%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:23:59 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n007.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 12:05:43 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(greater_or_equal_type, type, (
% 0.13/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_To_3_type, type, (
% 0.13/0.40 tptp_fun_To_3: $i > $i)).
% 0.13/0.40 tff(tptp_fun_E_4_type, type, (
% 0.13/0.40 tptp_fun_E_4: $i)).
% 0.13/0.40 tff(tptp_fun_T_0_type, type, (
% 0.13/0.40 tptp_fun_T_0: ( $i * $i ) > $i)).
% 0.13/0.40 tff(subpopulations_type, type, (
% 0.13/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.40 tff(efficient_producers_type, type, (
% 0.13/0.40 efficient_producers: $i)).
% 0.13/0.40 tff(first_movers_type, type, (
% 0.13/0.40 first_movers: $i)).
% 0.13/0.40 tff(greater_type, type, (
% 0.13/0.40 greater: ( $i * $i ) > $o)).
% 0.13/0.40 tff(growth_rate_type, type, (
% 0.13/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.40 tff(in_environment_type, type, (
% 0.13/0.40 in_environment: ( $i * $i ) > $o)).
% 0.13/0.40 tff(stable_type, type, (
% 0.13/0.40 stable: $i > $o)).
% 0.13/0.40 tff(environment_type, type, (
% 0.13/0.40 environment: $i > $o)).
% 0.13/0.40 tff(critical_point_type, type, (
% 0.13/0.40 critical_point: $i > $i)).
% 0.13/0.40 tff(tptp_fun_To_1_type, type, (
% 0.13/0.40 tptp_fun_To_1: $i > $i)).
% 0.13/0.40 tff(tptp_fun_T_2_type, type, (
% 0.13/0.40 tptp_fun_T_2: ( $i * $i ) > $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 ((~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((~![E: $i] : ((environment(E) & stable(E)) => in_environment(E, critical_point(E)))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,axiom,(~![E: $i] : ((environment(E) & stable(E)) => in_environment(E, critical_point(E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l5')).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.40 tff(8,plain,(
% 0.13/0.40 ~((~(environment(E!4) & stable(E!4))) | in_environment(E!4, critical_point(E!4)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (environment(E!4) & stable(E!4)),
% 0.13/0.40 inference(or_elim,[status(thm)],[8])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (stable(E!4)),
% 0.13/0.40 inference(and_elim,[status(thm)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (environment(E!4)),
% 0.13/0.40 inference(and_elim,[status(thm)],[9])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (^[E: $i] : rewrite(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[15, 13])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (^[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_3(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_3(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_3(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_3(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_3(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_3(E)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(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_3(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_3(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_3(E))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(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_3(E))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(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_3(E)))))), ((in_environment(E, tptp_fun_To_3(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (in_environment(E, tptp_fun_To_3(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_3(E))))))), rewrite((in_environment(E, tptp_fun_To_3(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_3(E))))) <=> (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))), ((in_environment(E, tptp_fun_To_3(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_3(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_3(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_3(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_3(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_3(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (^[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)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.40 tff(22,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/sandbox/benchmark/theBenchmark.p','l1')).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.13/0.41 tff(25,plain,(
% 0.13/0.41 ![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_3(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_3(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[24])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))) | ((~environment(E!4)) | (~stable(E!4)) | (~((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))) | (~environment(E!4)) | (~stable(E!4)) | (~((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))) | ((~environment(E!4)) | (~stable(E!4)) | (~((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_3(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_3(E))))))))) | (~environment(E!4)) | (~stable(E!4)) | (~((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (~((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[30, 27, 11, 10])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4)))))) | in_environment(E!4, tptp_fun_To_3(E!4))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (in_environment(E!4, tptp_fun_To_3(E!4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.41 tff(34,assumption,(~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))))), introduced(assumption)).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.13/0.41 tff(37,assumption,(~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))), introduced(assumption)).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ((greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))) | greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 ((greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))) | subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 ((greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[42, 37])).
% 0.13/0.41 tff(44,assumption,(![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))), introduced(assumption)).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[47, 44, 43, 41, 39])).
% 0.13/0.41 tff(49,plain,((greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[49, 36])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))) | (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[51, 34])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))) | in_environment(E!4, tptp_fun_To_1(E!4))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (in_environment(E!4, tptp_fun_To_1(E!4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[53, 34])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (^[E: $i, To: $i] : refl((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To))))) <=> ![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (^[E: $i, To: $i] : trans(monotonicity(rewrite((~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))))) <=> (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To))))), ((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To))))))), rewrite((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))), ((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) <=> ![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (^[E: $i, To: $i] : trans(monotonicity(rewrite(((~environment(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))))))), ((((~environment(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) | (To = critical_point(E))) <=> ((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) | (To = critical_point(E))))), rewrite(((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) | (To = critical_point(E))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))))))), ((((~environment(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) | (To = critical_point(E))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (![E: $i, To: $i] : (((~environment(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) | (To = critical_point(E))) <=> ![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (![E: $i, To: $i] : ((~(environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E))) <=> ![E: $i, To: $i] : ((~(environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (^[E: $i, To: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & in_environment(E, To)) <=> (environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, To))), 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))))), ((((environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & in_environment(E, 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) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & in_environment(E, 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) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & in_environment(E, 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 = critical_point(E))) <=> ((environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E))))), rewrite(((environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E))) <=> ((~(environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E)))), (((((environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & in_environment(E, 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 = critical_point(E))) <=> ((~(environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(63,plain,
% 0.13/0.42 (![E: $i, To: $i] : ((((environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & in_environment(E, 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 = critical_point(E))) <=> ![E: $i, To: $i] : ((~(environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.13/0.42 tff(64,axiom,(![E: $i, To: $i] : ((((environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & in_environment(E, 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 = critical_point(E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1')).
% 0.13/0.42 tff(65,plain,
% 0.13/0.42 (![E: $i, To: $i] : ((~(environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.13/0.42 tff(66,plain,
% 0.13/0.42 (![E: $i, To: $i] : ((~(environment(E) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & in_environment(E, 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 = critical_point(E)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.13/0.42 tff(67,plain,(
% 0.13/0.42 ![E: $i, To: $i] : (((~environment(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E)))))) | (To = critical_point(E)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[66])).
% 0.13/0.42 tff(68,plain,
% 0.13/0.42 (![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E)) & greater(tptp_fun_T_2(To, E), To))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.13/0.42 tff(69,plain,
% 0.13/0.42 (![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.13/0.42 tff(70,plain,
% 0.13/0.42 (![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[69, 56])).
% 0.13/0.42 tff(71,plain,
% 0.13/0.42 (((~![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))) | ((~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))) <=> ((~![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(72,plain,
% 0.13/0.42 ((greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))))) <=> ((~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(73,plain,
% 0.13/0.42 ((~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))) <=> (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(74,plain,
% 0.13/0.42 ((greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))))) <=> (greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[73])).
% 0.13/0.42 tff(75,plain,
% 0.13/0.42 ((greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))))) <=> ((~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[74, 72])).
% 0.13/0.42 tff(76,plain,
% 0.13/0.42 (((~![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))) | (greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))) <=> ((~![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))) | ((~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.13/0.42 tff(77,plain,
% 0.13/0.42 (((~![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))) | (greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))) <=> ((~![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[76, 71])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 ((~![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))) | (greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 ((~![E: $i, To: $i] : (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (To = critical_point(E)) | (~in_environment(E, To)) | (~environment(E)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(To, E)), growth_rate(first_movers, tptp_fun_T_2(To, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_2(To, E))) | (~greater(tptp_fun_T_2(To, E), To)))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~environment(E!4)) | (tptp_fun_To_1(E!4) = critical_point(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.13/0.43 tff(80,plain,
% 0.13/0.43 ((tptp_fun_To_1(E!4) = critical_point(E!4)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_2(tptp_fun_To_1(E!4), E!4))) | (~greater(tptp_fun_T_2(tptp_fun_To_1(E!4), E!4), tptp_fun_To_1(E!4)))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[79, 70, 11, 54, 52])).
% 0.13/0.43 tff(81,plain,
% 0.13/0.43 (tptp_fun_To_1(E!4) = critical_point(E!4)),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[80, 50])).
% 0.13/0.43 tff(82,plain,
% 0.13/0.43 (in_environment(E!4, tptp_fun_To_1(E!4)) <=> in_environment(E!4, critical_point(E!4))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[81])).
% 0.13/0.43 tff(83,plain,
% 0.13/0.43 (in_environment(E!4, critical_point(E!4)) <=> in_environment(E!4, tptp_fun_To_1(E!4))),
% 0.13/0.43 inference(symmetry,[status(thm)],[82])).
% 0.13/0.43 tff(84,plain,
% 0.13/0.43 ((~in_environment(E!4, critical_point(E!4))) <=> (~in_environment(E!4, tptp_fun_To_1(E!4)))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[83])).
% 0.13/0.43 tff(85,plain,
% 0.13/0.43 (~in_environment(E!4, critical_point(E!4))),
% 0.13/0.43 inference(or_elim,[status(thm)],[8])).
% 0.13/0.43 tff(86,plain,
% 0.13/0.43 (~in_environment(E!4, tptp_fun_To_1(E!4))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.13/0.43 tff(87,plain,
% 0.13/0.43 ($false),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[54, 86])).
% 0.13/0.43 tff(88,plain,((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.43 tff(89,plain,
% 0.13/0.43 (^[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)))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(90,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[89])).
% 0.13/0.43 tff(91,plain,
% 0.13/0.43 (^[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)))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(92,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[91])).
% 0.13/0.43 tff(93,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[92, 90])).
% 0.13/0.43 tff(94,plain,
% 0.13/0.43 (^[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))))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(95,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[94])).
% 0.13/0.43 tff(96,plain,
% 0.13/0.43 (^[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)))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(97,plain,
% 0.13/0.44 (![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)) | (~((~(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)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[96])).
% 0.13/0.44 tff(98,plain,
% 0.13/0.44 (![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)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(99,plain,
% 0.13/0.44 (^[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)))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(100,plain,
% 0.13/0.44 (![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)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[99])).
% 0.13/0.44 tff(101,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/sandbox/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds')).
% 0.13/0.44 tff(102,plain,
% 0.13/0.44 (![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)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.13/0.44 tff(103,plain,
% 0.13/0.44 (![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)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.13/0.44 tff(104,plain,(
% 0.13/0.44 ![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)))))),
% 0.13/0.44 inference(skolemize,[status(sab)],[103])).
% 0.13/0.44 tff(105,plain,
% 0.13/0.44 (![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)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.13/0.44 tff(106,plain,
% 0.13/0.44 (![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))))))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.13/0.44 tff(107,plain,
% 0.13/0.44 (![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))))))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[106, 93])).
% 0.13/0.44 tff(108,plain,
% 0.13/0.44 (((~![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))))))))) | (![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~environment(E!4)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))))))) <=> ((~![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!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~environment(E!4)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(109,plain,
% 0.13/0.44 (((~environment(E!4)) | ![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))))) <=> (![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~environment(E!4)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(110,plain,
% 0.13/0.44 ((~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))))) <=> (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(111,plain,
% 0.13/0.45 (((~environment(E!4)) | ![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4)))))))) <=> ((~environment(E!4)) | ![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[110])).
% 0.13/0.45 tff(112,plain,
% 0.13/0.45 (((~environment(E!4)) | ![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4)))))))) <=> (![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~environment(E!4)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[111, 109])).
% 0.13/0.45 tff(113,plain,
% 0.13/0.45 (((~![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))))))))) | ((~environment(E!4)) | ![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))))))) <=> ((~![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!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~environment(E!4)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[112])).
% 0.13/0.45 tff(114,plain,
% 0.13/0.45 (((~![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))))))))) | ((~environment(E!4)) | ![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))))))) <=> ((~![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!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~environment(E!4)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[113, 108])).
% 0.13/0.45 tff(115,plain,
% 0.13/0.45 ((~![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))))))))) | ((~environment(E!4)) | ![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(116,plain,
% 0.13/0.45 ((~![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!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~environment(E!4)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.13/0.45 tff(117,plain,
% 0.13/0.45 (![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To))))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater(T, tptp_fun_To_1(E!4))))) | (~in_environment(E!4, tptp_fun_To_1(E!4))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!4)), growth_rate(first_movers, tptp_fun_To_1(E!4)))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[116, 107, 11])).
% 0.13/0.45 tff(118,plain,
% 0.13/0.45 (![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To)))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[117, 88])).
% 0.13/0.45 tff(119,plain,
% 0.13/0.45 (((~![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To)))))) | ((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))))))) <=> ((~![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To)))))) | (~in_environment(E!4, tptp_fun_To_3(E!4))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(120,plain,
% 0.13/0.45 ((~![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To)))))) | ((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(121,plain,
% 0.13/0.45 ((~![To: $i] : ((~in_environment(E!4, To)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(To, E!4)), growth_rate(first_movers, tptp_fun_T_0(To, E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(To, E!4))) | (~greater_or_equal(tptp_fun_T_0(To, E!4), To)))))) | (~in_environment(E!4, tptp_fun_To_3(E!4))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4)))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.13/0.45 tff(122,plain,
% 0.13/0.45 (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[121, 118, 33])).
% 0.13/0.45 tff(123,plain,
% 0.13/0.45 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4)))) | greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(124,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.13/0.45 tff(125,plain,
% 0.13/0.45 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4)))) | subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(126,plain,
% 0.13/0.46 (subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.13/0.46 tff(127,plain,
% 0.13/0.46 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(128,plain,
% 0.13/0.46 (~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[127, 122])).
% 0.13/0.46 tff(129,plain,
% 0.13/0.46 (((~in_environment(E!4, tptp_fun_To_3(E!4))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4)))))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(130,plain,
% 0.13/0.46 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[129, 31])).
% 0.13/0.46 tff(131,plain,
% 0.13/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(132,plain,
% 0.13/0.46 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4))))),
% 0.13/0.46 inference(quant_inst,[status(thm)],[])).
% 0.13/0.46 tff(133,plain,
% 0.13/0.46 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!4, T)) | (~greater_or_equal(T, tptp_fun_To_3(E!4))))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~subpopulations(first_movers, efficient_producers, E!4, tptp_fun_T_0(tptp_fun_To_3(E!4), E!4))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_3(E!4), E!4), tptp_fun_To_3(E!4)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.23/0.46 tff(134,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[133, 130, 128, 126, 124])).
% 0.23/0.46 % SZS output end Proof
% 0.23/0.46 % E exiting
%------------------------------------------------------------------------------