%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT034+2 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n005.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 06:24:02 AM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT034+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.06/0.33 % Computer : n005.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon Sep 7 12:32:07 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(greater_type, type, (
% 0.12/0.40 greater: ( $i * $i ) > $o)).
% 0.12/0.40 tff(growth_rate_type, type, (
% 0.12/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_T_0_type, type, (
% 0.12/0.40 tptp_fun_T_0: $i)).
% 0.12/0.40 tff(efficient_producers_type, type, (
% 0.12/0.40 efficient_producers: $i)).
% 0.12/0.40 tff(first_movers_type, type, (
% 0.12/0.40 first_movers: $i)).
% 0.12/0.40 tff(subpopulations_type, type, (
% 0.12/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_E_1_type, type, (
% 0.12/0.40 tptp_fun_E_1: $i)).
% 0.12/0.40 tff(appear_type, type, (
% 0.12/0.40 appear: ( $i * $i ) > $i)).
% 0.12/0.40 tff(in_environment_type, type, (
% 0.12/0.40 in_environment: ( $i * $i ) > $o)).
% 0.12/0.40 tff(critical_point_type, type, (
% 0.12/0.40 critical_point: $i > $i)).
% 0.12/0.40 tff(greater_or_equal_type, type, (
% 0.12/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.12/0.40 tff(environment_type, type, (
% 0.12/0.40 environment: $i > $o)).
% 0.12/0.40 tff(selection_favors_type, type, (
% 0.12/0.40 selection_favors: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(zero_type, type, (
% 0.12/0.40 zero: $i)).
% 0.12/0.40 tff(difference_type, type, (
% 0.12/0.40 difference: ( $i * $i ) > $i)).
% 0.12/0.40 tff(decreases_type, type, (
% 0.12/0.40 decreases: $i > $o)).
% 0.12/0.40 tff(disbanding_rate_type, type, (
% 0.12/0.40 disbanding_rate: ( $i * $i ) > $i)).
% 0.12/0.40 tff(founding_rate_type, type, (
% 0.12/0.40 founding_rate: ( $i * $i ) > $i)).
% 0.12/0.40 tff(1,assumption,(~in_environment(E!1, appear(efficient_producers, E!1))), introduced(assumption)).
% 0.12/0.40 tff(2,assumption,(~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))), introduced(assumption)).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.40 tff(8,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal')).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.40 tff(11,plain,(
% 0.12/0.40 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[10])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 ((greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> $true) <=> greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (($true | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) <=> ($true | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) <=> $true),
% 0.12/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 ((greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))) <=> (greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> $true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 ((greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))) <=> greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))),
% 0.12/0.40 inference(transitivity,[status(thm)],[19, 14])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[21, 13])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[24, 12, 2])).
% 0.12/0.40 tff(26,plain,(greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 ((~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 ((~![E: $i, T: $i] : ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => selection_favors(first_movers, efficient_producers, T))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(29,axiom,(~![E: $i, T: $i] : ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => selection_favors(first_movers, efficient_producers, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t3')).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.12/0.40 tff(34,plain,(
% 0.12/0.40 ~((~(environment(E!1) & in_environment(E!1, critical_point(E!1)) & greater_or_equal(T!0, appear(efficient_producers, E!1)) & greater(critical_point(E!1), T!0))) | selection_favors(first_movers, efficient_producers, T!0))),
% 0.12/0.40 inference(skolemize,[status(sab)],[33])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (environment(E!1) & in_environment(E!1, critical_point(E!1)) & greater_or_equal(T!0, appear(efficient_producers, E!1)) & greater(critical_point(E!1), T!0)),
% 0.12/0.40 inference(or_elim,[status(thm)],[34])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (in_environment(E!1, critical_point(E!1))),
% 0.12/0.40 inference(and_elim,[status(thm)],[35])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (environment(E!1)),
% 0.12/0.40 inference(and_elim,[status(thm)],[35])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (^[E: $i, T: $i] : refl((in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))) <=> (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T)) <=> (~((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))), ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) <=> (~(~((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))) <=> ((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))), ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) <=> ((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))), (((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T)) <=> (((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))) | in_environment(E, T)))), rewrite((((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))), (((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)))), ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) <=> ((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)))), rewrite(((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) <=> (environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))), ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) <=> (environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T)))), (((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => in_environment(E, T)) <=> ((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T)) => in_environment(E, T)))), rewrite(((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T)) => in_environment(E, T)) <=> ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))), (((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => in_environment(E, T)) <=> ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (![E: $i, T: $i] : ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.40 tff(45,axiom,(![E: $i, T: $i] : ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => in_environment(E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_critical_time_points')).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.12/0.40 tff(48,plain,(
% 0.12/0.40 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.12/0.40 inference(skolemize,[status(sab)],[47])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((in_environment(E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1)))) <=> ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (in_environment(E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[52])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (in_environment(E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[53, 51])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (in_environment(E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 (in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[56, 50, 37, 36, 26])).
% 0.12/0.41 tff(58,plain,
% 0.12/0.41 (~greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[57, 1])).
% 0.12/0.41 tff(59,plain,
% 0.12/0.41 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(60,plain,
% 0.12/0.41 (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[59, 12])).
% 0.12/0.41 tff(61,plain,
% 0.12/0.41 (^[E: $i] : refl((subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E)))) <=> (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(62,plain,
% 0.12/0.41 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E)))) <=> ![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.12/0.41 tff(63,plain,
% 0.12/0.41 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, critical_point(E))) <=> (~((~environment(E)) | (~in_environment(E, critical_point(E)))))), ((~(environment(E) & in_environment(E, critical_point(E)))) <=> (~(~((~environment(E)) | (~in_environment(E, critical_point(E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, critical_point(E)))))) <=> ((~environment(E)) | (~in_environment(E, critical_point(E))))), ((~(environment(E) & in_environment(E, critical_point(E)))) <=> ((~environment(E)) | (~in_environment(E, critical_point(E)))))), (((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> (((~environment(E)) | (~in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))))), rewrite((((~environment(E)) | (~in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))), (((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(64,plain,
% 0.12/0.41 (![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> ![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.12/0.41 tff(65,plain,
% 0.12/0.41 (![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> ![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(66,plain,
% 0.12/0.41 (^[E: $i] : rewrite(((environment(E) & in_environment(E, critical_point(E))) => subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(67,plain,
% 0.12/0.41 (![E: $i] : ((environment(E) & in_environment(E, critical_point(E))) => subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> ![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.41 tff(68,axiom,(![E: $i] : ((environment(E) & in_environment(E, critical_point(E))) => subpopulations(first_movers, efficient_producers, E, critical_point(E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_critical_point_means_FM_and_EP')).
% 0.12/0.41 tff(69,plain,
% 0.12/0.41 (![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.12/0.41 tff(70,plain,
% 0.12/0.41 (![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.12/0.41 tff(71,plain,(
% 0.12/0.41 ![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[70])).
% 0.12/0.41 tff(72,plain,
% 0.12/0.41 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.12/0.41 tff(73,plain,
% 0.12/0.41 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 (((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))) | (subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))))) <=> ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))) | subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(75,plain,
% 0.12/0.41 ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))) | (subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(76,plain,
% 0.12/0.41 ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))) | subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.12/0.41 tff(77,plain,
% 0.12/0.41 (subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[76, 73, 37, 36])).
% 0.12/0.41 tff(78,plain,
% 0.12/0.41 (^[E: $i, T: $i] : refl((greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(79,plain,
% 0.12/0.41 (![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.12/0.41 tff(80,plain,
% 0.12/0.41 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(81,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> ![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.12/0.41 tff(82,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(83,plain,
% 0.12/0.41 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater_or_equal(T, appear(efficient_producers, E))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(84,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater_or_equal(T, appear(efficient_producers, E))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.12/0.41 tff(85,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater_or_equal(T, appear(efficient_producers, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_FM_and_EP_members_EP_appeared')).
% 0.12/0.41 tff(86,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.12/0.41 tff(87,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.12/0.41 tff(88,plain,(
% 0.12/0.41 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[87])).
% 0.12/0.41 tff(89,plain,
% 0.12/0.41 (![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.12/0.41 tff(90,plain,
% 0.12/0.41 (![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.12/0.41 tff(91,plain,
% 0.12/0.41 (((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))) <=> ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(92,plain,
% 0.12/0.41 ((greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(93,plain,
% 0.12/0.41 (((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[92])).
% 0.12/0.41 tff(94,plain,
% 0.12/0.41 (((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[93, 91])).
% 0.12/0.41 tff(95,plain,
% 0.12/0.41 ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(96,plain,
% 0.12/0.41 ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.12/0.41 tff(97,plain,
% 0.12/0.41 (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[96, 90, 37, 77])).
% 0.12/0.41 tff(98,plain,
% 0.12/0.41 ((~(greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))) | (~greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))) | ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.12/0.42 inference(tautology,[status(thm)],[])).
% 0.12/0.42 tff(99,plain,
% 0.12/0.42 ((~(greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))) | ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.12/0.42 tff(100,plain,
% 0.12/0.42 ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[99, 60])).
% 0.12/0.42 tff(101,plain,
% 0.12/0.42 ((~((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))) | (critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.12/0.42 inference(tautology,[status(thm)],[])).
% 0.12/0.42 tff(102,plain,
% 0.12/0.42 ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.12/0.42 tff(103,plain,
% 0.12/0.42 (critical_point(E!1) = appear(efficient_producers, E!1)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[102, 58])).
% 0.12/0.42 tff(104,plain,
% 0.12/0.42 (in_environment(E!1, critical_point(E!1)) <=> in_environment(E!1, appear(efficient_producers, E!1))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[103])).
% 0.12/0.42 tff(105,plain,
% 0.12/0.42 (in_environment(E!1, appear(efficient_producers, E!1)) <=> in_environment(E!1, critical_point(E!1))),
% 0.12/0.42 inference(symmetry,[status(thm)],[104])).
% 0.12/0.42 tff(106,plain,
% 0.12/0.42 ((~in_environment(E!1, appear(efficient_producers, E!1))) <=> (~in_environment(E!1, critical_point(E!1)))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[105])).
% 0.12/0.42 tff(107,plain,
% 0.12/0.42 (~in_environment(E!1, critical_point(E!1))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[1, 106])).
% 0.12/0.42 tff(108,plain,
% 0.12/0.42 ($false),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[36, 107])).
% 0.12/0.42 tff(109,plain,(in_environment(E!1, appear(efficient_producers, E!1))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.42 tff(110,plain,
% 0.12/0.42 (^[E: $i] : refl((subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))) <=> (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(111,plain,
% 0.12/0.42 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))) <=> ![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.12/0.42 tff(112,plain,
% 0.12/0.42 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, appear(efficient_producers, E))) <=> (~((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))), ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) <=> (~(~((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))) <=> ((~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))), ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) <=> ((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))), (((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> (((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))))), rewrite((((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))), (((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(113,plain,
% 0.12/0.42 (![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> ![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[112])).
% 0.12/0.42 tff(114,plain,
% 0.12/0.42 (![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> ![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(115,plain,
% 0.12/0.42 (^[E: $i] : rewrite(((environment(E) & in_environment(E, appear(efficient_producers, E))) => subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(116,plain,
% 0.12/0.42 (![E: $i] : ((environment(E) & in_environment(E, appear(efficient_producers, E))) => subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> ![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[115])).
% 0.12/0.42 tff(117,axiom,(![E: $i] : ((environment(E) & in_environment(E, appear(efficient_producers, E))) => subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_FM_and_EP_when_EP_appears')).
% 0.12/0.42 tff(118,plain,
% 0.12/0.42 (![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.12/0.42 tff(119,plain,
% 0.12/0.42 (![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.12/0.42 tff(120,plain,(
% 0.12/0.42 ![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.12/0.42 inference(skolemize,[status(sab)],[119])).
% 0.12/0.42 tff(121,plain,
% 0.12/0.42 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.12/0.42 tff(122,plain,
% 0.12/0.42 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.12/0.42 tff(123,plain,
% 0.12/0.42 (((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | ((~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))) <=> ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(124,plain,
% 0.12/0.42 ((subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1)))) <=> ((~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(125,plain,
% 0.12/0.42 (((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))) <=> ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | ((~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1)))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[124])).
% 0.12/0.42 tff(126,plain,
% 0.12/0.42 (((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))) <=> ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[125, 123])).
% 0.12/0.42 tff(127,plain,
% 0.12/0.42 ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(128,plain,
% 0.12/0.42 ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.12/0.42 tff(129,plain,
% 0.12/0.42 (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1)))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[128, 122, 37])).
% 0.12/0.42 tff(130,plain,
% 0.12/0.42 (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[129, 109])).
% 0.12/0.42 tff(131,assumption,(~subpopulations(first_movers, efficient_producers, E!1, T!0)), introduced(assumption)).
% 0.12/0.42 tff(132,plain,
% 0.12/0.42 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(critical_point(E!1), T!0) <=> ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(133,plain,
% 0.12/0.42 (greater_or_equal(critical_point(E!1), T!0) <=> ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[132, 12])).
% 0.12/0.42 tff(134,plain,
% 0.12/0.42 (greater(critical_point(E!1), T!0)),
% 0.12/0.42 inference(and_elim,[status(thm)],[35])).
% 0.12/0.42 tff(135,plain,
% 0.12/0.42 (((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)) | (~greater(critical_point(E!1), T!0))),
% 0.12/0.42 inference(tautology,[status(thm)],[])).
% 0.12/0.42 tff(136,plain,
% 0.12/0.42 ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.12/0.42 tff(137,plain,
% 0.12/0.42 ((~(greater_or_equal(critical_point(E!1), T!0) <=> ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)))) | greater_or_equal(critical_point(E!1), T!0) | (~((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)))),
% 0.12/0.42 inference(tautology,[status(thm)],[])).
% 0.12/0.42 tff(138,plain,
% 0.12/0.42 ((~(greater_or_equal(critical_point(E!1), T!0) <=> ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)))) | greater_or_equal(critical_point(E!1), T!0)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.12/0.42 tff(139,plain,
% 0.12/0.42 (greater_or_equal(critical_point(E!1), T!0)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[138, 133])).
% 0.12/0.42 tff(140,assumption,(subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))), introduced(assumption)).
% 0.12/0.42 tff(141,plain,
% 0.12/0.42 (greater_or_equal(T!0, appear(efficient_producers, E!1))),
% 0.12/0.42 inference(and_elim,[status(thm)],[35])).
% 0.12/0.42 tff(142,plain,
% 0.12/0.42 (^[E: $i, T1: $i, T2: $i, T: $i] : refl((subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(143,plain,
% 0.12/0.42 (![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))) <=> ![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[142])).
% 0.12/0.42 tff(144,plain,
% 0.12/0.42 (^[E: $i, T1: $i, T2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T)) <=> (~((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) <=> (~(~((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))))), rewrite((~(~((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))) <=> ((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) <=> ((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))) | subpopulations(first_movers, efficient_producers, E, T)))), rewrite((((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(145,plain,
% 0.12/0.42 (![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[144])).
% 0.12/0.42 tff(146,plain,
% 0.12/0.42 (![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(147,plain,
% 0.12/0.42 (^[E: $i, T1: $i, T2: $i, T: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1)))), (((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))), (((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T)))), ((((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))), ((((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(148,plain,
% 0.12/0.42 (![E: $i, T1: $i, T2: $i, T: $i] : (((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[147])).
% 0.12/0.42 tff(149,axiom,(![E: $i, T1: $i, T2: $i, T: $i] : (((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a10')).
% 0.12/0.43 tff(150,plain,
% 0.12/0.43 (![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.12/0.43 tff(151,plain,
% 0.12/0.43 (![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.12/0.43 tff(152,plain,(
% 0.12/0.43 ![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.12/0.43 inference(skolemize,[status(sab)],[151])).
% 0.12/0.43 tff(153,plain,
% 0.12/0.43 (![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.12/0.43 tff(154,plain,
% 0.12/0.43 (![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[153, 143])).
% 0.12/0.43 tff(155,plain,
% 0.12/0.43 (((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | ((~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))))) <=> ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(156,plain,
% 0.12/0.43 ((subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~greater_or_equal(critical_point(E!1), T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)))) <=> ((~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(157,plain,
% 0.12/0.43 (((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~greater_or_equal(critical_point(E!1), T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | ((~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)))))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[156])).
% 0.12/0.43 tff(158,plain,
% 0.12/0.43 (((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~greater_or_equal(critical_point(E!1), T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))))),
% 0.12/0.43 inference(transitivity,[status(thm)],[157, 155])).
% 0.12/0.43 tff(159,plain,
% 0.12/0.43 ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~greater_or_equal(critical_point(E!1), T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(160,plain,
% 0.12/0.43 ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.12/0.43 tff(161,plain,
% 0.12/0.43 ($false),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[160, 154, 37, 141, 77, 140, 139, 131])).
% 0.12/0.43 tff(162,plain,(subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.43 tff(163,plain,
% 0.12/0.43 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[162, 130])).
% 0.12/0.43 tff(164,plain,
% 0.12/0.43 (^[E: $i, T: $i] : refl((subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(165,plain,
% 0.12/0.43 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[164])).
% 0.12/0.43 tff(166,plain,
% 0.12/0.43 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(167,plain,
% 0.12/0.43 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[166])).
% 0.12/0.43 tff(168,plain,
% 0.12/0.43 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(169,plain,
% 0.12/0.43 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(170,plain,
% 0.12/0.43 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[169])).
% 0.12/0.43 tff(171,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_symmetry_of_subpopulations')).
% 0.12/0.43 tff(172,plain,
% 0.12/0.43 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.12/0.43 tff(173,plain,
% 0.12/0.43 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.12/0.43 tff(174,plain,(
% 0.12/0.43 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.43 inference(skolemize,[status(sab)],[173])).
% 0.12/0.43 tff(175,plain,
% 0.12/0.43 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.12/0.43 tff(176,plain,
% 0.12/0.43 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[175, 165])).
% 0.12/0.43 tff(177,plain,
% 0.12/0.43 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(178,plain,
% 0.12/0.43 ((subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(179,plain,
% 0.12/0.43 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[178])).
% 0.12/0.43 tff(180,plain,
% 0.12/0.43 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.44 inference(transitivity,[status(thm)],[179, 177])).
% 0.12/0.44 tff(181,plain,
% 0.12/0.44 ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(182,plain,
% 0.12/0.44 ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.12/0.44 tff(183,plain,
% 0.12/0.44 (subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[182, 176, 37, 163])).
% 0.12/0.44 tff(184,plain,
% 0.12/0.44 (~selection_favors(first_movers, efficient_producers, T!0)),
% 0.12/0.44 inference(or_elim,[status(thm)],[34])).
% 0.12/0.44 tff(185,plain,
% 0.12/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(186,plain,
% 0.12/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[185])).
% 0.12/0.44 tff(187,plain,
% 0.12/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(188,plain,
% 0.12/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[187])).
% 0.12/0.44 tff(189,plain,
% 0.12/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(190,plain,
% 0.12/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) <=> (environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)))), rewrite(((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(191,plain,
% 0.12/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[190])).
% 0.12/0.44 tff(192,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp1_high_growth_rates')).
% 0.12/0.44 tff(193,plain,
% 0.12/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.12/0.44 tff(194,plain,
% 0.12/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.12/0.44 tff(195,plain,(
% 0.12/0.44 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.12/0.44 inference(skolemize,[status(sab)],[194])).
% 0.12/0.44 tff(196,plain,
% 0.12/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.12/0.44 tff(197,plain,
% 0.12/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[196, 186])).
% 0.12/0.44 tff(198,plain,
% 0.12/0.44 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(first_movers, efficient_producers, T!0) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(first_movers, efficient_producers, T!0) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(199,plain,
% 0.12/0.44 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(first_movers, efficient_producers, T!0) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(200,plain,
% 0.12/0.44 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(first_movers, efficient_producers, T!0) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.12/0.44 tff(201,plain,
% 0.12/0.44 (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[200, 197, 37, 184, 183])).
% 0.12/0.44 tff(202,plain,
% 0.12/0.44 (^[E: $i, T: $i] : refl(((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(203,plain,
% 0.12/0.44 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[202])).
% 0.12/0.44 tff(204,plain,
% 0.12/0.44 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(205,plain,
% 0.12/0.44 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[204])).
% 0.12/0.44 tff(206,plain,
% 0.12/0.44 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(207,plain,
% 0.12/0.44 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(208,plain,
% 0.12/0.44 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[207])).
% 0.12/0.44 tff(209,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3')).
% 0.12/0.44 tff(210,plain,
% 0.12/0.44 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.12/0.44 tff(211,plain,
% 0.12/0.44 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.12/0.44 tff(212,plain,(
% 0.12/0.44 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.12/0.44 inference(skolemize,[status(sab)],[211])).
% 0.12/0.44 tff(213,plain,
% 0.12/0.44 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.12/0.44 tff(214,plain,
% 0.12/0.44 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[213, 203])).
% 0.12/0.44 tff(215,plain,
% 0.12/0.44 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(216,plain,
% 0.12/0.44 (((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(217,plain,
% 0.12/0.44 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))),
% 0.12/0.44 inference(monotonicity,[status(thm)],[216])).
% 0.12/0.44 tff(218,plain,
% 0.12/0.44 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.12/0.44 inference(transitivity,[status(thm)],[217, 215])).
% 0.12/0.44 tff(219,plain,
% 0.12/0.44 ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(220,plain,
% 0.12/0.44 ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.12/0.44 tff(221,plain,
% 0.12/0.44 (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[220, 214, 37, 163])).
% 0.12/0.44 tff(222,plain,
% 0.12/0.44 (^[E: $i, T: $i] : refl((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(223,plain,
% 0.12/0.44 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[222])).
% 0.12/0.44 tff(224,plain,
% 0.12/0.44 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))), rewrite((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(225,plain,
% 0.12/0.44 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))) <=> ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[224])).
% 0.12/0.44 tff(226,plain,
% 0.12/0.44 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))) <=> ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(227,plain,
% 0.12/0.44 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(228,plain,
% 0.12/0.45 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))) <=> ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[227])).
% 0.12/0.45 tff(229,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a12')).
% 0.12/0.45 tff(230,plain,
% 0.12/0.45 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.12/0.45 tff(231,plain,
% 0.12/0.45 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.12/0.45 tff(232,plain,(
% 0.12/0.45 ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.45 inference(skolemize,[status(sab)],[231])).
% 0.12/0.45 tff(233,plain,
% 0.12/0.45 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.12/0.45 tff(234,plain,
% 0.12/0.45 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[233, 223])).
% 0.12/0.45 tff(235,plain,
% 0.12/0.45 (((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))) <=> ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(236,plain,
% 0.12/0.45 ((decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(237,plain,
% 0.12/0.45 (((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))))),
% 0.12/0.45 inference(monotonicity,[status(thm)],[236])).
% 0.12/0.45 tff(238,plain,
% 0.12/0.45 (((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[237, 235])).
% 0.12/0.45 tff(239,plain,
% 0.12/0.45 ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.12/0.45 inference(quant_inst,[status(thm)],[])).
% 0.12/0.45 tff(240,plain,
% 0.12/0.45 ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.12/0.45 tff(241,plain,
% 0.12/0.45 (decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[240, 234, 37, 163])).
% 0.12/0.45 tff(242,plain,
% 0.12/0.45 (^[T: $i] : refl((decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(243,plain,
% 0.12/0.45 (![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))) <=> ![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[242])).
% 0.12/0.45 tff(244,plain,
% 0.12/0.45 (^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> (~(decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))), ((~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))) <=> (~(~(decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))))), rewrite((~(~(decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))), ((~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))), ((decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))))), rewrite((decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))), ((decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(245,plain,
% 0.12/0.45 (![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[244])).
% 0.12/0.45 tff(246,plain,
% 0.12/0.45 (![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(247,plain,
% 0.12/0.45 (^[T: $i] : rewrite(((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) => decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) <=> (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(248,plain,
% 0.12/0.45 (![T: $i] : ((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) => decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) <=> ![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[247])).
% 0.12/0.45 tff(249,axiom,(![T: $i] : ((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) => decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_difference_between_founding_rates')).
% 0.12/0.45 tff(250,plain,
% 0.12/0.45 (![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.12/0.45 tff(251,plain,
% 0.12/0.45 (![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.12/0.45 tff(252,plain,(
% 0.12/0.45 ![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.12/0.45 inference(skolemize,[status(sab)],[251])).
% 0.12/0.45 tff(253,plain,
% 0.12/0.45 (![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[252, 245])).
% 0.12/0.45 tff(254,plain,
% 0.12/0.45 (![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[253, 243])).
% 0.12/0.45 tff(255,plain,
% 0.12/0.45 (((~![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) | (decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))) | (~decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))))) <=> ((~![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) | decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))) | (~decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(256,plain,
% 0.12/0.45 ((~![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) | (decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))) | (~decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))))),
% 0.12/0.45 inference(quant_inst,[status(thm)],[])).
% 0.12/0.45 tff(257,plain,
% 0.12/0.45 ((~![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) | decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))) | (~decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.12/0.45 tff(258,plain,
% 0.12/0.45 (decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[257, 254, 241, 221])).
% 0.12/0.45 tff(259,plain,
% 0.12/0.45 (^[T: $i] : refl((greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(260,plain,
% 0.12/0.45 (![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[259])).
% 0.12/0.45 tff(261,plain,
% 0.12/0.45 (![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.46 tff(262,axiom,(![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_negative_growth_rate_difference')).
% 0.12/0.46 tff(263,plain,
% 0.12/0.46 (![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.12/0.46 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.12/0.46 tff(264,plain,(
% 0.12/0.46 ![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.12/0.46 inference(skolemize,[status(sab)],[263])).
% 0.12/0.46 tff(265,plain,
% 0.12/0.46 (![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.12/0.46 inference(modus_ponens,[status(thm)],[264, 260])).
% 0.12/0.46 tff(266,plain,
% 0.12/0.46 ((~![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) <=> greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))),
% 0.12/0.46 inference(quant_inst,[status(thm)],[])).
% 0.12/0.46 tff(267,plain,
% 0.12/0.46 (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) <=> greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))),
% 0.12/0.46 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.12/0.46 tff(268,plain,
% 0.12/0.46 (^[E: $i] : refl(((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E)))))))) <=> ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E)))))))))),
% 0.12/0.46 inference(bind,[status(th)],[])).
% 0.12/0.46 tff(269,plain,
% 0.12/0.46 (![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))),
% 0.12/0.46 inference(quant_intro,[status(thm)],[268])).
% 0.12/0.46 tff(270,plain,
% 0.12/0.46 (^[E: $i] : rewrite(((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E)))))))) <=> ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E)))))))))),
% 0.12/0.46 inference(bind,[status(th)],[])).
% 0.12/0.46 tff(271,plain,
% 0.12/0.46 (![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))),
% 0.12/0.46 inference(quant_intro,[status(thm)],[270])).
% 0.12/0.46 tff(272,plain,
% 0.12/0.46 (![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))),
% 0.12/0.46 inference(transitivity,[status(thm)],[271, 269])).
% 0.12/0.46 tff(273,plain,
% 0.12/0.46 (^[E: $i] : rewrite(((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E)))))))))),
% 0.12/0.46 inference(bind,[status(th)],[])).
% 0.12/0.46 tff(274,plain,
% 0.12/0.46 (![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))),
% 0.12/0.46 inference(quant_intro,[status(thm)],[273])).
% 0.12/0.46 tff(275,plain,
% 0.12/0.46 (![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.12/0.46 inference(rewrite,[status(thm)],[])).
% 0.12/0.46 tff(276,plain,
% 0.12/0.46 (^[E: $i] : trans(monotonicity(rewrite(((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), ((((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E))) <=> (((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E))))), rewrite((((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E))) <=> ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), ((((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E))) <=> ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(277,plain,
% 0.23/0.46 (![E: $i] : (((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E))) <=> ![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[276])).
% 0.23/0.46 tff(278,plain,
% 0.23/0.46 (![E: $i, Tc: $i] : (((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E))) <=> ![E: $i] : (((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E)))),
% 0.23/0.46 inference(elim_unused_vars,[status(thm)],[])).
% 0.23/0.46 tff(279,plain,
% 0.23/0.46 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i, Tc: $i] : (((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E)))),
% 0.23/0.46 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.23/0.46 tff(280,plain,
% 0.23/0.46 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : (((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (~environment(E)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[279, 278])).
% 0.23/0.46 tff(281,plain,
% 0.23/0.46 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[280, 277])).
% 0.23/0.46 tff(282,plain,
% 0.23/0.46 (^[E: $i, Tc: $i] : trans(monotonicity(rewrite(((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), (((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))), rewrite(((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(283,plain,
% 0.23/0.46 (![E: $i, Tc: $i] : ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[282])).
% 0.23/0.46 tff(284,plain,
% 0.23/0.46 (![E: $i, Tc: $i] : ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[283, 281])).
% 0.23/0.46 tff(285,axiom,(![E: $i, Tc: $i] : ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1')).
% 0.23/0.46 tff(286,plain,
% 0.23/0.46 (![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.23/0.46 tff(287,plain,
% 0.23/0.46 (![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[286, 275])).
% 0.23/0.46 tff(288,plain,(
% 0.23/0.46 ![E: $i] : ((~environment(E)) | ((~greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E)))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, critical_point(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.23/0.46 inference(skolemize,[status(sab)],[287])).
% 0.23/0.46 tff(289,plain,
% 0.23/0.46 (![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[288, 274])).
% 0.23/0.46 tff(290,plain,
% 0.23/0.46 (![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[289, 272])).
% 0.23/0.46 tff(291,plain,
% 0.23/0.46 (((~![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))) | ((~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))) <=> ((~![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))) | (~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(292,plain,
% 0.23/0.46 (((~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1)))))))) <=> ((~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(293,plain,
% 0.23/0.46 (((~![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))) | ((~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))) | ((~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[292])).
% 0.23/0.46 tff(294,plain,
% 0.23/0.46 (((~![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))) | ((~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))) | (~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[293, 291])).
% 0.23/0.47 tff(295,plain,
% 0.23/0.47 ((~![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))) | ((~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(296,plain,
% 0.23/0.47 ((~![E: $i] : ((~environment(E)) | (~(greater(growth_rate(efficient_producers, critical_point(E)), growth_rate(first_movers, critical_point(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, critical_point(E))))))))) | (~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.23/0.47 tff(297,plain,
% 0.23/0.47 (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[296, 290, 37])).
% 0.23/0.47 tff(298,plain,
% 0.23/0.47 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))) | (~greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(299,plain,
% 0.23/0.47 (~greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[298, 297])).
% 0.23/0.47 tff(300,plain,
% 0.23/0.47 ((~(greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) <=> greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))) | (~greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(301,plain,
% 0.23/0.47 ((~(greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) <=> greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))) | (~greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[300, 299])).
% 0.23/0.47 tff(302,plain,
% 0.23/0.47 (~greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[301, 267])).
% 0.23/0.47 tff(303,plain,
% 0.23/0.47 (^[E: $i, T: $i] : refl((greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(304,plain,
% 0.23/0.47 (![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[303])).
% 0.23/0.47 tff(305,plain,
% 0.23/0.47 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(306,plain,
% 0.23/0.47 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[305])).
% 0.23/0.47 tff(307,plain,
% 0.23/0.47 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(308,plain,
% 0.23/0.47 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(309,plain,
% 0.23/0.47 (![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[308])).
% 0.23/0.47 tff(310,axiom,(![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_relationship_of_growth_rates')).
% 0.23/0.47 tff(311,plain,
% 0.23/0.47 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.23/0.47 tff(312,plain,
% 0.23/0.47 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[311, 307])).
% 0.23/0.47 tff(313,plain,(
% 0.23/0.47 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.23/0.47 inference(skolemize,[status(sab)],[312])).
% 0.23/0.47 tff(314,plain,
% 0.23/0.47 (![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[313, 306])).
% 0.23/0.47 tff(315,plain,
% 0.23/0.47 (![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[314, 304])).
% 0.23/0.47 tff(316,plain,
% 0.23/0.47 (((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))) <=> ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(317,plain,
% 0.23/0.47 ((greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)))) <=> ((~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(318,plain,
% 0.23/0.47 (((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[317])).
% 0.23/0.47 tff(319,plain,
% 0.23/0.47 (((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[318, 316])).
% 0.23/0.48 tff(320,plain,
% 0.23/0.48 ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(321,plain,
% 0.23/0.48 ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.23/0.48 tff(322,plain,
% 0.23/0.48 (greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[321, 315, 37, 77])).
% 0.23/0.48 tff(323,plain,
% 0.23/0.48 (greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[322, 302])).
% 0.23/0.48 tff(324,plain,
% 0.23/0.48 (^[E: $i, T: $i, To: $i] : refl((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(325,plain,
% 0.23/0.48 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))) <=> ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[324])).
% 0.23/0.48 tff(326,plain,
% 0.23/0.48 (^[E: $i, T: $i, To: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)) <=> (~((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))), ((~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))) <=> (~(~((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))) <=> ((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))), ((~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))) <=> ((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))), ((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | ((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))))), rewrite((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | ((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))), ((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(327,plain,
% 0.23/0.48 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))) <=> ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[326])).
% 0.23/0.48 tff(328,plain,
% 0.23/0.48 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))) <=> ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(329,plain,
% 0.23/0.48 (^[E: $i, T: $i, To: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero))), ((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) <=> ((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))))), rewrite(((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)))), ((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E))))), (((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) <=> ((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)))), rewrite(((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))), (((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))), rewrite((decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ((~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))), ((((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) => (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))) <=> ((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)) => ((~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))))), rewrite(((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)) => ((~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))), ((((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) => (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(330,plain,
% 0.23/0.48 (![E: $i, T: $i, To: $i] : (((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) => (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))) <=> ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[329])).
% 0.23/0.48 tff(331,axiom,(![E: $i, T: $i, To: $i] : (((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) => (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_decreasing_function')).
% 0.23/0.48 tff(332,plain,
% 0.23/0.48 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.23/0.48 tff(333,plain,
% 0.23/0.48 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[332, 328])).
% 0.23/0.48 tff(334,plain,(
% 0.23/0.48 ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.23/0.48 inference(skolemize,[status(sab)],[333])).
% 0.23/0.48 tff(335,plain,
% 0.23/0.48 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[334, 327])).
% 0.23/0.48 tff(336,plain,
% 0.23/0.48 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[335, 325])).
% 0.23/0.49 tff(337,plain,
% 0.23/0.49 (((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))) <=> ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(338,plain,
% 0.23/0.49 ((greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0))) <=> ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(339,plain,
% 0.23/0.49 (((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))) <=> ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[338])).
% 0.23/0.49 tff(340,plain,
% 0.23/0.49 (((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))) <=> ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[339, 337])).
% 0.23/0.49 tff(341,plain,
% 0.23/0.49 ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(342,plain,
% 0.23/0.49 ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.23/0.49 tff(343,plain,
% 0.23/0.49 (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[342, 336, 37, 36, 141, 134])).
% 0.23/0.49 tff(344,plain,
% 0.23/0.49 (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[343, 323])).
% 0.23/0.49 tff(345,plain,
% 0.23/0.49 (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[344, 258])).
% 0.23/0.49 tff(346,assumption,(~(greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) <=> greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))), introduced(assumption)).
% 0.23/0.49 tff(347,plain,
% 0.23/0.49 (^[T: $i] : refl((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(348,plain,
% 0.23/0.49 (![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> ![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[347])).
% 0.23/0.49 tff(349,plain,
% 0.23/0.49 (![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> ![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(350,axiom,(![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_positive_growth_rate_difference')).
% 0.23/0.50 tff(351,plain,
% 0.23/0.50 (![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.23/0.50 tff(352,plain,(
% 0.23/0.50 ![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.23/0.50 inference(skolemize,[status(sab)],[351])).
% 0.23/0.50 tff(353,plain,
% 0.23/0.50 (![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[352, 348])).
% 0.23/0.50 tff(354,plain,
% 0.23/0.50 ((~![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) <=> greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(355,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[354, 353, 346])).
% 0.23/0.50 tff(356,plain,(greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) <=> greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(357,plain,
% 0.23/0.50 ((~(greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) <=> greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero)) | greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(358,plain,
% 0.23/0.50 ((~greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero)) | greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[357, 356])).
% 0.23/0.50 tff(359,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[358, 345, 201])).
% 0.23/0.50 % SZS output end Proof
% 0.23/0.50 % E exiting
%------------------------------------------------------------------------------