%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT032+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 : n007.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 06:17:22 AM UTC 2026 % Result : Theorem 6.43s 1.61s % Output : Proof 9.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT032+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.35 % Computer : n007.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 12:20:10 UTC 2026 % 0.08/0.35 % 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. % 0.66/0.70 ________ _____ % 0.66/0.70 ___ __ \_________(_)________________________________ % 0.66/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.70 % 0.66/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.70 (2023-06-19) % 0.66/0.70 % 0.66/0.70 (c) Philipp Rümmer, 2009-2023 % 0.66/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.70 Amanda Stjerna. % 0.66/0.70 Free software under BSD-3-Clause. % 0.66/0.70 % 0.66/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.70 % 0.66/0.70 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.72 Running up to 7 provers in parallel. % 0.66/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.26/1.06 Prover 4: Preprocessing ... % 2.26/1.06 Prover 1: Preprocessing ... % 2.93/1.15 Prover 5: Preprocessing ... % 2.93/1.15 Prover 3: Preprocessing ... % 2.93/1.16 Prover 2: Preprocessing ... % 2.93/1.16 Prover 0: Preprocessing ... % 2.93/1.16 Prover 6: Preprocessing ... % 4.08/1.32 Prover 5: Constructing countermodel ... % 4.86/1.41 Prover 2: Proving ... % 4.86/1.41 Prover 3: Constructing countermodel ... % 4.86/1.41 Prover 1: Constructing countermodel ... % 4.86/1.45 Prover 6: Proving ... % 5.65/1.51 Prover 4: Constructing countermodel ... % 6.43/1.60 Prover 5: proved (870ms) % 6.43/1.60 % 6.43/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.43/1.61 % 6.43/1.61 Prover 3: gave up % 6.43/1.61 Prover 1: gave up % 6.43/1.61 Prover 0: Proving ... % 6.43/1.61 Prover 2: proved (880ms) % 6.43/1.61 % 6.43/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.43/1.61 % 6.43/1.61 Prover 6: stopped % 6.43/1.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.43/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.43/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.43/1.62 Prover 0: stopped % 6.43/1.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.43/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.43/1.62 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.43/1.66 Prover 7: Preprocessing ... % 6.43/1.66 Prover 11: Preprocessing ... % 6.43/1.68 Prover 13: Preprocessing ... % 6.43/1.69 Prover 8: Preprocessing ... % 6.43/1.69 Prover 10: Preprocessing ... % 7.18/1.70 Prover 16: Preprocessing ... % 7.18/1.75 Prover 7: Constructing countermodel ... % 7.18/1.77 Prover 10: Constructing countermodel ... % 7.18/1.77 Prover 16: Constructing countermodel ... % 7.18/1.78 Prover 13: Constructing countermodel ... % 7.18/1.80 Prover 8: Warning: ignoring some quantifiers % 8.01/1.81 Prover 8: Constructing countermodel ... % 8.01/1.84 Prover 7: gave up % 8.01/1.84 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.01/1.85 Prover 10: gave up % 8.01/1.86 Prover 19: Preprocessing ... % 8.74/1.91 Prover 11: Constructing countermodel ... % 8.74/1.92 Prover 16: Found proof (size 21) % 8.74/1.92 Prover 16: proved (300ms) % 8.74/1.92 Prover 13: stopped % 8.74/1.92 Prover 4: stopped % 8.74/1.92 Prover 11: stopped % 8.74/1.93 Prover 8: stopped % 8.74/1.98 Prover 19: Warning: ignoring some quantifiers % 8.74/1.99 Prover 19: Constructing countermodel ... % 8.74/2.00 Prover 19: stopped % 8.74/2.00 % 8.74/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.74/2.00 % 8.74/2.01 % SZS output start Proof for theBenchmark % 8.74/2.02 Assumptions after simplification: % 8.74/2.02 --------------------------------- % 8.74/2.02 % 8.74/2.02 (l1) % 9.48/2.07 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ $i(v0) | ~ % 9.48/2.07 stable(v0) | ~ environment(v0) | ? [v1: $i] : ($i(v1) & in_environment(v0, % 9.48/2.07 v1) & ! [v2: $i] : ( ~ $i(v2) | ~ greater_or_equal(v2, v1) | ~ % 9.48/2.07 subpopulations(first_movers, efficient_producers, v0, v2) | ? [v3: $i] % 9.48/2.07 : ? [v4: $i] : (growth_rate(efficient_producers, v2) = v3 & % 9.48/2.07 growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) & greater(v3, % 9.48/2.07 v4))))) % 9.48/2.07 % 9.48/2.07 (mp1_high_growth_rates) % 9.48/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 9.48/2.08 | ~ $i(v1) | ~ $i(v0) | ~ subpopulations(v1, v2, v0, v3) | ~ % 9.48/2.08 environment(v0) | selection_favors(v2, v1, v3) | ? [v4: $i] : ? [v5: $i] : % 9.48/2.08 (growth_rate(v2, v3) = v4 & growth_rate(v1, v3) = v5 & $i(v5) & $i(v4) & ~ % 9.48/2.08 greater(v4, v5))) % 9.48/2.08 % 9.48/2.08 (prove_t1) % 9.48/2.09 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ($i(v0) & % 9.48/2.09 stable(v0) & environment(v0) & ! [v1: $i] : ( ~ $i(v1) | ~ % 9.48/2.09 in_environment(v0, v1) | ? [v2: $i] : ($i(v2) & greater_or_equal(v2, v1) % 9.48/2.09 & subpopulations(first_movers, efficient_producers, v0, v2) & ~ % 9.48/2.09 selection_favors(efficient_producers, first_movers, v2)))) % 9.48/2.09 % 9.48/2.09 (function-axioms) % 9.48/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.48/2.09 (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) % 9.48/2.09 % 9.48/2.09 Those formulas are unsatisfiable: % 9.48/2.09 --------------------------------- % 9.48/2.09 % 9.48/2.09 Begin of proof % 9.48/2.09 | % 9.48/2.09 | ALPHA: (l1) implies: % 9.48/2.10 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ stable(v0) | ~ environment(v0) | ? [v1: % 9.48/2.10 | $i] : ($i(v1) & in_environment(v0, v1) & ! [v2: $i] : ( ~ $i(v2) | % 9.48/2.10 | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, % 9.48/2.10 | efficient_producers, v0, v2) | ? [v3: $i] : ? [v4: $i] : % 9.48/2.10 | (growth_rate(efficient_producers, v2) = v3 & % 9.48/2.10 | growth_rate(first_movers, v2) = v4 & $i(v4) & $i(v3) & % 9.48/2.10 | greater(v3, v4))))) % 9.48/2.10 | % 9.48/2.10 | ALPHA: (prove_t1) implies: % 9.48/2.10 | (2) $i(first_movers) % 9.48/2.10 | (3) $i(efficient_producers) % 9.48/2.11 | (4) ? [v0: $i] : ($i(v0) & stable(v0) & environment(v0) & ! [v1: $i] : ( % 9.48/2.11 | ~ $i(v1) | ~ in_environment(v0, v1) | ? [v2: $i] : ($i(v2) & % 9.48/2.11 | greater_or_equal(v2, v1) & subpopulations(first_movers, % 9.48/2.11 | efficient_producers, v0, v2) & ~ % 9.48/2.11 | selection_favors(efficient_producers, first_movers, v2)))) % 9.48/2.11 | % 9.48/2.11 | DELTA: instantiating (4) with fresh symbol all_6_0 gives: % 9.48/2.11 | (5) $i(all_6_0) & stable(all_6_0) & environment(all_6_0) & ! [v0: $i] : ( % 9.48/2.11 | ~ $i(v0) | ~ in_environment(all_6_0, v0) | ? [v1: $i] : ($i(v1) & % 9.48/2.11 | greater_or_equal(v1, v0) & subpopulations(first_movers, % 9.48/2.11 | efficient_producers, all_6_0, v1) & ~ % 9.48/2.11 | selection_favors(efficient_producers, first_movers, v1))) % 9.48/2.11 | % 9.48/2.11 | ALPHA: (5) implies: % 9.48/2.11 | (6) environment(all_6_0) % 9.48/2.12 | (7) stable(all_6_0) % 9.48/2.12 | (8) $i(all_6_0) % 9.48/2.12 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ in_environment(all_6_0, v0) | ? [v1: $i] % 9.48/2.12 | : ($i(v1) & greater_or_equal(v1, v0) & subpopulations(first_movers, % 9.48/2.12 | efficient_producers, all_6_0, v1) & ~ % 9.48/2.12 | selection_favors(efficient_producers, first_movers, v1))) % 9.48/2.12 | % 9.48/2.12 | GROUND_INST: instantiating (1) with all_6_0, simplifying with (6), (7), (8) % 9.48/2.12 | gives: % 9.48/2.13 | (10) ? [v0: $i] : ($i(v0) & in_environment(all_6_0, v0) & ! [v1: $i] : ( % 9.48/2.13 | ~ $i(v1) | ~ greater_or_equal(v1, v0) | ~ % 9.48/2.13 | subpopulations(first_movers, efficient_producers, all_6_0, v1) | % 9.48/2.13 | ? [v2: $i] : ? [v3: $i] : (growth_rate(efficient_producers, v1) = % 9.48/2.13 | v2 & growth_rate(first_movers, v1) = v3 & $i(v3) & $i(v2) & % 9.48/2.13 | greater(v2, v3)))) % 9.48/2.13 | % 9.48/2.13 | DELTA: instantiating (10) with fresh symbol all_14_0 gives: % 9.48/2.13 | (11) $i(all_14_0) & in_environment(all_6_0, all_14_0) & ! [v0: $i] : ( ~ % 9.48/2.13 | $i(v0) | ~ greater_or_equal(v0, all_14_0) | ~ % 9.48/2.13 | subpopulations(first_movers, efficient_producers, all_6_0, v0) | ? % 9.48/2.13 | [v1: $i] : ? [v2: $i] : (growth_rate(efficient_producers, v0) = v1 % 9.48/2.13 | & growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) & % 9.48/2.13 | greater(v1, v2))) % 9.48/2.13 | % 9.48/2.13 | ALPHA: (11) implies: % 9.98/2.13 | (12) in_environment(all_6_0, all_14_0) % 9.98/2.13 | (13) $i(all_14_0) % 9.98/2.14 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ greater_or_equal(v0, all_14_0) | ~ % 9.98/2.14 | subpopulations(first_movers, efficient_producers, all_6_0, v0) | ? % 9.98/2.14 | [v1: $i] : ? [v2: $i] : (growth_rate(efficient_producers, v0) = v1 % 9.98/2.14 | & growth_rate(first_movers, v0) = v2 & $i(v2) & $i(v1) & % 9.98/2.14 | greater(v1, v2))) % 9.98/2.14 | % 9.98/2.14 | GROUND_INST: instantiating (9) with all_14_0, simplifying with (12), (13) % 9.98/2.14 | gives: % 9.98/2.14 | (15) ? [v0: $i] : ($i(v0) & greater_or_equal(v0, all_14_0) & % 9.98/2.14 | subpopulations(first_movers, efficient_producers, all_6_0, v0) & ~ % 9.98/2.14 | selection_favors(efficient_producers, first_movers, v0)) % 9.98/2.14 | % 9.98/2.14 | DELTA: instantiating (15) with fresh symbol all_22_0 gives: % 9.98/2.14 | (16) $i(all_22_0) & greater_or_equal(all_22_0, all_14_0) & % 9.98/2.14 | subpopulations(first_movers, efficient_producers, all_6_0, all_22_0) & % 9.98/2.14 | ~ selection_favors(efficient_producers, first_movers, all_22_0) % 9.98/2.14 | % 9.98/2.14 | ALPHA: (16) implies: % 9.98/2.14 | (17) ~ selection_favors(efficient_producers, first_movers, all_22_0) % 9.98/2.14 | (18) subpopulations(first_movers, efficient_producers, all_6_0, all_22_0) % 9.98/2.14 | (19) greater_or_equal(all_22_0, all_14_0) % 9.98/2.15 | (20) $i(all_22_0) % 9.98/2.15 | % 9.98/2.15 | GROUND_INST: instantiating (mp1_high_growth_rates) with all_6_0, first_movers, % 9.98/2.15 | efficient_producers, all_22_0, simplifying with (2), (3), (6), % 9.98/2.15 | (8), (17), (18), (20) gives: % 9.98/2.15 | (21) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers, % 9.98/2.15 | all_22_0) = v0 & growth_rate(first_movers, all_22_0) = v1 & $i(v1) % 9.98/2.15 | & $i(v0) & ~ greater(v0, v1)) % 9.98/2.15 | % 9.98/2.15 | GROUND_INST: instantiating (14) with all_22_0, simplifying with (18), (19), % 9.98/2.15 | (20) gives: % 9.98/2.15 | (22) ? [v0: $i] : ? [v1: $i] : (growth_rate(efficient_producers, % 9.98/2.15 | all_22_0) = v0 & growth_rate(first_movers, all_22_0) = v1 & $i(v1) % 9.98/2.15 | & $i(v0) & greater(v0, v1)) % 9.98/2.15 | % 9.98/2.15 | DELTA: instantiating (22) with fresh symbols all_29_0, all_29_1 gives: % 9.98/2.15 | (23) growth_rate(efficient_producers, all_22_0) = all_29_1 & % 9.98/2.15 | growth_rate(first_movers, all_22_0) = all_29_0 & $i(all_29_0) & % 9.98/2.15 | $i(all_29_1) & greater(all_29_1, all_29_0) % 9.98/2.15 | % 9.98/2.15 | ALPHA: (23) implies: % 9.98/2.16 | (24) greater(all_29_1, all_29_0) % 9.98/2.16 | (25) growth_rate(first_movers, all_22_0) = all_29_0 % 9.98/2.16 | (26) growth_rate(efficient_producers, all_22_0) = all_29_1 % 9.98/2.16 | % 9.98/2.16 | DELTA: instantiating (21) with fresh symbols all_31_0, all_31_1 gives: % 9.98/2.16 | (27) growth_rate(efficient_producers, all_22_0) = all_31_1 & % 9.98/2.16 | growth_rate(first_movers, all_22_0) = all_31_0 & $i(all_31_0) & % 9.98/2.16 | $i(all_31_1) & ~ greater(all_31_1, all_31_0) % 9.98/2.16 | % 9.98/2.16 | ALPHA: (27) implies: % 9.98/2.16 | (28) ~ greater(all_31_1, all_31_0) % 9.98/2.16 | (29) growth_rate(first_movers, all_22_0) = all_31_0 % 9.98/2.16 | (30) growth_rate(efficient_producers, all_22_0) = all_31_1 % 9.98/2.16 | % 9.98/2.16 | GROUND_INST: instantiating (function-axioms) with all_29_0, all_31_0, % 9.98/2.16 | all_22_0, first_movers, simplifying with (25), (29) gives: % 9.98/2.16 | (31) all_31_0 = all_29_0 % 9.98/2.16 | % 9.98/2.16 | GROUND_INST: instantiating (function-axioms) with all_29_1, all_31_1, % 9.98/2.16 | all_22_0, efficient_producers, simplifying with (26), (30) gives: % 9.98/2.16 | (32) all_31_1 = all_29_1 % 9.98/2.16 | % 9.98/2.16 | REDUCE: (28), (31), (32) imply: % 9.98/2.16 | (33) ~ greater(all_29_1, all_29_0) % 9.98/2.16 | % 9.98/2.16 | PRED_UNIFY: (24), (33) imply: % 9.98/2.17 | (34) $false % 9.98/2.17 | % 9.98/2.17 | CLOSE: (34) is inconsistent. % 9.98/2.17 | % 9.98/2.17 End of proof % 9.98/2.17 % SZS output end Proof for theBenchmark % 9.98/2.17 % 9.98/2.17 1465ms %------------------------------------------------------------------------------