%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT032+2 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:01 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT032+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 12:25:24 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 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(tptp_fun_T_2_type, type, (
% 0.13/0.40 tptp_fun_T_2: $i > $i)).
% 0.13/0.40 tff(tptp_fun_To_0_type, type, (
% 0.13/0.40 tptp_fun_To_0: $i > $i)).
% 0.13/0.40 tff(tptp_fun_E_1_type, type, (
% 0.13/0.40 tptp_fun_E_1: $i)).
% 0.13/0.40 tff(first_movers_type, type, (
% 0.13/0.40 first_movers: $i)).
% 0.13/0.40 tff(efficient_producers_type, type, (
% 0.13/0.40 efficient_producers: $i)).
% 0.13/0.40 tff(subpopulations_type, type, (
% 0.13/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 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(selection_favors_type, type, (
% 0.13/0.40 selection_favors: ( $i * $i * $i ) > $o)).
% 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(1,plain,
% 0.13/0.40 (((environment(E!1) & stable(E!1)) & ![To: $i] : ((~in_environment(E!1, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To)) & greater_or_equal(tptp_fun_T_2(To), To))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)))))) <=> (environment(E!1) & stable(E!1) & ![To: $i] : ((~in_environment(E!1, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To)) & greater_or_equal(tptp_fun_T_2(To), To))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To))))))),
% 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))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | selection_favors(efficient_producers, 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))) | selection_favors(efficient_producers, first_movers, T)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,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)) => selection_favors(efficient_producers, 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))) | selection_favors(efficient_producers, first_movers, T)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,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)) => selection_favors(efficient_producers, first_movers, T))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t1')).
% 0.13/0.40 tff(5,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))) | selection_favors(efficient_producers, first_movers, T))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,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))) | selection_favors(efficient_producers, first_movers, T))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.40 tff(7,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))) | selection_favors(efficient_producers, first_movers, T))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,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))) | selection_favors(efficient_producers, first_movers, T))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (environment(E!1) & stable(E!1) & ![To: $i] : ((~in_environment(E!1, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To)) & greater_or_equal(tptp_fun_T_2(To), To))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (stable(E!1)),
% 0.13/0.40 inference(and_elim,[status(thm)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (environment(E!1)),
% 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_0(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_0(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(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_0(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_0(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(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_0(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_0(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(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_0(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_0(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(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_0(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_0(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(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_0(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(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_0(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_0(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_0(E))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(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_0(E))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(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_0(E)))))), ((in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (in_environment(E, tptp_fun_To_0(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_0(E))))))), rewrite((in_environment(E, tptp_fun_To_0(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_0(E))))) <=> (~((~in_environment(E, tptp_fun_To_0(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_0(E)))))))), ((in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (~((~in_environment(E, tptp_fun_To_0(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_0(E))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_0(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_0(E)))))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_0(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_0(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(E))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(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_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(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/sandbox2/benchmark/theBenchmark.p','l1')).
% 0.13/0.40 tff(23,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)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.40 tff(24,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)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.13/0.40 tff(25,plain,(
% 0.13/0.40 ![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[24])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(E))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(E))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(E))))))))) | ((~environment(E!1)) | (~stable(E!1)) | (~((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(E))))))))) | (~environment(E!1)) | (~stable(E!1)) | (~((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(E))))))))) | ((~environment(E!1)) | (~stable(E!1)) | (~((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(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_0(E))))))))) | (~environment(E!1)) | (~stable(E!1)) | (~((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (~((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 27, 11, 10])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1)))))) | in_environment(E!1, tptp_fun_To_0(E!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (in_environment(E!1, tptp_fun_To_0(E!1))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (^[To: $i] : refl(((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To))))) <=> ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To))))) <=> ![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (^[To: $i] : rewrite(((~in_environment(E!1, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To)) & greater_or_equal(tptp_fun_T_2(To), To))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To))))) <=> ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (![To: $i] : ((~in_environment(E!1, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To)) & greater_or_equal(tptp_fun_T_2(To), To))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To))))) <=> ![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 (![To: $i] : ((~in_environment(E!1, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To)) & greater_or_equal(tptp_fun_T_2(To), To))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)))))),
% 0.13/0.41 inference(and_elim,[status(thm)],[9])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (((~![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To)))))) | ((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))))))) <=> ((~![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To)))))) | (~in_environment(E!1, tptp_fun_To_0(E!1))) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 ((~![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To)))))) | ((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 ((~![To: $i] : ((~in_environment(E!1, To)) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(To)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(To))) | (~greater_or_equal(tptp_fun_T_2(To), To)))))) | (~in_environment(E!1, tptp_fun_To_0(E!1))) | (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (~(selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 ((selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1)))) | subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 ((selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1)))) | (~selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (~selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) <=> (environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)))), rewrite(((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.13/0.41 tff(56,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp1_high_growth_rates')).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.13/0.41 tff(59,plain,(
% 0.13/0.41 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.13/0.41 inference(skolemize,[status(sab)],[58])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | ((~environment(E!1)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (~environment(E!1)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 ((selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))))) <=> ((~environment(E!1)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | ((~environment(E!1)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (~environment(E!1)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[64, 62])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (~environment(E!1)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (~greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[67, 61, 11, 48, 46])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 ((selection_favors(efficient_producers, first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1)))) | greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[69, 44])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (((~in_environment(E!1, tptp_fun_To_0(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1)))))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[71, 31])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))) | ((~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))))),
% 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_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1)))) <=> ((~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(75,plain,
% 0.13/0.42 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))) | ((~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.13/0.42 tff(76,plain,
% 0.13/0.42 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[75, 73])).
% 0.13/0.42 tff(77,plain,
% 0.13/0.42 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!1))))) | (~subpopulations(first_movers, efficient_producers, E!1, tptp_fun_T_2(tptp_fun_To_0(E!1)))) | (~greater_or_equal(tptp_fun_T_2(tptp_fun_To_0(E!1)), tptp_fun_To_0(E!1))) | greater(growth_rate(efficient_producers, tptp_fun_T_2(tptp_fun_To_0(E!1))), growth_rate(first_movers, tptp_fun_T_2(tptp_fun_To_0(E!1))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[78, 72, 46, 70, 68])).
% 0.13/0.42 % SZS output end Proof
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------