%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT030+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n026.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 06:24:01 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 12:21:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(greater_or_equal_type, type, (
% 0.14/0.41 greater_or_equal: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_To_2_type, type, (
% 0.14/0.41 tptp_fun_To_2: $i > $i)).
% 0.14/0.41 tff(tptp_fun_E_3_type, type, (
% 0.14/0.41 tptp_fun_E_3: $i)).
% 0.14/0.41 tff(tptp_fun_T_0_type, type, (
% 0.14/0.41 tptp_fun_T_0: ( $i * $i ) > $i)).
% 0.14/0.41 tff(subpopulations_type, type, (
% 0.14/0.41 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.14/0.41 tff(efficient_producers_type, type, (
% 0.14/0.41 efficient_producers: $i)).
% 0.14/0.41 tff(first_movers_type, type, (
% 0.14/0.41 first_movers: $i)).
% 0.14/0.41 tff(greater_type, type, (
% 0.14/0.41 greater: ( $i * $i ) > $o)).
% 0.14/0.41 tff(growth_rate_type, type, (
% 0.14/0.41 growth_rate: ( $i * $i ) > $i)).
% 0.14/0.41 tff(in_environment_type, type, (
% 0.14/0.41 in_environment: ( $i * $i ) > $o)).
% 0.14/0.41 tff(stable_type, type, (
% 0.14/0.41 stable: $i > $o)).
% 0.14/0.41 tff(tptp_fun_T_4_type, type, (
% 0.14/0.41 tptp_fun_T_4: $i > $i)).
% 0.14/0.41 tff(environment_type, type, (
% 0.14/0.41 environment: $i > $o)).
% 0.14/0.41 tff(tptp_fun_To_1_type, type, (
% 0.14/0.41 tptp_fun_To_1: $i > $i)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (((environment(E!3) & stable(E!3)) & ![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))))))) <=> (environment(E!3) & stable(E!3) & ![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (^[To: $i] : rewrite(((~in_environment(E!3, To)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (![To: $i] : ((~in_environment(E!3, To)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> ![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (((environment(E!3) & stable(E!3)) & ![To: $i] : ((~in_environment(E!3, To)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))))))) <=> ((environment(E!3) & stable(E!3)) & ![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[3])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.42 (((environment(E!3) & stable(E!3)) & ![To: $i] : ((~in_environment(E!3, To)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))))))) <=> (environment(E!3) & stable(E!3) & ![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[4, 1])).
% 0.14/0.42 tff(6,plain,
% 0.14/0.42 ((~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(7,plain,
% 0.14/0.42 ((~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(8,axiom,(~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l12')).
% 0.14/0.42 tff(9,plain,
% 0.14/0.42 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.14/0.42 tff(10,plain,
% 0.14/0.42 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.14/0.42 tff(11,plain,
% 0.14/0.42 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.14/0.42 tff(12,plain,
% 0.14/0.42 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.14/0.42 tff(13,plain,
% 0.14/0.42 (environment(E!3) & stable(E!3) & ![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.42 tff(14,plain,
% 0.14/0.42 (stable(E!3)),
% 0.14/0.42 inference(and_elim,[status(thm)],[13])).
% 0.14/0.42 tff(15,plain,
% 0.14/0.42 (environment(E!3)),
% 0.14/0.42 inference(and_elim,[status(thm)],[13])).
% 0.14/0.42 tff(16,plain,
% 0.14/0.42 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(17,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.42 tff(18,plain,
% 0.14/0.42 (^[E: $i] : rewrite(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(19,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.42 tff(20,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[19, 17])).
% 0.14/0.42 tff(21,plain,
% 0.14/0.42 (^[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)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | greater(growth_rate(efficient_producers, T), 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), 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), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~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)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, 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), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(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), growth_rate(first_movers, T)))) <=> (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))), rewrite((in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))) <=> (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(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), growth_rate(first_movers, T)))) <=> (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))), (((~(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), growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))), (((~(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), growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(22,plain,
% 0.14/0.42 (![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), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.14/0.42 tff(23,plain,
% 0.14/0.42 (![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), 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), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(24,plain,
% 0.14/0.42 (^[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), 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), 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), 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), 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), 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), 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), 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), 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), 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), growth_rate(first_movers, T)))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(25,plain,
% 0.14/0.42 (![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), 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), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.14/0.42 tff(26,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), growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1')).
% 0.14/0.42 tff(27,plain,
% 0.14/0.42 (![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), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.14/0.42 tff(28,plain,
% 0.14/0.42 (![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), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.14/0.42 tff(29,plain,(
% 0.14/0.42 ![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), growth_rate(first_movers, T)))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[28])).
% 0.14/0.42 tff(30,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.14/0.42 tff(31,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.14/0.42 tff(32,plain,
% 0.14/0.42 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))) | ((~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))) | (~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(33,plain,
% 0.14/0.42 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))) | ((~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(34,plain,
% 0.14/0.42 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))))))) | (~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3)))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.14/0.42 tff(35,plain,
% 0.14/0.42 (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[34, 31, 15, 14])).
% 0.14/0.42 tff(36,plain,
% 0.14/0.42 (((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3)))))) | in_environment(E!3, tptp_fun_To_2(E!3))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(37,plain,
% 0.14/0.42 (in_environment(E!3, tptp_fun_To_2(E!3))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.14/0.42 tff(38,assumption,(~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))))), introduced(assumption)).
% 0.14/0.42 tff(39,plain,
% 0.14/0.42 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))) | (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(40,plain,
% 0.14/0.43 (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.14/0.43 tff(41,plain,
% 0.14/0.43 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))) | in_environment(E!3, tptp_fun_To_1(E!3))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(42,plain,
% 0.14/0.43 (in_environment(E!3, tptp_fun_To_1(E!3))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.14/0.43 tff(43,plain,
% 0.14/0.43 (^[To: $i] : refl((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(44,plain,
% 0.14/0.43 (![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To))))) <=> ![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[43])).
% 0.14/0.43 tff(45,plain,
% 0.14/0.43 (^[To: $i] : trans(monotonicity(rewrite((~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))))) <=> (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To))))), ((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To))))))), rewrite((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))), ((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(46,plain,
% 0.14/0.43 (![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> ![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.14/0.43 tff(47,plain,
% 0.14/0.43 (![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater(tptp_fun_T_4(To), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))))))),
% 0.14/0.43 inference(and_elim,[status(thm)],[13])).
% 0.14/0.43 tff(48,plain,
% 0.14/0.43 (![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.14/0.43 tff(49,plain,
% 0.14/0.43 (![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.14/0.43 tff(50,plain,
% 0.14/0.43 (((~![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))) | ((~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))) <=> ((~![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(51,plain,
% 0.14/0.43 ((greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))))) <=> ((~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(52,plain,
% 0.14/0.43 ((~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))) <=> (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(53,plain,
% 0.14/0.43 ((greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))))) <=> (greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.14/0.43 tff(54,plain,
% 0.14/0.43 ((greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))))) <=> ((~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[53, 51])).
% 0.14/0.43 tff(55,plain,
% 0.14/0.43 (((~![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))) | (greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))) <=> ((~![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))) | ((~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[54])).
% 0.14/0.43 tff(56,plain,
% 0.14/0.43 (((~![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))) | (greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))) <=> ((~![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[55, 50])).
% 0.14/0.43 tff(57,plain,
% 0.14/0.43 ((~![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))) | (greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(58,plain,
% 0.14/0.43 ((~![To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(To)), growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater(tptp_fun_T_4(To), To)))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.14/0.43 tff(59,plain,
% 0.14/0.43 (~(greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[58, 49, 42, 40])).
% 0.14/0.43 tff(60,plain,
% 0.14/0.43 ((greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))) | greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(61,plain,
% 0.14/0.43 (greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.14/0.43 tff(62,plain,
% 0.14/0.43 ((greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))) | subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(63,plain,
% 0.14/0.43 (subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.14/0.43 tff(64,plain,
% 0.14/0.43 ((greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(65,plain,
% 0.14/0.43 (~greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[64, 59])).
% 0.14/0.43 tff(66,plain,
% 0.14/0.43 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(67,plain,
% 0.14/0.44 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[66, 38])).
% 0.14/0.44 tff(68,plain,
% 0.14/0.44 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(69,plain,
% 0.14/0.44 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3))))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(70,plain,
% 0.14/0.44 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | greater(growth_rate(efficient_producers, tptp_fun_T_4(tptp_fun_To_1(E!3))), growth_rate(first_movers, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_To_1(E!3)))) | (~greater(tptp_fun_T_4(tptp_fun_To_1(E!3)), tptp_fun_To_1(E!3)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.14/0.44 tff(71,plain,
% 0.14/0.44 ($false),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[70, 67, 65, 63, 61])).
% 0.14/0.44 tff(72,plain,((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.44 tff(73,plain,
% 0.14/0.44 (^[E: $i] : refl(((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))) <=> ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(74,plain,
% 0.14/0.44 (![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[73])).
% 0.14/0.44 tff(75,plain,
% 0.14/0.44 (^[E: $i] : rewrite(((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))) <=> ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(76,plain,
% 0.14/0.44 (![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.14/0.44 tff(77,plain,
% 0.14/0.44 (![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))),
% 0.14/0.44 inference(transitivity,[status(thm)],[76, 74])).
% 0.14/0.44 tff(78,plain,
% 0.14/0.44 (^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[To: $i] : rewrite(((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) <=> ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))))), (![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) <=> ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), rewrite((((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))), ((in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))), rewrite((in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))) <=> (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))), ((in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))), (((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))))), rewrite(((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E)))))))) <=> ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))), (((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(79,plain,
% 0.14/0.44 (![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[78])).
% 0.14/0.44 tff(80,plain,
% 0.14/0.44 (^[E: $i] : trans(monotonicity(rewrite(((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))))))) <=> ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))))), rewrite((in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), ((((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> (((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))), rewrite((((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), ((((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(81,plain,
% 0.14/0.45 (![E: $i] : (((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.14/0.45 tff(82,plain,
% 0.14/0.45 (![E: $i] : ((~(environment(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), growth_rate(first_movers, T)))))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(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), growth_rate(first_movers, T)))))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(83,plain,
% 0.14/0.45 (^[E: $i] : trans(monotonicity(rewrite((environment(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), growth_rate(first_movers, T))))) <=> (environment(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), growth_rate(first_movers, T)))))), quant_intro(proof_bind(^[To: $i] : trans(monotonicity(quant_intro(proof_bind(^[T: $i] : rewrite(((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), (![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), (((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), rewrite(((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), (((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))), (?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (((environment(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), growth_rate(first_movers, T))))) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((environment(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), growth_rate(first_movers, T))))) => ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))), rewrite(((environment(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), growth_rate(first_movers, T))))) => ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(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), growth_rate(first_movers, T)))))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (((environment(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), growth_rate(first_movers, T))))) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(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), growth_rate(first_movers, T)))))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(84,plain,
% 0.14/0.45 (![E: $i] : ((environment(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), growth_rate(first_movers, T))))) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(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), growth_rate(first_movers, T)))))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.14/0.45 tff(85,axiom,(![E: $i] : ((environment(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), growth_rate(first_movers, T))))) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds')).
% 0.14/0.45 tff(86,plain,
% 0.14/0.45 (![E: $i] : ((~(environment(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), growth_rate(first_movers, T)))))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.14/0.45 tff(87,plain,
% 0.14/0.45 (![E: $i] : ((~(environment(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), growth_rate(first_movers, T)))))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.14/0.45 tff(88,plain,(
% 0.14/0.45 ![E: $i] : (((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.45 inference(skolemize,[status(sab)],[87])).
% 0.14/0.45 tff(89,plain,
% 0.14/0.45 (![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater_or_equal(tptp_fun_T_0(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E)))))) | (in_environment(E, tptp_fun_To_1(E)) & (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, tptp_fun_To_1(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.14/0.45 tff(90,plain,
% 0.14/0.45 (![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.14/0.45 tff(91,plain,
% 0.14/0.45 (![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[90, 77])).
% 0.14/0.45 tff(92,plain,
% 0.14/0.45 (((~![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))) | (![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~environment(E!3)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))))))) <=> ((~![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~environment(E!3)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))))))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(93,plain,
% 0.14/0.45 (((~environment(E!3)) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))))) <=> (![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~environment(E!3)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))))))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(94,plain,
% 0.14/0.46 ((~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))))) <=> (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(95,plain,
% 0.14/0.46 (((~environment(E!3)) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3)))))))) <=> ((~environment(E!3)) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))))))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[94])).
% 0.14/0.46 tff(96,plain,
% 0.14/0.46 (((~environment(E!3)) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3)))))))) <=> (![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~environment(E!3)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))))))),
% 0.14/0.46 inference(transitivity,[status(thm)],[95, 93])).
% 0.14/0.46 tff(97,plain,
% 0.14/0.46 (((~![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))) | ((~environment(E!3)) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))))))) <=> ((~![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))) | (![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~environment(E!3)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))))))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[96])).
% 0.14/0.46 tff(98,plain,
% 0.14/0.46 (((~![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))) | ((~environment(E!3)) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))))))) <=> ((~![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~environment(E!3)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[97, 92])).
% 0.23/0.46 tff(99,plain,
% 0.23/0.46 ((~![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))) | ((~environment(E!3)) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(100,plain,
% 0.23/0.46 ((~![E: $i] : ((~environment(E)) | ![To: $i] : ((~in_environment(E, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E)), growth_rate(first_movers, tptp_fun_T_0(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E))) | (~greater_or_equal(tptp_fun_T_0(To, E), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E)), growth_rate(first_movers, tptp_fun_To_1(E))) | (~in_environment(E, tptp_fun_To_1(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, tptp_fun_To_1(E))))))))) | ![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~environment(E!3)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.23/0.46 tff(101,plain,
% 0.23/0.46 (![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To))))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater(T, tptp_fun_To_1(E!3))))) | (~in_environment(E!3, tptp_fun_To_1(E!3))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!3)), growth_rate(first_movers, tptp_fun_To_1(E!3)))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[100, 91, 15])).
% 0.23/0.46 tff(102,plain,
% 0.23/0.46 (![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To)))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[101, 72])).
% 0.23/0.46 tff(103,plain,
% 0.23/0.46 (((~![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To)))))) | ((~in_environment(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)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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))))))) <=> ((~![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To)))))) | (~in_environment(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)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(104,plain,
% 0.23/0.46 ((~![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To)))))) | ((~in_environment(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)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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))))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(105,plain,
% 0.23/0.46 ((~![To: $i] : ((~in_environment(E!3, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!3)), growth_rate(first_movers, tptp_fun_T_0(To, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(To, E!3))) | (~greater_or_equal(tptp_fun_T_0(To, E!3), To)))))) | (~in_environment(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)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.23/0.46 tff(106,plain,
% 0.23/0.46 (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[105, 102, 37])).
% 0.23/0.46 tff(107,plain,
% 0.23/0.46 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(108,plain,
% 0.23/0.46 (greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.23/0.46 tff(109,plain,
% 0.23/0.46 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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)))) | subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(110,plain,
% 0.23/0.46 (subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.23/0.46 tff(111,plain,
% 0.23/0.46 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(112,plain,
% 0.23/0.46 (~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[111, 106])).
% 0.23/0.46 tff(113,plain,
% 0.23/0.46 (((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3)))))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(114,plain,
% 0.23/0.46 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[113, 35])).
% 0.23/0.46 tff(115,plain,
% 0.23/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(116,plain,
% 0.23/0.47 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~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))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(117,plain,
% 0.23/0.47 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.23/0.47 tff(118,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[117, 114, 112, 110, 108])).
% 0.23/0.47 % SZS output end Proof
% 0.23/0.47 % E exiting
%------------------------------------------------------------------------------