%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT029+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n008.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 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT029+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n008.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 12:17:54 UTC 2026
% 0.07/0.34 % 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(equilibrium_type, type, (
% 0.13/0.42 equilibrium: $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_1_type, type, (
% 0.13/0.42 tptp_fun_T_1: $i > $i)).
% 0.13/0.42 tff(tptp_fun_To_0_type, type, (
% 0.13/0.42 tptp_fun_To_0: $i > $i)).
% 0.13/0.42 tff(tptp_fun_T_3_type, type, (
% 0.13/0.42 tptp_fun_T_3: $i > $i)).
% 0.13/0.42 tff(greater_or_equal_type, type, (
% 0.13/0.42 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.42 tff(growth_rate_type, type, (
% 0.13/0.42 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.42 tff(first_movers_type, type, (
% 0.13/0.42 first_movers: $i)).
% 0.13/0.42 tff(efficient_producers_type, type, (
% 0.13/0.42 efficient_producers: $i)).
% 0.13/0.42 tff(zero_type, type, (
% 0.13/0.42 zero: $i)).
% 0.13/0.42 tff(subpopulations_type, type, (
% 0.13/0.42 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 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,plain,
% 0.13/0.42 (^[X: $i, Y: $i] : refl((greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(2,plain,
% 0.13/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.43 tff(3,plain,
% 0.13/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(4,plain,
% 0.13/0.43 (^[X: $i, Y: $i] : rewrite((greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(5,plain,
% 0.13/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.43 tff(6,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal')).
% 0.13/0.43 tff(7,plain,
% 0.13/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.43 tff(8,plain,
% 0.13/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.43 tff(9,plain,(
% 0.13/0.43 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.13/0.43 inference(skolemize,[status(sab)],[8])).
% 0.13/0.43 tff(10,plain,
% 0.13/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.43 tff(11,plain,
% 0.13/0.43 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(12,plain,
% 0.13/0.43 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.43 tff(13,plain,
% 0.13/0.43 (((environment(E!2) & stable(E!2)) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))) <=> (environment(E!2) & stable(E!2) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(14,plain,
% 0.13/0.43 ((~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(15,plain,
% 0.13/0.43 ((~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(16,axiom,(~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l11')).
% 0.13/0.43 tff(17,plain,
% 0.13/0.43 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.43 tff(18,plain,
% 0.13/0.43 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.13/0.43 tff(19,plain,
% 0.13/0.43 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.43 tff(20,plain,
% 0.13/0.43 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.13/0.43 tff(21,plain,
% 0.13/0.43 (environment(E!2) & stable(E!2) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.43 tff(22,plain,
% 0.13/0.43 (stable(E!2)),
% 0.13/0.43 inference(and_elim,[status(thm)],[21])).
% 0.13/0.43 tff(23,plain,
% 0.13/0.43 (environment(E!2)),
% 0.13/0.43 inference(and_elim,[status(thm)],[21])).
% 0.13/0.43 tff(24,plain,
% 0.13/0.43 (^[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)))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(25,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.43 tff(26,plain,
% 0.13/0.43 (^[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)))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(27,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.43 tff(28,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[27, 25])).
% 0.13/0.43 tff(29,plain,
% 0.13/0.43 (^[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))))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(30,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.43 tff(31,plain,
% 0.13/0.43 (![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)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(32,plain,
% 0.13/0.43 (^[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)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(33,plain,
% 0.13/0.43 (![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)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.43 tff(34,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')).
% 0.13/0.43 tff(35,plain,
% 0.13/0.43 (![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)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.43 tff(36,plain,
% 0.13/0.43 (![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)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.13/0.43 tff(37,plain,(
% 0.13/0.43 ![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)))))),
% 0.13/0.43 inference(skolemize,[status(sab)],[36])).
% 0.13/0.43 tff(38,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.13/0.43 tff(39,plain,
% 0.13/0.43 (![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))))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.13/0.43 tff(40,plain,
% 0.13/0.43 (((~![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!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))))))) <=> ((~![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!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(41,plain,
% 0.13/0.43 ((~![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!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(42,plain,
% 0.13/0.43 ((~![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!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2)))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.43 tff(43,plain,
% 0.13/0.43 (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[42, 39, 23, 22])).
% 0.13/0.43 tff(44,plain,
% 0.13/0.43 (((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2)))))) | in_environment(E!2, tptp_fun_To_0(E!2))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(45,plain,
% 0.13/0.43 (in_environment(E!2, tptp_fun_To_0(E!2))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.13/0.43 tff(46,plain,
% 0.13/0.43 (^[To: $i] : refl(((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))) <=> ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(47,plain,
% 0.13/0.43 (![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))) <=> ![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.13/0.43 tff(48,plain,
% 0.13/0.43 (^[To: $i] : rewrite(((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))) <=> ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(49,plain,
% 0.13/0.43 (![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))) <=> ![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.13/0.43 tff(50,plain,
% 0.13/0.43 (![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))),
% 0.13/0.43 inference(and_elim,[status(thm)],[21])).
% 0.13/0.43 tff(51,plain,
% 0.13/0.43 (![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.13/0.43 tff(52,plain,
% 0.13/0.43 (![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.13/0.43 tff(53,plain,
% 0.13/0.43 (((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))))))) <=> ((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(54,plain,
% 0.13/0.43 ((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(55,plain,
% 0.13/0.43 ((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.43 tff(56,plain,
% 0.13/0.43 (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[55, 52, 45])).
% 0.13/0.43 tff(57,plain,
% 0.13/0.43 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(58,plain,
% 0.13/0.43 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.13/0.43 tff(59,plain,
% 0.13/0.43 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(60,plain,
% 0.13/0.43 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.13/0.43 tff(61,plain,
% 0.13/0.43 (((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2)))))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(62,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_or_equal(T, tptp_fun_To_0(E!2))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[61, 43])).
% 0.13/0.43 tff(63,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_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(64,plain,
% 0.13/0.43 ((greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))) <=> ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(65,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_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[64])).
% 0.13/0.43 tff(66,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_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[65, 63])).
% 0.13/0.43 tff(67,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_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(68,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_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.43 tff(69,plain,
% 0.13/0.43 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[68, 62, 60, 58])).
% 0.13/0.43 tff(70,assumption,(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.13/0.43 tff(71,assumption,(~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))), introduced(assumption)).
% 0.13/0.43 tff(72,assumption,(greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))), introduced(assumption)).
% 0.13/0.43 tff(73,plain,
% 0.13/0.43 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(74,plain,
% 0.13/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(X, Y) & greater(Y, Z)) <=> (~((~greater(X, Y)) | (~greater(Y, Z))))), ((~(greater(X, Y) & greater(Y, Z))) <=> (~(~((~greater(X, Y)) | (~greater(Y, Z))))))), rewrite((~(~((~greater(X, Y)) | (~greater(Y, Z))))) <=> ((~greater(X, Y)) | (~greater(Y, Z)))), ((~(greater(X, Y) & greater(Y, Z))) <=> ((~greater(X, Y)) | (~greater(Y, Z))))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)))), rewrite((((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(75,plain,
% 0.13/0.43 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.13/0.43 tff(76,plain,
% 0.13/0.43 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(77,plain,
% 0.13/0.43 (^[X: $i, Y: $i, Z: $i] : rewrite(((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(78,plain,
% 0.13/0.43 (![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.13/0.43 tff(79,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_transitivity')).
% 0.13/0.43 tff(80,plain,
% 0.13/0.43 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.13/0.43 tff(81,plain,
% 0.13/0.43 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.13/0.43 tff(82,plain,(
% 0.13/0.43 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.13/0.43 inference(skolemize,[status(sab)],[81])).
% 0.13/0.43 tff(83,plain,
% 0.13/0.43 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.13/0.43 tff(84,plain,
% 0.13/0.43 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.13/0.43 tff(85,plain,
% 0.13/0.43 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(86,plain,
% 0.13/0.43 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(87,plain,
% 0.13/0.43 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.13/0.43 tff(88,plain,
% 0.13/0.43 ($false),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[87, 84, 71, 72, 69])).
% 0.13/0.43 tff(89,plain,((~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.43 tff(90,plain,
% 0.13/0.43 (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[89, 71])).
% 0.13/0.43 tff(91,plain,
% 0.13/0.43 (((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))) | greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(92,plain,
% 0.13/0.43 ((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.13/0.43 tff(93,plain,
% 0.13/0.43 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))) | ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(94,plain,
% 0.13/0.43 ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[93, 56])).
% 0.13/0.43 tff(95,plain,
% 0.13/0.43 (^[E: $i, T: $i] : refl(((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(96,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))) <=> ![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[95])).
% 0.13/0.44 tff(97,plain,
% 0.13/0.44 (^[E: $i, T: $i] : trans(monotonicity(rewrite((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) <=> (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))), rewrite((greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) <=> (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T)))))), rewrite(((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) <=> (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero))))), trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))), (((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))))), rewrite(((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))), (((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(98,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))) <=> ![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[97])).
% 0.13/0.44 tff(99,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))) <=> ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(100,plain,
% 0.13/0.44 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))), rewrite(((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))) => ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))) => ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(101,plain,
% 0.13/0.44 (![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[100])).
% 0.13/0.44 tff(102,axiom,(![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l6')).
% 0.13/0.44 tff(103,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.13/0.44 tff(104,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.13/0.44 tff(105,plain,(
% 0.13/0.44 ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.44 inference(skolemize,[status(sab)],[104])).
% 0.13/0.44 tff(106,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.13/0.44 tff(107,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.13/0.44 tff(108,plain,
% 0.13/0.44 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(109,plain,
% 0.13/0.44 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(110,plain,
% 0.13/0.44 ((~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) <=> (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(111,plain,
% 0.13/0.44 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(112,plain,
% 0.13/0.44 ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(113,plain,
% 0.13/0.44 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))) <=> ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[112, 111, 110])).
% 0.13/0.44 tff(114,plain,
% 0.13/0.44 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[113, 109])).
% 0.13/0.44 tff(115,plain,
% 0.13/0.44 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[114])).
% 0.13/0.44 tff(116,plain,
% 0.13/0.44 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[115, 108])).
% 0.13/0.44 tff(117,plain,
% 0.13/0.44 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(118,plain,
% 0.13/0.44 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.13/0.44 tff(119,plain,
% 0.13/0.44 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[118, 107, 23, 60, 94])).
% 0.13/0.44 tff(120,plain,
% 0.13/0.44 (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[119, 92, 70])).
% 0.13/0.44 tff(121,plain,
% 0.13/0.44 (((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))) | (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(122,plain,
% 0.13/0.44 (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.13/0.44 tff(123,plain,
% 0.13/0.44 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[122])).
% 0.13/0.44 tff(124,plain,
% 0.13/0.44 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.44 inference(symmetry,[status(thm)],[123])).
% 0.13/0.44 tff(125,plain,
% 0.13/0.44 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) <=> (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[124])).
% 0.13/0.44 tff(126,plain,
% 0.13/0.44 (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[71, 125])).
% 0.13/0.44 tff(127,plain,
% 0.13/0.44 ($false),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[69, 126])).
% 0.13/0.44 tff(128,plain,(greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.44 tff(129,plain,
% 0.13/0.44 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[128, 70])).
% 0.13/0.44 tff(130,assumption,(~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))), introduced(assumption)).
% 0.13/0.44 tff(131,plain,
% 0.13/0.44 (((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))) | (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(132,plain,
% 0.13/0.44 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.13/0.44 tff(133,plain,
% 0.13/0.44 (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[121, 130])).
% 0.13/0.44 tff(134,plain,
% 0.13/0.44 (zero = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.13/0.44 inference(symmetry,[status(thm)],[133])).
% 0.13/0.44 tff(135,plain,
% 0.13/0.44 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.13/0.44 inference(monotonicity,[status(thm)],[134, 132])).
% 0.13/0.44 tff(136,plain,
% 0.13/0.44 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.44 inference(symmetry,[status(thm)],[135])).
% 0.13/0.44 tff(137,plain,
% 0.13/0.44 ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) <=> (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[136])).
% 0.13/0.44 tff(138,assumption,(greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))), introduced(assumption)).
% 0.13/0.44 tff(139,plain,
% 0.13/0.44 ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(140,plain,
% 0.13/0.44 ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[139, 94])).
% 0.13/0.44 tff(141,plain,
% 0.13/0.44 (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[140, 138])).
% 0.13/0.44 tff(142,plain,
% 0.13/0.44 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.13/0.44 tff(143,plain,
% 0.13/0.44 ($false),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[138, 142])).
% 0.13/0.44 tff(144,plain,(((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.44 tff(145,plain,
% 0.13/0.44 ((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[144, 129])).
% 0.13/0.44 tff(146,plain,
% 0.13/0.44 (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[119, 145, 70])).
% 0.13/0.44 tff(147,plain,
% 0.13/0.44 (((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))) | greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(148,plain,
% 0.13/0.44 (greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.13/0.44 tff(149,plain,
% 0.13/0.44 (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[140, 129])).
% 0.13/0.44 tff(150,plain,
% 0.13/0.44 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(151,plain,
% 0.13/0.44 ((greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))) <=> (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(152,plain,
% 0.13/0.44 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[151])).
% 0.13/0.44 tff(153,plain,
% 0.13/0.44 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[152, 150])).
% 0.13/0.44 tff(154,plain,
% 0.13/0.44 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(155,plain,
% 0.13/0.44 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.13/0.45 tff(156,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[155, 84, 149, 148, 69])).
% 0.13/0.45 tff(157,plain,(~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(158,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(159,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) | (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.13/0.45 tff(160,plain,
% 0.13/0.45 (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[159, 12])).
% 0.13/0.45 tff(161,plain,
% 0.13/0.45 (((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(162,plain,
% 0.13/0.45 (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.13/0.45 tff(163,assumption,(~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.13/0.45 tff(164,assumption,(greater(tptp_fun_To_0(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.13/0.45 tff(165,assumption,(greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.13/0.45 tff(166,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(167,plain,
% 0.13/0.45 ((greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))) <=> ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(168,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[167])).
% 0.13/0.45 tff(169,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[168, 166])).
% 0.13/0.45 tff(170,plain,
% 0.13/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(171,plain,
% 0.13/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.13/0.45 tff(172,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[171, 84, 165, 163, 164])).
% 0.13/0.45 tff(173,plain,((~greater(tptp_fun_To_0(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(174,plain,
% 0.13/0.45 (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[173, 164, 163])).
% 0.13/0.45 tff(175,plain,
% 0.13/0.45 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(176,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[175, 10])).
% 0.13/0.45 tff(177,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(178,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))) | ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[177, 58])).
% 0.13/0.45 tff(179,plain,
% 0.13/0.45 ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[178, 176])).
% 0.13/0.45 tff(180,plain,
% 0.13/0.45 ((~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))) | (tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(181,plain,
% 0.13/0.45 ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.13/0.45 tff(182,plain,
% 0.13/0.45 (tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[181, 174])).
% 0.13/0.45 tff(183,plain,
% 0.13/0.45 (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[182])).
% 0.13/0.45 tff(184,plain,
% 0.13/0.45 (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.13/0.45 inference(symmetry,[status(thm)],[183])).
% 0.13/0.45 tff(185,plain,
% 0.13/0.45 (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[164, 184])).
% 0.13/0.45 tff(186,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[163, 185])).
% 0.13/0.45 tff(187,plain,((~greater(tptp_fun_To_0(E!2), equilibrium(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(188,plain,
% 0.13/0.45 (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[187, 162])).
% 0.13/0.45 tff(189,assumption,(greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.13/0.45 tff(190,plain,
% 0.13/0.45 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(191,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[190, 10])).
% 0.13/0.45 tff(192,assumption,(tptp_fun_T_1(E!2) = equilibrium(E!2)), introduced(assumption)).
% 0.13/0.45 tff(193,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[192])).
% 0.13/0.45 tff(194,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(symmetry,[status(thm)],[193])).
% 0.13/0.45 tff(195,plain,
% 0.13/0.45 ((~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) <=> (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[194])).
% 0.13/0.45 tff(196,assumption,(~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.13/0.45 tff(197,plain,
% 0.13/0.45 (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.13/0.45 tff(198,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(199,plain,
% 0.13/0.45 (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[198, 197, 191])).
% 0.13/0.45 tff(200,plain,
% 0.13/0.45 (((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(201,plain,
% 0.13/0.45 (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.13/0.45 tff(202,plain,
% 0.13/0.45 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(203,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[202, 10])).
% 0.13/0.45 tff(204,plain,
% 0.13/0.45 (((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(205,plain,
% 0.13/0.45 ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[204, 189])).
% 0.13/0.45 tff(206,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))) | greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (~((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(207,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))) | greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.13/0.45 tff(208,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[207, 203])).
% 0.13/0.45 tff(209,plain,
% 0.13/0.45 (equilibrium(E!2) = tptp_fun_T_1(E!2)),
% 0.13/0.45 inference(symmetry,[status(thm)],[192])).
% 0.13/0.45 tff(210,assumption,(tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)), introduced(assumption)).
% 0.13/0.45 tff(211,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[210, 209])).
% 0.13/0.45 tff(212,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.13/0.45 inference(symmetry,[status(thm)],[211])).
% 0.13/0.45 tff(213,assumption,(greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.13/0.45 tff(214,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.13/0.45 tff(215,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[196, 214])).
% 0.13/0.45 tff(216,plain,((~(tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~(tptp_fun_T_1(E!2) = equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(217,plain,
% 0.13/0.45 (~(tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[216, 208, 196, 192])).
% 0.13/0.45 tff(218,plain,
% 0.13/0.45 (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[181, 217])).
% 0.13/0.45 tff(219,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(220,plain,
% 0.13/0.45 ((greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))) <=> ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(221,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[220])).
% 0.13/0.45 tff(222,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[221, 219])).
% 0.13/0.45 tff(223,plain,
% 0.13/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(224,plain,
% 0.13/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.13/0.45 tff(225,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[224, 84, 218, 201, 189])).
% 0.13/0.45 tff(226,plain,((~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~(tptp_fun_T_1(E!2) = equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(227,plain,
% 0.13/0.45 (~(tptp_fun_T_1(E!2) = equilibrium(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[226, 189, 157])).
% 0.13/0.45 tff(228,assumption,(~greater(tptp_fun_To_0(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.13/0.45 tff(229,assumption,(greater(tptp_fun_T_1(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.13/0.45 tff(230,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(231,plain,
% 0.13/0.45 ((greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2)))) <=> ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(232,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[231])).
% 0.13/0.45 tff(233,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.13/0.45 inference(transitivity,[status(thm)],[232, 230])).
% 0.13/0.45 tff(234,plain,
% 0.13/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(235,plain,
% 0.13/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.13/0.45 tff(236,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[235, 84, 229, 189, 228])).
% 0.13/0.45 tff(237,plain,((~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(238,plain,
% 0.13/0.45 (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[237, 189, 188])).
% 0.13/0.45 tff(239,plain,
% 0.13/0.45 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(240,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[239, 10])).
% 0.13/0.45 tff(241,plain,
% 0.13/0.45 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(242,plain,
% 0.13/0.45 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[241])).
% 0.13/0.45 tff(243,plain,
% 0.13/0.45 (^[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))))), rewrite((in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E))) <=> (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))) <=> (((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(244,plain,
% 0.13/0.45 (![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[243])).
% 0.13/0.45 tff(245,plain,
% 0.13/0.45 (![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E)))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(246,plain,
% 0.13/0.45 (^[E: $i] : rewrite(((environment(E) & stable(E)) => ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E)))) <=> ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(247,plain,
% 0.13/0.45 (![E: $i] : ((environment(E) & stable(E)) => ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E)))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[246])).
% 0.13/0.45 tff(248,axiom,(![E: $i] : ((environment(E) & stable(E)) => ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a4')).
% 0.13/0.45 tff(249,plain,
% 0.13/0.45 (![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.13/0.45 tff(250,plain,
% 0.13/0.45 (![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.13/0.45 tff(251,plain,(
% 0.13/0.45 ![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))),
% 0.13/0.45 inference(skolemize,[status(sab)],[250])).
% 0.13/0.45 tff(252,plain,
% 0.13/0.45 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.13/0.45 tff(253,plain,
% 0.13/0.45 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[252, 242])).
% 0.13/0.45 tff(254,plain,
% 0.13/0.45 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(255,plain,
% 0.13/0.45 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(256,plain,
% 0.13/0.45 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.13/0.45 tff(257,plain,
% 0.13/0.45 (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[256, 253, 23, 22])).
% 0.13/0.45 tff(258,plain,
% 0.13/0.45 (((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))) | greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(259,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.13/0.45 tff(260,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2)))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(261,plain,
% 0.13/0.45 ((~(greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) | ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.13/0.45 tff(262,plain,
% 0.13/0.45 ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[261, 240])).
% 0.13/0.45 tff(263,plain,
% 0.13/0.45 ((~((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2)))) | (tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(264,plain,
% 0.13/0.45 ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.13/0.45 tff(265,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[264, 238, 227])).
% 0.13/0.45 tff(266,plain,(~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(267,assumption,(~(tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.13/0.45 tff(268,assumption,(~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.13/0.45 tff(269,plain,
% 0.13/0.45 (((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))) | in_environment(E!2, tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(270,plain,
% 0.13/0.45 (in_environment(E!2, tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[269, 257])).
% 0.13/0.45 tff(271,plain,
% 0.13/0.45 (^[E: $i, T1: $i, T2: $i] : refl((greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(272,plain,
% 0.13/0.45 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2))) <=> ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[271])).
% 0.13/0.45 tff(273,plain,
% 0.13/0.45 (^[E: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite((in_environment(E, T1) & in_environment(E, T2)) <=> (~((~in_environment(E, T1)) | (~in_environment(E, T2))))), ((~(in_environment(E, T1) & in_environment(E, T2))) <=> (~(~((~in_environment(E, T1)) | (~in_environment(E, T2))))))), rewrite((~(~((~in_environment(E, T1)) | (~in_environment(E, T2))))) <=> ((~in_environment(E, T1)) | (~in_environment(E, T2)))), ((~(in_environment(E, T1) & in_environment(E, T2))) <=> ((~in_environment(E, T1)) | (~in_environment(E, T2))))), ((greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2)))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | ((~in_environment(E, T1)) | (~in_environment(E, T2)))))), rewrite((greater(T1, T2) | (T2 = T1) | greater(T2, T1) | ((~in_environment(E, T1)) | (~in_environment(E, T2)))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))), ((greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2)))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(274,plain,
% 0.13/0.45 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2)))) <=> ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[273])).
% 0.13/0.45 tff(275,plain,
% 0.13/0.45 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2)))) <=> ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(276,plain,
% 0.13/0.45 (^[E: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(T2, T1) | (T2 = T1)) <=> ((T2 = T1) | greater(T2, T1))), (((greater(T2, T1) | (T2 = T1)) | greater(T1, T2)) <=> (((T2 = T1) | greater(T2, T1)) | greater(T1, T2)))), rewrite((((T2 = T1) | greater(T2, T1)) | greater(T1, T2)) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1))), (((greater(T2, T1) | (T2 = T1)) | greater(T1, T2)) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1)))), (((in_environment(E, T1) & in_environment(E, T2)) => ((greater(T2, T1) | (T2 = T1)) | greater(T1, T2))) <=> ((in_environment(E, T1) & in_environment(E, T2)) => (greater(T1, T2) | (T2 = T1) | greater(T2, T1))))), rewrite(((in_environment(E, T1) & in_environment(E, T2)) => (greater(T1, T2) | (T2 = T1) | greater(T2, T1))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))), (((in_environment(E, T1) & in_environment(E, T2)) => ((greater(T2, T1) | (T2 = T1)) | greater(T1, T2))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(277,plain,
% 0.13/0.45 (![E: $i, T1: $i, T2: $i] : ((in_environment(E, T1) & in_environment(E, T2)) => ((greater(T2, T1) | (T2 = T1)) | greater(T1, T2))) <=> ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[276])).
% 0.13/0.45 tff(278,axiom,(![E: $i, T1: $i, T2: $i] : ((in_environment(E, T1) & in_environment(E, T2)) => ((greater(T2, T1) | (T2 = T1)) | greater(T1, T2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_times_in_environment')).
% 0.13/0.45 tff(279,plain,
% 0.13/0.45 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.13/0.45 tff(280,plain,
% 0.13/0.45 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.13/0.45 tff(281,plain,(
% 0.13/0.45 ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.13/0.45 inference(skolemize,[status(sab)],[280])).
% 0.13/0.45 tff(282,plain,
% 0.13/0.45 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[281, 274])).
% 0.13/0.45 tff(283,plain,
% 0.13/0.45 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[282, 272])).
% 0.13/0.45 tff(284,plain,
% 0.13/0.45 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(285,plain,
% 0.13/0.45 ((greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~in_environment(E!2, tptp_fun_To_0(E!2)))) <=> ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(286,plain,
% 0.13/0.45 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~in_environment(E!2, tptp_fun_To_0(E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[285])).
% 0.13/0.45 tff(287,plain,
% 0.13/0.45 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~in_environment(E!2, tptp_fun_To_0(E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)))),
% 0.13/0.45 inference(transitivity,[status(thm)],[286, 284])).
% 0.13/0.45 tff(288,plain,
% 0.13/0.45 ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~in_environment(E!2, tptp_fun_To_0(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(289,plain,
% 0.13/0.45 ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.13/0.45 tff(290,plain,
% 0.13/0.45 (greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[289, 283, 45, 270])).
% 0.13/0.45 tff(291,plain,
% 0.13/0.45 (greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[290, 268, 267])).
% 0.13/0.45 tff(292,plain,
% 0.13/0.45 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(293,plain,
% 0.13/0.45 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[292, 10])).
% 0.13/0.45 tff(294,assumption,(greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))), introduced(assumption)).
% 0.13/0.45 tff(295,assumption,(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero), introduced(assumption)).
% 0.13/0.45 tff(296,plain,
% 0.13/0.45 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[295])).
% 0.13/0.45 tff(297,plain,
% 0.13/0.45 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.13/0.45 inference(symmetry,[status(thm)],[296])).
% 0.13/0.45 tff(298,plain,
% 0.13/0.45 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) <=> (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[297])).
% 0.13/0.45 tff(299,assumption,(~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)), introduced(assumption)).
% 0.13/0.45 tff(300,assumption,(greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)), introduced(assumption)).
% 0.13/0.45 tff(301,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(302,plain,
% 0.13/0.45 ((greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))) <=> (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(303,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[302])).
% 0.13/0.45 tff(304,plain,
% 0.13/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.13/0.46 inference(transitivity,[status(thm)],[303, 301])).
% 0.13/0.46 tff(305,plain,
% 0.13/0.46 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))),
% 0.13/0.46 inference(quant_inst,[status(thm)],[])).
% 0.13/0.46 tff(306,plain,
% 0.13/0.46 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.13/0.46 tff(307,plain,
% 0.13/0.46 ($false),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[306, 84, 299, 300, 294])).
% 0.13/0.46 tff(308,plain,((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.46 tff(309,plain,
% 0.13/0.46 (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[308, 294, 299])).
% 0.13/0.46 tff(310,plain,
% 0.13/0.46 (((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))) | greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(311,plain,
% 0.13/0.46 ((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.13/0.46 tff(312,plain,
% 0.13/0.46 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.13/0.46 inference(quant_inst,[status(thm)],[])).
% 0.13/0.46 tff(313,plain,
% 0.13/0.46 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[312, 10])).
% 0.13/0.46 tff(314,assumption,(~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.13/0.46 tff(315,plain,
% 0.13/0.46 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(316,plain,
% 0.13/0.46 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) | (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.13/0.46 tff(317,plain,
% 0.13/0.46 (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[316, 313])).
% 0.13/0.46 tff(318,plain,
% 0.13/0.46 (((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(319,plain,
% 0.13/0.46 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.13/0.46 tff(320,plain,
% 0.13/0.46 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.13/0.46 inference(monotonicity,[status(thm)],[192])).
% 0.13/0.46 tff(321,plain,
% 0.13/0.46 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.46 inference(symmetry,[status(thm)],[320])).
% 0.13/0.46 tff(322,plain,
% 0.13/0.46 ((~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) <=> (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.13/0.46 inference(monotonicity,[status(thm)],[321])).
% 0.13/0.46 tff(323,plain,
% 0.13/0.46 (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[314, 322])).
% 0.13/0.46 tff(324,plain,
% 0.13/0.46 (((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | ((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))))))) <=> ((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))))))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(325,plain,
% 0.13/0.46 ((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | ((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))))))),
% 0.13/0.46 inference(quant_inst,[status(thm)],[])).
% 0.13/0.46 tff(326,plain,
% 0.13/0.46 ((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.13/0.46 tff(327,plain,
% 0.13/0.46 (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[326, 52, 270])).
% 0.13/0.46 tff(328,plain,
% 0.13/0.46 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(329,plain,
% 0.13/0.46 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[328, 327])).
% 0.13/0.46 tff(330,plain,
% 0.13/0.46 ($false),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[329, 323])).
% 0.13/0.46 tff(331,plain,((~(tptp_fun_T_1(E!2) = equilibrium(E!2))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.46 tff(332,plain,
% 0.13/0.46 (~(tptp_fun_T_1(E!2) = equilibrium(E!2))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[331, 314])).
% 0.13/0.46 tff(333,plain,
% 0.13/0.46 (greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[264, 332])).
% 0.13/0.46 tff(334,assumption,(~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.13/0.46 tff(335,assumption,(greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.13/0.46 tff(336,plain,
% 0.13/0.46 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(337,plain,
% 0.13/0.46 ((greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2)))) <=> ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(338,plain,
% 0.13/0.46 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.13/0.46 inference(monotonicity,[status(thm)],[337])).
% 0.13/0.46 tff(339,plain,
% 0.13/0.46 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.13/0.46 inference(transitivity,[status(thm)],[338, 336])).
% 0.13/0.46 tff(340,plain,
% 0.13/0.46 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.13/0.46 inference(quant_inst,[status(thm)],[])).
% 0.13/0.46 tff(341,plain,
% 0.13/0.46 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.13/0.46 tff(342,plain,
% 0.13/0.46 ($false),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[341, 84, 229, 335, 334])).
% 0.13/0.46 tff(343,plain,((~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.46 tff(344,plain,
% 0.13/0.46 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[343, 333, 319])).
% 0.13/0.46 tff(345,plain,
% 0.13/0.46 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))),
% 0.13/0.46 inference(quant_inst,[status(thm)],[])).
% 0.13/0.46 tff(346,plain,
% 0.13/0.46 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[345, 10])).
% 0.13/0.46 tff(347,plain,
% 0.13/0.46 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(348,plain,
% 0.13/0.46 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))) | ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[347, 329])).
% 0.13/0.46 tff(349,plain,
% 0.13/0.46 ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[348, 346])).
% 0.13/0.46 tff(350,plain,
% 0.13/0.46 ((~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))) | (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(351,plain,
% 0.13/0.46 ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[350, 349])).
% 0.13/0.46 tff(352,plain,
% 0.13/0.46 (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[351, 344])).
% 0.13/0.46 tff(353,plain,
% 0.13/0.46 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.13/0.46 inference(monotonicity,[status(thm)],[352])).
% 0.13/0.46 tff(354,plain,
% 0.13/0.46 (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.13/0.46 inference(symmetry,[status(thm)],[353])).
% 0.13/0.46 tff(355,plain,
% 0.13/0.46 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[259, 354])).
% 0.13/0.46 tff(356,plain,
% 0.13/0.46 ($false),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[314, 355])).
% 0.13/0.46 tff(357,plain,(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.46 tff(358,plain,
% 0.13/0.46 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))) | ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(359,plain,
% 0.13/0.46 ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[358, 327])).
% 0.13/0.46 tff(360,plain,
% 0.13/0.46 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.13/0.46 inference(tautology,[status(thm)],[])).
% 0.13/0.46 tff(361,plain,
% 0.13/0.46 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[360, 327])).
% 0.13/0.46 tff(362,plain,
% 0.13/0.46 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(363,plain,
% 0.13/0.46 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(364,plain,
% 0.22/0.46 ((~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) <=> (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(365,plain,
% 0.22/0.46 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(366,plain,
% 0.22/0.46 ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(367,plain,
% 0.22/0.46 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))) <=> ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[366, 365, 364])).
% 0.22/0.46 tff(368,plain,
% 0.22/0.46 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[367, 363])).
% 0.22/0.46 tff(369,plain,
% 0.22/0.46 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[368])).
% 0.22/0.46 tff(370,plain,
% 0.22/0.46 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[369, 362])).
% 0.22/0.46 tff(371,plain,
% 0.22/0.46 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(372,plain,
% 0.22/0.46 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.22/0.46 tff(373,plain,
% 0.22/0.46 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[372, 107, 23, 361, 359])).
% 0.22/0.46 tff(374,plain,
% 0.22/0.46 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[373, 357])).
% 0.22/0.46 tff(375,plain,
% 0.22/0.46 (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[374, 311])).
% 0.22/0.46 tff(376,plain,
% 0.22/0.46 (((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))) | (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(377,plain,
% 0.22/0.46 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[376, 375])).
% 0.22/0.46 tff(378,plain,
% 0.22/0.46 (((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))) | (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(379,plain,
% 0.22/0.46 (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[378, 375])).
% 0.22/0.46 tff(380,plain,
% 0.22/0.46 (zero = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.22/0.46 inference(symmetry,[status(thm)],[379])).
% 0.22/0.46 tff(381,plain,
% 0.22/0.46 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.22/0.46 inference(monotonicity,[status(thm)],[380, 377])).
% 0.22/0.46 tff(382,plain,
% 0.22/0.46 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.46 inference(symmetry,[status(thm)],[381])).
% 0.22/0.46 tff(383,plain,
% 0.22/0.46 ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) <=> (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[382])).
% 0.22/0.46 tff(384,plain,
% 0.22/0.46 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[299, 383])).
% 0.22/0.46 tff(385,plain,
% 0.22/0.46 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[379])).
% 0.22/0.46 tff(386,plain,
% 0.22/0.46 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[294, 385])).
% 0.22/0.46 tff(387,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[386, 384])).
% 0.22/0.46 tff(388,plain,((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(389,plain,
% 0.22/0.46 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[388, 294])).
% 0.22/0.46 tff(390,plain,
% 0.22/0.46 ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(391,plain,
% 0.22/0.46 ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[390, 359])).
% 0.22/0.46 tff(392,plain,
% 0.22/0.46 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[391, 389])).
% 0.22/0.46 tff(393,plain,
% 0.22/0.46 (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[392, 298])).
% 0.22/0.46 tff(394,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[294, 393])).
% 0.22/0.46 tff(395,plain,((~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(396,plain,
% 0.22/0.46 (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[395, 294])).
% 0.22/0.46 tff(397,plain,
% 0.22/0.46 ((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[378, 396])).
% 0.22/0.46 tff(398,plain,
% 0.22/0.46 (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[374, 397])).
% 0.22/0.46 tff(399,plain,
% 0.22/0.46 (((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))) | greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(400,plain,
% 0.22/0.46 (greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[399, 398])).
% 0.22/0.46 tff(401,plain,
% 0.22/0.46 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(402,plain,
% 0.22/0.46 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(403,plain,
% 0.22/0.46 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.22/0.46 tff(404,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[403, 84, 392, 400, 294])).
% 0.22/0.46 tff(405,plain,(~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(406,plain,
% 0.22/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(407,plain,
% 0.22/0.46 ((greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))) <=> ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(408,plain,
% 0.22/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[407])).
% 0.22/0.46 tff(409,plain,
% 0.22/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[408, 406])).
% 0.22/0.47 tff(410,plain,
% 0.22/0.47 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(411,plain,
% 0.22/0.47 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.22/0.47 tff(412,plain,
% 0.22/0.47 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[411, 62, 361])).
% 0.22/0.47 tff(413,plain,
% 0.22/0.47 (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[412, 405])).
% 0.22/0.47 tff(414,plain,
% 0.22/0.47 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(415,plain,
% 0.22/0.47 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) | (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[414, 413])).
% 0.22/0.47 tff(416,plain,
% 0.22/0.47 (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[415, 293])).
% 0.22/0.47 tff(417,plain,
% 0.22/0.47 (((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(418,plain,
% 0.22/0.47 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[417, 416])).
% 0.22/0.47 tff(419,assumption,(~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.22/0.47 tff(420,assumption,(greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.22/0.47 tff(421,plain,
% 0.22/0.47 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(422,plain,
% 0.22/0.47 ((greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))) <=> ((~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(423,plain,
% 0.22/0.47 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[422])).
% 0.22/0.47 tff(424,plain,
% 0.22/0.47 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[423, 421])).
% 0.22/0.47 tff(425,plain,
% 0.22/0.47 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(426,plain,
% 0.22/0.47 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.22/0.47 tff(427,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[426, 84, 335, 420, 419])).
% 0.22/0.47 tff(428,plain,((~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(429,plain,
% 0.22/0.47 ((~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[428, 418])).
% 0.22/0.47 tff(430,plain,
% 0.22/0.47 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[429, 291])).
% 0.22/0.47 tff(431,plain,
% 0.22/0.47 (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[351, 430])).
% 0.22/0.47 tff(432,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[431])).
% 0.22/0.47 tff(433,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(symmetry,[status(thm)],[432])).
% 0.22/0.47 tff(434,assumption,(~((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))), introduced(assumption)).
% 0.22/0.47 tff(435,plain,
% 0.22/0.47 (((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | (~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(436,plain,
% 0.22/0.47 (~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[435, 434])).
% 0.22/0.47 tff(437,plain,
% 0.22/0.47 (((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(438,plain,
% 0.22/0.47 (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[437, 434])).
% 0.22/0.47 tff(439,plain,
% 0.22/0.47 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(440,plain,
% 0.22/0.47 ((greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2)))) <=> ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(441,plain,
% 0.22/0.47 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[440])).
% 0.22/0.47 tff(442,plain,
% 0.22/0.47 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[441, 439])).
% 0.22/0.47 tff(443,plain,
% 0.22/0.47 ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(444,plain,
% 0.22/0.47 ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.22/0.47 tff(445,plain,
% 0.22/0.47 ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[444, 283, 45, 270, 268])).
% 0.22/0.47 tff(446,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[445, 438, 436])).
% 0.22/0.47 tff(447,plain,(((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(448,plain,
% 0.22/0.47 ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[447, 268])).
% 0.22/0.47 tff(449,assumption,(~(greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))), introduced(assumption)).
% 0.22/0.47 tff(450,plain,
% 0.22/0.47 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(451,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[450, 10, 449])).
% 0.22/0.47 tff(452,plain,(greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(453,plain,
% 0.22/0.47 ((~(greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) | greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(454,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[453, 452])).
% 0.22/0.47 tff(455,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[454, 448])).
% 0.22/0.47 tff(456,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[455, 433])).
% 0.22/0.47 tff(457,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[413, 456])).
% 0.22/0.47 tff(458,plain,(greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(459,plain,
% 0.22/0.47 (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[458, 266])).
% 0.22/0.47 tff(460,assumption,(tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)), introduced(assumption)).
% 0.22/0.47 tff(461,plain,
% 0.22/0.47 (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[460])).
% 0.22/0.47 tff(462,plain,
% 0.22/0.47 (greater(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.22/0.47 inference(symmetry,[status(thm)],[461])).
% 0.22/0.47 tff(463,plain,
% 0.22/0.47 (greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[229, 462])).
% 0.22/0.47 tff(464,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[228, 463])).
% 0.22/0.47 tff(465,plain,((~(tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(466,plain,
% 0.22/0.47 (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[465, 459, 188])).
% 0.22/0.47 tff(467,plain,
% 0.22/0.47 (tptp_fun_To_0(E!2) = equilibrium(E!2)),
% 0.22/0.47 inference(transitivity,[status(thm)],[460, 192])).
% 0.22/0.47 tff(468,plain,
% 0.22/0.47 (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_3(equilibrium(E!2))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[192])).
% 0.22/0.47 tff(469,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> greater_or_equal(tptp_fun_T_3(equilibrium(E!2)), equilibrium(E!2))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[468, 467])).
% 0.22/0.47 tff(470,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_3(equilibrium(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(symmetry,[status(thm)],[469])).
% 0.22/0.47 tff(471,plain,
% 0.22/0.47 (tptp_fun_T_3(equilibrium(E!2)) = tptp_fun_T_3(tptp_fun_T_1(E!2))),
% 0.22/0.47 inference(symmetry,[status(thm)],[468])).
% 0.22/0.47 tff(472,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_3(equilibrium(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[471])).
% 0.22/0.47 tff(473,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(equilibrium(E!2)), equilibrium(E!2))),
% 0.22/0.47 inference(symmetry,[status(thm)],[472])).
% 0.22/0.47 tff(474,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_3(equilibrium(E!2)), equilibrium(E!2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[357, 473])).
% 0.22/0.47 tff(475,plain,
% 0.22/0.47 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[474, 470])).
% 0.22/0.47 tff(476,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[413, 475])).
% 0.22/0.47 tff(477,plain,((~(tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2))) | (~(tptp_fun_T_1(E!2) = equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(478,plain,
% 0.22/0.47 (~(tptp_fun_T_1(E!2) = equilibrium(E!2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[477, 459])).
% 0.22/0.47 tff(479,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[264, 478, 466])).
% 0.22/0.47 % SZS output end Proof
% 0.22/0.47 % E exiting
%------------------------------------------------------------------------------