%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n018.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 0.42s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 12:08:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start Proof
% 0.13/0.42 tff(greater_type, type, (
% 0.13/0.42 greater: ( $i * $i ) > $o)).
% 0.13/0.42 tff(tptp_fun_To_1_type, type, (
% 0.13/0.42 tptp_fun_To_1: $i > $i)).
% 0.13/0.42 tff(tptp_fun_E_2_type, type, (
% 0.13/0.42 tptp_fun_E_2: $i)).
% 0.13/0.42 tff(tptp_fun_T_0_type, type, (
% 0.13/0.42 tptp_fun_T_0: ( $i * $i ) > $i)).
% 0.13/0.42 tff(subpopulations_type, type, (
% 0.13/0.42 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.42 tff(efficient_producers_type, type, (
% 0.13/0.42 efficient_producers: $i)).
% 0.13/0.42 tff(first_movers_type, type, (
% 0.13/0.42 first_movers: $i)).
% 0.13/0.42 tff(growth_rate_type, type, (
% 0.13/0.42 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.42 tff(critical_point_type, type, (
% 0.13/0.42 critical_point: $i > $i)).
% 0.13/0.42 tff(in_environment_type, type, (
% 0.13/0.42 in_environment: ( $i * $i ) > $o)).
% 0.13/0.42 tff(stable_type, type, (
% 0.13/0.42 stable: $i > $o)).
% 0.13/0.42 tff(environment_type, type, (
% 0.13/0.42 environment: $i > $o)).
% 0.13/0.42 tff(1,assumption,(tptp_fun_To_1(E!2) = critical_point(E!2)), introduced(assumption)).
% 0.13/0.42 tff(2,plain,
% 0.13/0.42 (in_environment(E!2, tptp_fun_To_1(E!2)) <=> in_environment(E!2, critical_point(E!2))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.13/0.42 tff(3,plain,
% 0.13/0.42 (in_environment(E!2, critical_point(E!2)) <=> in_environment(E!2, tptp_fun_To_1(E!2))),
% 0.13/0.42 inference(symmetry,[status(thm)],[2])).
% 0.13/0.42 tff(4,plain,
% 0.13/0.42 ((~in_environment(E!2, critical_point(E!2))) <=> (~in_environment(E!2, tptp_fun_To_1(E!2)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.13/0.42 tff(5,plain,
% 0.13/0.42 ((~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(6,plain,
% 0.13/0.42 ((~![E: $i] : ((environment(E) & stable(E)) => in_environment(E, critical_point(E)))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(7,axiom,(~![E: $i] : ((environment(E) & stable(E)) => in_environment(E, critical_point(E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l5')).
% 0.13/0.42 tff(8,plain,
% 0.13/0.42 (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.42 tff(9,plain,
% 0.13/0.42 (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.13/0.42 tff(10,plain,
% 0.13/0.42 (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.42 tff(11,plain,
% 0.13/0.42 (~![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, critical_point(E)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.13/0.42 tff(12,plain,(
% 0.13/0.42 ~((~(environment(E!2) & stable(E!2))) | in_environment(E!2, critical_point(E!2)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[11])).
% 0.13/0.42 tff(13,plain,
% 0.13/0.42 (~in_environment(E!2, critical_point(E!2))),
% 0.13/0.42 inference(or_elim,[status(thm)],[12])).
% 0.13/0.42 tff(14,plain,
% 0.13/0.42 (~in_environment(E!2, tptp_fun_To_1(E!2))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.13/0.42 tff(15,plain,
% 0.13/0.42 (environment(E!2) & stable(E!2)),
% 0.13/0.42 inference(or_elim,[status(thm)],[12])).
% 0.13/0.42 tff(16,plain,
% 0.13/0.42 (stable(E!2)),
% 0.13/0.42 inference(and_elim,[status(thm)],[15])).
% 0.13/0.42 tff(17,plain,
% 0.13/0.42 (environment(E!2)),
% 0.13/0.42 inference(and_elim,[status(thm)],[15])).
% 0.13/0.42 tff(18,plain,
% 0.13/0.42 (^[E: $i] : refl(((~environment(E)) | (~stable(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)))))))) <=> ((~environment(E)) | (~stable(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)))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(19,plain,
% 0.13/0.42 (![E: $i] : ((~environment(E)) | (~stable(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)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(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))))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.42 tff(20,plain,
% 0.13/0.42 (^[E: $i] : rewrite(((~environment(E)) | (~stable(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)))))))) <=> ((~environment(E)) | (~stable(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)))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(21,plain,
% 0.13/0.42 (![E: $i] : ((~environment(E)) | (~stable(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)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(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))))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.42 tff(22,plain,
% 0.13/0.42 (![E: $i] : ((~environment(E)) | (~stable(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)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(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))))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[21, 19])).
% 0.13/0.42 tff(23,plain,
% 0.13/0.42 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & stable(E)) <=> (~((~environment(E)) | (~stable(E))))), ((~(environment(E) & stable(E))) <=> (~(~((~environment(E)) | (~stable(E))))))), rewrite((~(~((~environment(E)) | (~stable(E))))) <=> ((~environment(E)) | (~stable(E)))), ((~(environment(E) & stable(E))) <=> ((~environment(E)) | (~stable(E))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater(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) & stable(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)) | (~stable(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)))))))))), rewrite((((~environment(E)) | (~stable(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)))))))) <=> ((~environment(E)) | (~stable(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))))))))), (((~(environment(E) & stable(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)) | (~stable(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))))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(24,plain,
% 0.13/0.42 (![E: $i] : ((~(environment(E) & stable(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)) | (~stable(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))))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.42 tff(25,plain,
% 0.13/0.42 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(26,plain,
% 0.13/0.42 (^[E: $i] : trans(monotonicity(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) & stable(E)) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))), rewrite(((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(27,plain,
% 0.13/0.43 (![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.43 tff(28,axiom,(![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : ((in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l12')).
% 0.13/0.43 tff(29,plain,
% 0.13/0.43 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.43 tff(30,plain,
% 0.13/0.43 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & (~greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.43 tff(31,plain,(
% 0.13/0.43 ![E: $i] : ((~(environment(E) & stable(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)))))),
% 0.13/0.43 inference(skolemize,[status(sab)],[30])).
% 0.13/0.43 tff(32,plain,
% 0.13/0.43 (![E: $i] : ((~environment(E)) | (~stable(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))))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.43 tff(33,plain,
% 0.13/0.43 (![E: $i] : ((~environment(E)) | (~stable(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))))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.13/0.43 tff(34,plain,
% 0.13/0.43 (((~![E: $i] : ((~environment(E)) | (~stable(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))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(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))))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(35,plain,
% 0.13/0.43 (((~environment(E!2)) | (~stable(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2)))))))) <=> ((~environment(E!2)) | (~stable(E!2)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(36,plain,
% 0.13/0.43 (((~![E: $i] : ((~environment(E)) | (~stable(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))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(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))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2)))))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.13/0.43 tff(37,plain,
% 0.13/0.43 (((~![E: $i] : ((~environment(E)) | (~stable(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))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(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))))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[36, 34])).
% 0.13/0.43 tff(38,plain,
% 0.13/0.43 ((~![E: $i] : ((~environment(E)) | (~stable(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))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(39,plain,
% 0.13/0.43 ((~![E: $i] : ((~environment(E)) | (~stable(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))))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.13/0.43 tff(40,plain,
% 0.13/0.43 (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[39, 33, 17, 16])).
% 0.13/0.43 tff(41,plain,
% 0.13/0.43 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2)))) | in_environment(E!2, tptp_fun_To_1(E!2))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(42,plain,
% 0.13/0.43 (in_environment(E!2, tptp_fun_To_1(E!2))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.13/0.43 tff(43,plain,
% 0.13/0.43 ($false),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[42, 14])).
% 0.13/0.43 tff(44,plain,(~(tptp_fun_To_1(E!2) = critical_point(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.43 tff(45,plain,
% 0.13/0.43 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(46,plain,
% 0.13/0.43 (~greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2)))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[45, 40])).
% 0.13/0.43 tff(47,plain,
% 0.13/0.43 (^[E: $i, To: $i] : refl(((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To))))) <=> ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(48,plain,
% 0.13/0.43 (![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To))))) <=> ![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.13/0.43 tff(49,plain,
% 0.13/0.43 (^[E: $i, To: $i] : trans(monotonicity(rewrite((~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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))))) <=> (~(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(tptp_fun_T_0(To, E), To))))), (((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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 = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To))))))), rewrite(((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To))))) <=> ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))), (((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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 = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(50,plain,
% 0.13/0.43 (![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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)))))) <=> ![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.43 tff(51,plain,
% 0.13/0.43 (^[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_0(To, E)) & greater(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)))))) <=> (greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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 = critical_point(E))) <=> ((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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 = critical_point(E))))), rewrite(((greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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 = critical_point(E))) <=> ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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 = critical_point(E))) <=> ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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))))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(52,plain,
% 0.13/0.44 (![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_0(To, E)) & greater(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 = critical_point(E))) <=> ![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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))))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[51])).
% 0.13/0.44 tff(53,plain,
% 0.13/0.44 (![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)))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(54,plain,
% 0.13/0.44 (^[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)))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(55,plain,
% 0.13/0.44 (![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)))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[54])).
% 0.13/0.44 tff(56,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/sandbox2/benchmark/theBenchmark.p','d1')).
% 0.13/0.44 tff(57,plain,
% 0.13/0.44 (![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)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.44 tff(58,plain,
% 0.13/0.44 (![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)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.13/0.44 tff(59,plain,(
% 0.13/0.44 ![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_0(To, E)) & greater(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 = critical_point(E)))),
% 0.13/0.44 inference(skolemize,[status(sab)],[58])).
% 0.13/0.44 tff(60,plain,
% 0.13/0.44 (![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(To, E)) & greater(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))))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.13/0.44 tff(61,plain,
% 0.13/0.44 (![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.13/0.44 tff(62,plain,
% 0.13/0.44 (![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[61, 48])).
% 0.13/0.44 tff(63,plain,
% 0.13/0.44 (((~![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))) | ((~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (tptp_fun_To_1(E!2) = critical_point(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))) <=> ((~![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (tptp_fun_To_1(E!2) = critical_point(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(64,plain,
% 0.13/0.44 (((tptp_fun_To_1(E!2) = critical_point(E!2)) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))))) <=> ((~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (tptp_fun_To_1(E!2) = critical_point(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(65,plain,
% 0.13/0.44 ((~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))) <=> (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(66,plain,
% 0.13/0.44 (((tptp_fun_To_1(E!2) = critical_point(E!2)) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))))) <=> ((tptp_fun_To_1(E!2) = critical_point(E!2)) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[65])).
% 0.13/0.44 tff(67,plain,
% 0.13/0.44 (((tptp_fun_To_1(E!2) = critical_point(E!2)) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))))) <=> ((~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (tptp_fun_To_1(E!2) = critical_point(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[66, 64])).
% 0.13/0.44 tff(68,plain,
% 0.13/0.44 (((~![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))) | ((tptp_fun_To_1(E!2) = critical_point(E!2)) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))) <=> ((~![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))) | ((~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (tptp_fun_To_1(E!2) = critical_point(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[67])).
% 0.13/0.44 tff(69,plain,
% 0.13/0.44 (((~![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))) | ((tptp_fun_To_1(E!2) = critical_point(E!2)) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))) <=> ((~![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (tptp_fun_To_1(E!2) = critical_point(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[68, 63])).
% 0.13/0.45 tff(70,plain,
% 0.13/0.45 ((~![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))) | ((tptp_fun_To_1(E!2) = critical_point(E!2)) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(71,plain,
% 0.13/0.45 ((~![E: $i, To: $i] : ((To = critical_point(E)) | greater(growth_rate(efficient_producers, To), growth_rate(first_movers, To)) | (~environment(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(tptp_fun_T_0(To, E), To)))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2))) | (~environment(E!2)) | (tptp_fun_To_1(E!2) = critical_point(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.13/0.45 tff(72,plain,
% 0.13/0.45 ((tptp_fun_To_1(E!2) = critical_point(E!2)) | (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[71, 62, 17, 42, 46])).
% 0.13/0.45 tff(73,plain,
% 0.13/0.45 (~(greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[72, 44])).
% 0.13/0.45 tff(74,plain,
% 0.13/0.45 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(75,plain,
% 0.13/0.45 (greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.13/0.45 tff(76,plain,
% 0.13/0.45 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(77,plain,
% 0.13/0.45 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.13/0.45 tff(78,plain,
% 0.13/0.45 ((greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(79,plain,
% 0.13/0.45 (~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[78, 73])).
% 0.13/0.45 tff(80,plain,
% 0.13/0.45 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_To_1(E!2)), growth_rate(first_movers, tptp_fun_To_1(E!2)))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(81,plain,
% 0.13/0.45 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[80, 40])).
% 0.13/0.45 tff(82,plain,
% 0.13/0.45 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(83,plain,
% 0.13/0.45 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(84,plain,
% 0.13/0.45 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater(T, tptp_fun_To_1(E!2))))) | greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2)), growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2), E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2), E!2), tptp_fun_To_1(E!2)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.13/0.45 tff(85,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[84, 81, 79, 77, 75])).
% 0.13/0.45 % SZS output end Proof
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------