%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n006.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 06:24:03 AM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.12s
% 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.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 12:42:17 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(outcompetes_type, type, (
% 0.12/0.40 outcompetes: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_T_0_type, type, (
% 0.12/0.40 tptp_fun_T_0: $i)).
% 0.12/0.40 tff(efficient_producers_type, type, (
% 0.12/0.40 efficient_producers: $i)).
% 0.12/0.40 tff(first_movers_type, type, (
% 0.12/0.40 first_movers: $i)).
% 0.12/0.40 tff(greater_type, type, (
% 0.12/0.40 greater: ( $i * $i ) > $o)).
% 0.12/0.40 tff(growth_rate_type, type, (
% 0.12/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.12/0.40 tff(zero_type, type, (
% 0.12/0.40 zero: $i)).
% 0.12/0.40 tff(greater_or_equal_type, type, (
% 0.12/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.12/0.40 tff(subpopulations_type, type, (
% 0.12/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_E_1_type, type, (
% 0.12/0.40 tptp_fun_E_1: $i)).
% 0.12/0.40 tff(environment_type, type, (
% 0.12/0.40 environment: $i > $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) <=> ?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (?[E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))) <=> ?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.40 tff(4,axiom,(?[E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a13_star')).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.40 tff(7,plain,(
% 0.12/0.40 environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & greater_or_equal(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))),
% 0.12/0.40 inference(skolemize,[status(sab)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (greater(zero, growth_rate(efficient_producers, T!0))),
% 0.12/0.40 inference(and_elim,[status(thm)],[7])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (greater_or_equal(growth_rate(first_movers, T!0), zero)),
% 0.12/0.40 inference(and_elim,[status(thm)],[7])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 ((~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[10, 9, 8])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (^[E: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (^[E: $i, T: $i] : trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![E: $i, T: $i] : (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 ((~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))) <=> (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 ((~?[E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & outcompetes(first_movers, efficient_producers, T))) <=> (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(18,axiom,(~?[E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & outcompetes(first_movers, efficient_producers, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t5_star')).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (^[E: $i, T: $i] : refl($oeq((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))), (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(24,plain,(
% 0.12/0.40 ![E: $i, T: $i] : (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(nnf-neg,[status(sab)],[22, 23])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.12/0.40 inference(and_elim,[status(thm)],[7])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (environment(E!1)),
% 0.12/0.40 inference(and_elim,[status(thm)],[7])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~outcompetes(first_movers, efficient_producers, T!0)))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~outcompetes(first_movers, efficient_producers, T!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~outcompetes(first_movers, efficient_producers, T!0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~outcompetes(first_movers, efficient_producers, T!0))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (~outcompetes(first_movers, efficient_producers, T!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[31, 28, 27, 26])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 ((((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)) | ((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) | outcompetes(first_movers, efficient_producers, T!0)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[33, 32, 11])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E))) <=> (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T)) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.40 tff(42,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_symmetry_of_subpopulations')).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.12/0.40 tff(45,plain,(
% 0.12/0.40 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.12/0.40 inference(skolemize,[status(sab)],[44])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.12/0.41 tff(47,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 ((subpopulations(efficient_producers, first_movers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~environment(E!1))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(50,plain,
% 0.12/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~environment(E!1)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.12/0.41 tff(51,plain,
% 0.12/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~environment(E!1)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.41 inference(transitivity,[status(thm)],[50, 48])).
% 0.12/0.41 tff(52,plain,
% 0.12/0.41 ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~environment(E!1)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~subpopulations(S1, S2, E, T)) | (~environment(E)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[53, 47, 28, 27])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T)))) <=> ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T)) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T))))), trans(trans(monotonicity(rewrite((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> (~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))))), (((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))), rewrite(((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)) <=> (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T)))), (((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))), rewrite((~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))) <=> (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T)))), (((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T))) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T)))))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T))) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T)))) <=> ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(58,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.12/0.41 tff(59,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(60,plain,
% 0.12/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(61,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.12/0.41 tff(62,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2')).
% 0.12/0.41 tff(63,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.41 tff(64,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.12/0.41 tff(65,plain,(
% 0.12/0.41 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[64])).
% 0.12/0.41 tff(66,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.12/0.41 tff(67,plain,
% 0.12/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.12/0.41 tff(68,plain,
% 0.12/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))) | ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(69,plain,
% 0.12/0.41 (((~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~environment(E!1)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)))) <=> ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(70,plain,
% 0.12/0.41 ((~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))) <=> (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(71,plain,
% 0.12/0.41 ((((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)) <=> (((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(72,plain,
% 0.12/0.41 ((~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))) <=> (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[71])).
% 0.12/0.41 tff(73,plain,
% 0.12/0.41 ((~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))) <=> (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[72, 70])).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 (((~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~environment(E!1)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)))) <=> ((~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~environment(E!1)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[73])).
% 0.12/0.41 tff(75,plain,
% 0.12/0.41 (((~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~environment(E!1)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)))) <=> ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[74, 69])).
% 0.12/0.41 tff(76,plain,
% 0.12/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))) | ((~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~environment(E!1)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))) | ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.12/0.42 tff(77,plain,
% 0.12/0.42 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))) | ((~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~environment(E!1)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[76, 68])).
% 0.12/0.42 tff(78,plain,
% 0.12/0.42 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))) | ((~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~environment(E!1)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0))))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(79,plain,
% 0.12/0.42 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~subpopulations(S1, S2, E, T)) | (~environment(E)) | (~(((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T)))) <=> outcompetes(S2, S1, T))))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.42 tff(80,plain,
% 0.12/0.42 ($false),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[79, 67, 28, 54, 34])).
% 0.12/0.42 % SZS output end Proof
% 0.12/0.42 % E exiting
%------------------------------------------------------------------------------