3, all_7_2) % 8.47/2.05 | (9) greater_or_equal(all_7_1, zero) % 8.47/2.05 | (10) greater(zero, all_7_0) % 8.47/2.05 | (11) $i(all_7_3) % 8.47/2.05 | (12) $i(all_7_2) % 8.47/2.05 | (13) growth_rate(first_movers, all_7_2) = all_7_1 % 8.47/2.05 | (14) growth_rate(efficient_producers, all_7_2) = all_7_0 % 8.47/2.05 | % 8.47/2.05 | GROUND_INST: instantiating (mp_symmetry_of_subpopulations) with all_7_3, % 8.47/2.05 | first_movers, efficient_producers, all_7_2, simplifying with (3), % 8.47/2.05 | (4), (7), (8), (11), (12) gives: % 8.47/2.05 | (15) subpopulations(efficient_producers, first_movers, all_7_3, all_7_2) % 8.47/2.05 | % 8.47/2.06 | GROUND_INST: instantiating (1) with all_7_3, efficient_producers, % 8.47/2.06 | first_movers, all_7_2, all_7_1, all_7_0, simplifying with (3), % 8.47/2.06 | (4), (7), (9), (10), (11), (12), (13), (14), (15) gives: % 8.47/2.06 | (16) outcompetes(first_movers, efficient_producers, all_7_2) % 8.47/2.06 | % 8.47/2.06 | GROUND_INST: instantiating (5) with all_7_3, all_7_2, simplifying with (7), % 8.47/2.06 | (8), (11), (12), (16) gives: % 8.47/2.06 | (17) $false % 8.47/2.06 | % 8.47/2.06 | CLOSE: (17) is inconsistent. % 8.47/2.06 | % 8.47/2.06 End of proof % 8.47/2.06 % SZS output end Proof for theBenchmark % 8.47/2.06 % 8.47/2.06 1344ms %------------------------------------------------------------------------------