%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT028+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n016.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 06:24:00 AM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT028+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 12:19:34 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.11/0.40 % SZS status Theorem
% 0.11/0.40 % SZS output start Proof
% 0.11/0.40 tff(greater_or_equal_type, type, (
% 0.11/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.11/0.40 tff(tptp_fun_T2_1_type, type, (
% 0.11/0.40 tptp_fun_T2_1: $i > $i)).
% 0.11/0.40 tff(tptp_fun_E_3_type, type, (
% 0.11/0.40 tptp_fun_E_3: $i)).
% 0.11/0.40 tff(tptp_fun_T_4_type, type, (
% 0.11/0.40 tptp_fun_T_4: $i > $i)).
% 0.11/0.40 tff(subpopulations_type, type, (
% 0.11/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.11/0.40 tff(efficient_producers_type, type, (
% 0.11/0.40 efficient_producers: $i)).
% 0.11/0.40 tff(first_movers_type, type, (
% 0.11/0.40 first_movers: $i)).
% 0.11/0.40 tff(greater_type, type, (
% 0.11/0.40 greater: ( $i * $i ) > $o)).
% 0.11/0.40 tff(growth_rate_type, type, (
% 0.11/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.11/0.40 tff(zero_type, type, (
% 0.11/0.40 zero: $i)).
% 0.11/0.40 tff(appear_type, type, (
% 0.11/0.40 appear: ( $i * $i ) > $i)).
% 0.11/0.40 tff(tptp_fun_T_0_type, type, (
% 0.11/0.40 tptp_fun_T_0: ( $i * $i ) > $i)).
% 0.11/0.40 tff(in_environment_type, type, (
% 0.11/0.40 in_environment: ( $i * $i ) > $o)).
% 0.11/0.40 tff(tptp_fun_To_2_type, type, (
% 0.11/0.40 tptp_fun_To_2: $i > $i)).
% 0.11/0.40 tff(stable_type, type, (
% 0.11/0.40 stable: $i > $o)).
% 0.11/0.40 tff(environment_type, type, (
% 0.11/0.40 environment: $i > $o)).
% 0.11/0.40 tff(1,assumption,(~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))))), introduced(assumption)).
% 0.11/0.40 tff(2,plain,
% 0.11/0.40 (((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(3,plain,
% 0.11/0.40 (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.11/0.40 tff(4,plain,
% 0.11/0.40 (((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(5,plain,
% 0.11/0.40 ((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.11/0.40 tff(6,plain,
% 0.11/0.40 (((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))) | greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(7,plain,
% 0.11/0.40 (greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.11/0.40 tff(8,plain,
% 0.11/0.40 (((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))) | subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(9,plain,
% 0.11/0.40 (subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.11/0.40 tff(10,plain,
% 0.11/0.40 (((environment(E!3) & stable(E!3)) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))))))) <=> (environment(E!3) & stable(E!3) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To)))))))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(11,plain,
% 0.11/0.41 ((~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(12,plain,
% 0.11/0.41 ((~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(13,axiom,(~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l10')).
% 0.11/0.41 tff(14,plain,
% 0.11/0.41 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.41 tff(15,plain,
% 0.11/0.41 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.11/0.41 tff(16,plain,
% 0.11/0.41 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.11/0.41 tff(17,plain,
% 0.11/0.41 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.11/0.41 tff(18,plain,
% 0.11/0.41 (environment(E!3) & stable(E!3) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.11/0.41 tff(19,plain,
% 0.11/0.41 (stable(E!3)),
% 0.11/0.41 inference(and_elim,[status(thm)],[18])).
% 0.11/0.41 tff(20,plain,
% 0.11/0.41 (environment(E!3)),
% 0.11/0.41 inference(and_elim,[status(thm)],[18])).
% 0.11/0.41 tff(21,plain,
% 0.11/0.41 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(22,plain,
% 0.11/0.41 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.41 tff(23,plain,
% 0.11/0.41 (^[E: $i] : rewrite(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(24,plain,
% 0.11/0.41 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.41 tff(25,plain,
% 0.11/0.41 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.11/0.41 inference(transitivity,[status(thm)],[24, 22])).
% 0.11/0.41 tff(26,plain,
% 0.11/0.41 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & stable(E)) <=> (~((~environment(E)) | (~stable(E))))), ((~(environment(E) & stable(E))) <=> (~(~((~environment(E)) | (~stable(E))))))), rewrite((~(~((~environment(E)) | (~stable(E))))) <=> ((~environment(E)) | (~stable(E)))), ((~(environment(E) & stable(E))) <=> ((~environment(E)) | (~stable(E))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))), rewrite((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) <=> (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))), rewrite((((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> ![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))), ((in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))), rewrite((in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) <=> (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))), ((in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> (((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(27,plain,
% 0.11/0.41 (![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.11/0.41 tff(28,plain,
% 0.11/0.41 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(29,plain,
% 0.11/0.41 (^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[To: $i] : rewrite((in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))), (?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))), (((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))))), rewrite(((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))), (((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(30,plain,
% 0.11/0.41 (![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.11/0.41 tff(31,axiom,(![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l11')).
% 0.11/0.41 tff(32,plain,
% 0.11/0.41 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.11/0.41 tff(33,plain,
% 0.11/0.41 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.11/0.41 tff(34,plain,(
% 0.11/0.41 ![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.41 inference(skolemize,[status(sab)],[33])).
% 0.11/0.41 tff(35,plain,
% 0.11/0.41 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.11/0.41 tff(36,plain,
% 0.11/0.41 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.11/0.42 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.11/0.42 tff(37,plain,
% 0.11/0.42 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) | ((~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) | (~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.11/0.42 inference(rewrite,[status(thm)],[])).
% 0.11/0.42 tff(38,plain,
% 0.11/0.42 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) | ((~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.11/0.42 inference(quant_inst,[status(thm)],[])).
% 0.11/0.42 tff(39,plain,
% 0.11/0.42 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) | (~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))),
% 0.11/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.42 tff(40,plain,
% 0.11/0.42 (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))),
% 0.11/0.42 inference(unit_resolution,[status(thm)],[39, 36, 20, 19])).
% 0.11/0.42 tff(41,plain,
% 0.11/0.42 (((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))) | ![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.42 inference(tautology,[status(thm)],[])).
% 0.11/0.42 tff(42,plain,
% 0.11/0.42 (![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))),
% 0.11/0.42 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.11/0.42 tff(43,plain,
% 0.11/0.42 (((~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) | ((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))))))) <=> ((~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))))))),
% 0.11/0.42 inference(rewrite,[status(thm)],[])).
% 0.11/0.42 tff(44,plain,
% 0.11/0.42 ((~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) | ((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))))))),
% 0.11/0.42 inference(quant_inst,[status(thm)],[])).
% 0.11/0.42 tff(45,plain,
% 0.11/0.42 ((~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))))),
% 0.11/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.11/0.42 tff(46,plain,
% 0.11/0.42 ($false),
% 0.11/0.42 inference(unit_resolution,[status(thm)],[45, 42, 9, 7, 5])).
% 0.11/0.42 tff(47,plain,((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.42 tff(48,plain,
% 0.11/0.42 (((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))) | in_environment(E!3, tptp_fun_To_2(E!3))),
% 0.11/0.42 inference(tautology,[status(thm)],[])).
% 0.11/0.42 tff(49,plain,
% 0.11/0.42 (in_environment(E!3, tptp_fun_To_2(E!3))),
% 0.11/0.42 inference(unit_resolution,[status(thm)],[48, 40])).
% 0.11/0.42 tff(50,assumption,(![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))), introduced(assumption)).
% 0.11/0.42 tff(51,plain,
% 0.11/0.42 (((~![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))) | ((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))))))) <=> ((~![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))) | (~in_environment(E!3, tptp_fun_To_2(E!3))) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))))))),
% 0.11/0.42 inference(rewrite,[status(thm)],[])).
% 0.11/0.42 tff(52,plain,
% 0.11/0.42 ((~![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))) | ((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))))))),
% 0.11/0.42 inference(quant_inst,[status(thm)],[])).
% 0.11/0.42 tff(53,plain,
% 0.11/0.42 ((~![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))) | (~in_environment(E!3, tptp_fun_To_2(E!3))) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))))),
% 0.11/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.42 tff(54,plain,
% 0.11/0.42 ($false),
% 0.11/0.42 inference(unit_resolution,[status(thm)],[53, 50, 49, 47])).
% 0.11/0.42 tff(55,plain,(~![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.42 tff(56,plain,
% 0.11/0.42 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))))),
% 0.11/0.42 inference(bind,[status(th)],[])).
% 0.11/0.42 tff(57,plain,
% 0.11/0.42 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.11/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.11/0.42 tff(58,plain,
% 0.11/0.42 (^[E: $i] : rewrite(((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))))),
% 0.11/0.42 inference(bind,[status(th)],[])).
% 0.11/0.42 tff(59,plain,
% 0.11/0.42 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.11/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.11/0.42 tff(60,plain,
% 0.11/0.42 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.11/0.42 inference(transitivity,[status(thm)],[59, 57])).
% 0.11/0.42 tff(61,plain,
% 0.11/0.42 (^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[T1: $i] : rewrite(((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) <=> ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))))), (![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) <=> ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))), rewrite((((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))), ((greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))) <=> (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))), rewrite((greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))) <=> (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))), ((greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))) <=> (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))), (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))))), rewrite(((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))), (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))))),
% 0.11/0.43 inference(bind,[status(th)],[])).
% 0.11/0.43 tff(62,plain,
% 0.11/0.43 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.11/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.11/0.43 tff(63,plain,
% 0.11/0.43 (^[E: $i] : trans(monotonicity(rewrite(((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))))), rewrite((greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))) <=> (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))), ((((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))))), rewrite((((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))), ((((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))))),
% 0.11/0.43 inference(bind,[status(th)],[])).
% 0.11/0.43 tff(64,plain,
% 0.11/0.43 (![E: $i] : (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.43 inference(quant_intro,[status(thm)],[63])).
% 0.11/0.43 tff(65,plain,
% 0.11/0.43 (![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.43 inference(rewrite,[status(thm)],[])).
% 0.11/0.43 tff(66,plain,
% 0.11/0.43 (^[E: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[T1: $i] : rewrite((in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T)))) <=> (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))), (?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T)))) <=> ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) <=> ((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))))), rewrite(((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))) <=> (environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) <=> (environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))))), quant_intro(proof_bind(^[T2: $i] : rewrite((greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T)))) <=> (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))), (?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T)))) <=> ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))), ((((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T))))) <=> ((environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T))))))), rewrite(((environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))), ((((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))))),
% 0.11/0.43 inference(bind,[status(th)],[])).
% 0.11/0.43 tff(67,plain,
% 0.11/0.43 (![E: $i] : (((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.43 inference(quant_intro,[status(thm)],[66])).
% 0.11/0.43 tff(68,axiom,(![E: $i] : (((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_first_movers_negative_growth')).
% 0.11/0.43 tff(69,plain,
% 0.11/0.43 (![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.11/0.43 tff(70,plain,
% 0.11/0.43 (![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.43 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.11/0.43 tff(71,plain,(
% 0.11/0.43 ![E: $i] : (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.43 inference(skolemize,[status(sab)],[70])).
% 0.11/0.43 tff(72,plain,
% 0.11/0.43 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.11/0.43 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.11/0.43 tff(73,plain,
% 0.11/0.43 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.11/0.44 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.11/0.44 tff(74,plain,
% 0.11/0.44 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.11/0.44 inference(modus_ponens,[status(thm)],[73, 60])).
% 0.11/0.44 tff(75,plain,
% 0.11/0.44 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | ((~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) | (~stable(E!3)) | (~environment(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) | (~stable(E!3)) | (~environment(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))))),
% 0.11/0.44 inference(rewrite,[status(thm)],[])).
% 0.11/0.44 tff(76,plain,
% 0.11/0.44 (((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))))) <=> ((~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) | (~stable(E!3)) | (~environment(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))))),
% 0.11/0.44 inference(rewrite,[status(thm)],[])).
% 0.11/0.44 tff(77,plain,
% 0.11/0.44 ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) <=> (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))),
% 0.11/0.44 inference(rewrite,[status(thm)],[])).
% 0.11/0.44 tff(78,plain,
% 0.11/0.44 (((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))) <=> ((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))),
% 0.11/0.44 inference(monotonicity,[status(thm)],[77])).
% 0.11/0.44 tff(79,plain,
% 0.11/0.44 ((~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) <=> (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))))),
% 0.11/0.44 inference(monotonicity,[status(thm)],[78])).
% 0.11/0.44 tff(80,plain,
% 0.11/0.44 (^[T1: $i] : rewrite(((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) <=> ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))))),
% 0.11/0.44 inference(bind,[status(th)],[])).
% 0.11/0.44 tff(81,plain,
% 0.11/0.44 (![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) <=> ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))),
% 0.11/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.11/0.44 tff(82,plain,
% 0.11/0.44 (((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))))) <=> ((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))))),
% 0.11/0.44 inference(monotonicity,[status(thm)],[81, 79])).
% 0.11/0.44 tff(83,plain,
% 0.11/0.44 (((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))))) <=> ((~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) | (~stable(E!3)) | (~environment(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))))),
% 0.11/0.44 inference(transitivity,[status(thm)],[82, 76])).
% 0.11/0.44 tff(84,plain,
% 0.11/0.44 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | ((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | ((~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) | (~stable(E!3)) | (~environment(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))))),
% 0.11/0.44 inference(monotonicity,[status(thm)],[83])).
% 0.11/0.44 tff(85,plain,
% 0.11/0.44 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | ((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) | (~stable(E!3)) | (~environment(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))))),
% 0.11/0.44 inference(transitivity,[status(thm)],[84, 75])).
% 0.11/0.44 tff(86,plain,
% 0.11/0.44 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | ((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))))),
% 0.11/0.44 inference(quant_inst,[status(thm)],[])).
% 0.11/0.44 tff(87,plain,
% 0.11/0.44 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) | (~stable(E!3)) | (~environment(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))),
% 0.11/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.11/0.44 tff(88,plain,
% 0.11/0.44 ((~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))),
% 0.11/0.44 inference(unit_resolution,[status(thm)],[87, 74, 20, 19])).
% 0.11/0.44 tff(89,plain,
% 0.11/0.44 (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))),
% 0.11/0.44 inference(unit_resolution,[status(thm)],[88, 55])).
% 0.11/0.44 tff(90,plain,
% 0.11/0.44 (((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))) | greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))),
% 0.11/0.44 inference(tautology,[status(thm)],[])).
% 0.11/0.44 tff(91,plain,
% 0.11/0.44 (greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))),
% 0.11/0.44 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.11/0.44 tff(92,plain,
% 0.11/0.44 (^[To: $i] : refl(((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To))))) <=> ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To))))))),
% 0.11/0.44 inference(bind,[status(th)],[])).
% 0.11/0.44 tff(93,plain,
% 0.11/0.44 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To))))) <=> ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))),
% 0.11/0.44 inference(quant_intro,[status(thm)],[92])).
% 0.11/0.44 tff(94,plain,
% 0.11/0.44 (^[To: $i] : rewrite(((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To))))))),
% 0.11/0.44 inference(bind,[status(th)],[])).
% 0.11/0.44 tff(95,plain,
% 0.11/0.44 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))),
% 0.11/0.44 inference(quant_intro,[status(thm)],[94])).
% 0.11/0.44 tff(96,plain,
% 0.11/0.44 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))))))),
% 0.11/0.44 inference(and_elim,[status(thm)],[18])).
% 0.11/0.44 tff(97,plain,
% 0.11/0.44 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))),
% 0.11/0.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.11/0.44 tff(98,plain,
% 0.11/0.44 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))),
% 0.11/0.44 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.11/0.44 tff(99,plain,
% 0.11/0.44 (((~![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))) | ((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))))) <=> ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))) | (~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))))),
% 0.11/0.45 inference(rewrite,[status(thm)],[])).
% 0.11/0.45 tff(100,plain,
% 0.11/0.45 ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))) | ((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))))),
% 0.11/0.45 inference(quant_inst,[status(thm)],[])).
% 0.11/0.45 tff(101,plain,
% 0.11/0.45 ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))) | (~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))))),
% 0.11/0.45 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.11/0.45 tff(102,plain,
% 0.11/0.45 (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))),
% 0.11/0.45 inference(unit_resolution,[status(thm)],[101, 98, 91])).
% 0.11/0.45 tff(103,plain,
% 0.11/0.45 ((greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))) | greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))),
% 0.11/0.45 inference(tautology,[status(thm)],[])).
% 0.11/0.45 tff(104,plain,
% 0.11/0.45 (greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))),
% 0.11/0.45 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.11/0.45 tff(105,plain,
% 0.11/0.45 ((greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))) | subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))),
% 0.11/0.45 inference(tautology,[status(thm)],[])).
% 0.11/0.45 tff(106,plain,
% 0.11/0.45 (subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))),
% 0.11/0.45 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.11/0.45 tff(107,plain,
% 0.11/0.45 ((greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))))),
% 0.11/0.45 inference(tautology,[status(thm)],[])).
% 0.11/0.45 tff(108,plain,
% 0.11/0.45 (~greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3))))),
% 0.11/0.45 inference(unit_resolution,[status(thm)],[107, 102])).
% 0.11/0.45 tff(109,plain,
% 0.11/0.45 (((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))) | ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))),
% 0.11/0.45 inference(tautology,[status(thm)],[])).
% 0.11/0.45 tff(110,plain,
% 0.11/0.45 (![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))),
% 0.11/0.45 inference(unit_resolution,[status(thm)],[109, 89])).
% 0.11/0.45 tff(111,plain,
% 0.11/0.45 (((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))) <=> ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))),
% 0.11/0.45 inference(rewrite,[status(thm)],[])).
% 0.11/0.45 tff(112,plain,
% 0.11/0.45 ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))),
% 0.11/0.45 inference(quant_inst,[status(thm)],[])).
% 0.11/0.45 tff(113,plain,
% 0.11/0.45 ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))),
% 0.11/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.11/0.45 tff(114,plain,
% 0.11/0.45 ($false),
% 0.11/0.45 inference(unit_resolution,[status(thm)],[113, 110, 108, 106, 104])).
% 0.11/0.45 % SZS output end Proof
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------