%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT026+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n020.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 06:24:00 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n020.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 7 12:13:00 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(greater_type, type, (
% 0.14/0.41 greater: ( $i * $i ) > $o)).
% 0.14/0.41 tff(growth_rate_type, type, (
% 0.14/0.41 growth_rate: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_T_0_type, type, (
% 0.14/0.41 tptp_fun_T_0: $i)).
% 0.14/0.41 tff(first_movers_type, type, (
% 0.14/0.41 first_movers: $i)).
% 0.14/0.41 tff(efficient_producers_type, type, (
% 0.14/0.41 efficient_producers: $i)).
% 0.14/0.41 tff(subpopulations_type, type, (
% 0.14/0.41 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_E_1_type, type, (
% 0.14/0.41 tptp_fun_E_1: $i)).
% 0.14/0.41 tff(zero_type, type, (
% 0.14/0.41 zero: $i)).
% 0.14/0.41 tff(cardinality_at_time_type, type, (
% 0.14/0.41 cardinality_at_time: ( $i * $i ) > $i)).
% 0.14/0.41 tff(greater_or_equal_type, type, (
% 0.14/0.41 greater_or_equal: ( $i * $i ) > $o)).
% 0.14/0.41 tff(appear_type, type, (
% 0.14/0.41 appear: ( $i * $i ) > $i)).
% 0.14/0.41 tff(critical_point_type, type, (
% 0.14/0.41 critical_point: $i > $i)).
% 0.14/0.41 tff(in_environment_type, type, (
% 0.14/0.41 in_environment: ( $i * $i ) > $o)).
% 0.14/0.41 tff(environment_type, type, (
% 0.14/0.41 environment: $i > $o)).
% 0.14/0.41 tff(selection_favors_type, type, (
% 0.14/0.41 selection_favors: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(subpopulation_type, type, (
% 0.14/0.41 subpopulation: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (^[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))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (![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)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (![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)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (^[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))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (![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)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.41 tff(6,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')).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.41 tff(9,plain,(
% 0.14/0.41 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[8])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(T!0, appear(efficient_producers, E!1)) <=> ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (greater_or_equal(T!0, appear(efficient_producers, E!1)) <=> ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.14/0.41 tff(13,assumption,(~greater(T!0, appear(efficient_producers, E!1))), introduced(assumption)).
% 0.14/0.41 tff(14,assumption,(greater(critical_point(E!1), appear(efficient_producers, E!1))), introduced(assumption)).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 ((~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 ((~![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(17,axiom,(~![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l8')).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.14/0.41 tff(22,plain,(
% 0.14/0.41 ~((~(environment(E!1) & in_environment(E!1, T!0) & greater(T!0, critical_point(E!1)))) | selection_favors(efficient_producers, first_movers, T!0))),
% 0.14/0.41 inference(skolemize,[status(sab)],[21])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (environment(E!1) & in_environment(E!1, T!0) & greater(T!0, critical_point(E!1))),
% 0.14/0.41 inference(or_elim,[status(thm)],[22])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (greater(T!0, critical_point(E!1))),
% 0.14/0.41 inference(and_elim,[status(thm)],[23])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(X, Y) & greater(Y, Z)) <=> (~((~greater(X, Y)) | (~greater(Y, Z))))), ((~(greater(X, Y) & greater(Y, Z))) <=> (~(~((~greater(X, Y)) | (~greater(Y, Z))))))), rewrite((~(~((~greater(X, Y)) | (~greater(Y, Z))))) <=> ((~greater(X, Y)) | (~greater(Y, Z)))), ((~(greater(X, Y) & greater(Y, Z))) <=> ((~greater(X, Y)) | (~greater(Y, Z))))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)))), rewrite((((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (^[X: $i, Y: $i, Z: $i] : rewrite(((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.41 tff(31,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_transitivity')).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.14/0.41 tff(34,plain,(
% 0.14/0.41 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.14/0.41 inference(skolemize,[status(sab)],[33])).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(38,plain,
% 0.14/0.42 ((greater(T!0, appear(efficient_producers, E!1)) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1)))) <=> ((~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(39,plain,
% 0.14/0.42 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(T!0, appear(efficient_producers, E!1)) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[38])).
% 0.14/0.42 tff(40,plain,
% 0.14/0.42 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(T!0, appear(efficient_producers, E!1)) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1)))),
% 0.14/0.42 inference(transitivity,[status(thm)],[39, 37])).
% 0.14/0.42 tff(41,plain,
% 0.14/0.42 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(T!0, appear(efficient_producers, E!1)) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(42,plain,
% 0.14/0.42 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.14/0.42 tff(43,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[42, 36, 24, 14, 13])).
% 0.14/0.42 tff(44,plain,((~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(45,plain,
% 0.14/0.42 (~greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[44, 13])).
% 0.14/0.42 tff(46,plain,
% 0.14/0.42 ((~![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))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(47,plain,
% 0.14/0.42 (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)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[46, 10])).
% 0.14/0.42 tff(48,plain,
% 0.14/0.42 (environment(E!1)),
% 0.14/0.42 inference(and_elim,[status(thm)],[23])).
% 0.14/0.42 tff(49,plain,
% 0.14/0.42 (^[E: $i] : refl(((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(50,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.14/0.42 tff(51,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(52,plain,
% 0.14/0.42 (^[E: $i] : rewrite((environment(E) => greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(53,plain,
% 0.14/0.42 (![E: $i] : (environment(E) => greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.14/0.42 tff(54,axiom,(![E: $i] : (environment(E) => greater_or_equal(critical_point(E), appear(efficient_producers, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_critical_point_after_EP')).
% 0.14/0.42 tff(55,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.14/0.42 tff(56,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.14/0.42 tff(57,plain,(
% 0.14/0.42 ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[56])).
% 0.14/0.42 tff(58,plain,
% 0.14/0.42 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.14/0.42 tff(59,plain,
% 0.14/0.42 (((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | ((~environment(E!1)) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))) <=> ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | (~environment(E!1)) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(60,plain,
% 0.14/0.42 ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | ((~environment(E!1)) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(61,plain,
% 0.14/0.42 ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | (~environment(E!1)) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.14/0.42 tff(62,plain,
% 0.14/0.42 (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.14/0.42 tff(63,plain,
% 0.14/0.42 ((~(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))))) | (~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)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(64,plain,
% 0.14/0.42 ((~(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)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.14/0.42 tff(65,plain,
% 0.14/0.42 ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[64, 47])).
% 0.14/0.42 tff(66,plain,
% 0.14/0.42 ((~((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))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(67,plain,
% 0.14/0.42 ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.14/0.42 tff(68,plain,
% 0.14/0.42 (critical_point(E!1) = appear(efficient_producers, E!1)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[67, 45])).
% 0.14/0.42 tff(69,plain,
% 0.14/0.42 (greater(T!0, critical_point(E!1)) <=> greater(T!0, appear(efficient_producers, E!1))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.14/0.42 tff(70,plain,
% 0.14/0.42 (greater(T!0, appear(efficient_producers, E!1)) <=> greater(T!0, critical_point(E!1))),
% 0.14/0.42 inference(symmetry,[status(thm)],[69])).
% 0.14/0.42 tff(71,plain,
% 0.14/0.42 ((~greater(T!0, appear(efficient_producers, E!1))) <=> (~greater(T!0, critical_point(E!1)))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[70])).
% 0.14/0.42 tff(72,plain,
% 0.14/0.42 (~greater(T!0, critical_point(E!1))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[13, 71])).
% 0.14/0.42 tff(73,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[24, 72])).
% 0.14/0.42 tff(74,plain,(greater(T!0, appear(efficient_producers, E!1))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(75,plain,
% 0.14/0.42 (((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))) | (~greater(T!0, appear(efficient_producers, E!1)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(76,plain,
% 0.14/0.42 ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.14/0.42 tff(77,plain,
% 0.14/0.42 ((~(greater_or_equal(T!0, appear(efficient_producers, E!1)) <=> ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))))) | greater_or_equal(T!0, appear(efficient_producers, E!1)) | (~((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(78,plain,
% 0.14/0.42 ((~(greater_or_equal(T!0, appear(efficient_producers, E!1)) <=> ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))))) | greater_or_equal(T!0, appear(efficient_producers, E!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.14/0.42 tff(79,plain,
% 0.14/0.42 (greater_or_equal(T!0, appear(efficient_producers, E!1))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[78, 12])).
% 0.14/0.42 tff(80,plain,
% 0.14/0.42 (in_environment(E!1, T!0)),
% 0.14/0.42 inference(and_elim,[status(thm)],[23])).
% 0.14/0.42 tff(81,plain,
% 0.14/0.42 (^[E: $i, T: $i] : refl((greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(82,plain,
% 0.14/0.42 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) <=> ![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.14/0.42 tff(83,plain,
% 0.14/0.42 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(84,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.14/0.42 tff(85,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(86,plain,
% 0.14/0.42 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(87,plain,
% 0.14/0.42 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.14/0.42 tff(88,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6')).
% 0.14/0.42 tff(89,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.14/0.42 tff(90,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.14/0.42 tff(91,plain,(
% 0.14/0.42 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.14/0.42 inference(skolemize,[status(sab)],[90])).
% 0.14/0.42 tff(92,plain,
% 0.14/0.42 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.14/0.42 tff(93,plain,
% 0.14/0.42 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.14/0.42 tff(94,plain,
% 0.14/0.42 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (greater(cardinality_at_time(efficient_producers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))))) <=> ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | greater(cardinality_at_time(efficient_producers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(95,plain,
% 0.14/0.42 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (greater(cardinality_at_time(efficient_producers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(96,plain,
% 0.14/0.42 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | greater(cardinality_at_time(efficient_producers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.14/0.42 tff(97,plain,
% 0.14/0.42 (greater(cardinality_at_time(efficient_producers, T!0), zero) | (~greater_or_equal(T!0, appear(efficient_producers, E!1)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[96, 93, 48, 80])).
% 0.14/0.42 tff(98,plain,
% 0.14/0.42 (greater(cardinality_at_time(efficient_producers, T!0), zero)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[97, 79])).
% 0.14/0.42 tff(99,plain,
% 0.14/0.42 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(100,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.14/0.42 tff(101,plain,
% 0.14/0.42 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), rewrite((subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)) <=> (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))), (((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> (((~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))))), rewrite((((~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))), (((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(102,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[101])).
% 0.14/0.42 tff(103,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(104,plain,
% 0.14/0.42 (^[E: $i, T: $i] : rewrite(((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(105,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.14/0.42 tff(106,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_subpopulations')).
% 0.14/0.42 tff(107,plain,
% 0.14/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.14/0.43 tff(108,plain,
% 0.14/0.43 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.14/0.43 tff(109,plain,(
% 0.14/0.43 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.14/0.43 inference(skolemize,[status(sab)],[108])).
% 0.14/0.43 tff(110,plain,
% 0.14/0.43 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.14/0.43 tff(111,plain,
% 0.14/0.43 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.14/0.43 tff(112,plain,
% 0.14/0.43 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(113,plain,
% 0.14/0.43 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(114,plain,
% 0.14/0.43 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.14/0.43 tff(115,plain,
% 0.14/0.43 (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[114, 111, 48, 80])).
% 0.14/0.43 tff(116,plain,
% 0.14/0.43 (((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))) | subpopulation(efficient_producers, E!1, T!0)),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(117,plain,
% 0.14/0.43 (subpopulation(efficient_producers, E!1, T!0)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.14/0.43 tff(118,plain,
% 0.14/0.43 (((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))) | subpopulation(first_movers, E!1, T!0)),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(119,plain,
% 0.14/0.43 (subpopulation(first_movers, E!1, T!0)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.14/0.43 tff(120,plain,
% 0.14/0.43 (~selection_favors(efficient_producers, first_movers, T!0)),
% 0.14/0.43 inference(or_elim,[status(thm)],[22])).
% 0.14/0.43 tff(121,plain,
% 0.14/0.43 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))) <=> (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(122,plain,
% 0.14/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[121])).
% 0.14/0.43 tff(123,plain,
% 0.14/0.43 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero)) <=> (~((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))), ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) <=> (~(~((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))))), rewrite((~(~((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))) <=> ((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))), ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) <=> ((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))), (((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> (((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)))), rewrite((((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))), (((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(124,plain,
% 0.14/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[123])).
% 0.14/0.43 tff(125,plain,
% 0.14/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(126,plain,
% 0.14/0.43 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T))), ((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) <=> ((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)))), rewrite(((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero))), ((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero)))), (((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) <=> ((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)))), rewrite(((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))), (((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero)))), ((((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)) <=> ((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)))), rewrite(((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)) <=> ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))), ((((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)) <=> ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(127,plain,
% 0.14/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : (((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[126])).
% 0.14/0.43 tff(128,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp2_favour_members')).
% 0.14/0.43 tff(129,plain,
% 0.14/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.14/0.43 tff(130,plain,
% 0.14/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.14/0.43 tff(131,plain,(
% 0.14/0.43 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.14/0.43 inference(skolemize,[status(sab)],[130])).
% 0.14/0.43 tff(132,plain,
% 0.14/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.14/0.43 tff(133,plain,
% 0.14/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[132, 122])).
% 0.14/0.43 tff(134,plain,
% 0.14/0.43 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(135,plain,
% 0.14/0.43 ((selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero))) <=> (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(136,plain,
% 0.14/0.43 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[135])).
% 0.14/0.43 tff(137,plain,
% 0.14/0.43 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))),
% 0.14/0.43 inference(transitivity,[status(thm)],[136, 134])).
% 0.14/0.43 tff(138,plain,
% 0.14/0.43 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(139,plain,
% 0.14/0.43 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.14/0.43 tff(140,plain,
% 0.14/0.43 ((~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[139, 133, 48, 120, 119, 117])).
% 0.14/0.43 tff(141,plain,
% 0.14/0.43 (~(cardinality_at_time(first_movers, T!0) = zero)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[140, 98])).
% 0.14/0.43 tff(142,plain,
% 0.14/0.43 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) <=> ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(143,plain,
% 0.14/0.43 (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) <=> ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[142, 10])).
% 0.14/0.43 tff(144,plain,
% 0.14/0.43 (^[E: $i, T: $i] : refl((greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T))) <=> (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(145,plain,
% 0.14/0.43 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T))) <=> ![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[144])).
% 0.14/0.43 tff(146,plain,
% 0.14/0.43 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), (((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> (((~environment(E)) | (~in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)))), rewrite((((~environment(E)) | (~in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))), (((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(147,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> ![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.14/0.44 tff(148,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(149,plain,
% 0.14/0.44 (^[E: $i, T: $i] : rewrite(((environment(E) & in_environment(E, T)) => greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(150,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[149])).
% 0.14/0.44 tff(151,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(cardinality_at_time(first_movers, T), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_first_movers_exist')).
% 0.14/0.44 tff(152,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.14/0.44 tff(153,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.14/0.44 tff(154,plain,(
% 0.14/0.44 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.14/0.44 inference(skolemize,[status(sab)],[153])).
% 0.14/0.44 tff(155,plain,
% 0.14/0.44 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.14/0.44 tff(156,plain,
% 0.14/0.44 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[155, 145])).
% 0.14/0.44 tff(157,plain,
% 0.14/0.44 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(158,plain,
% 0.14/0.44 ((greater_or_equal(cardinality_at_time(first_movers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0))) <=> ((~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(159,plain,
% 0.14/0.44 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero)))),
% 0.14/0.44 inference(monotonicity,[status(thm)],[158])).
% 0.14/0.44 tff(160,plain,
% 0.14/0.44 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero))),
% 0.14/0.44 inference(transitivity,[status(thm)],[159, 157])).
% 0.14/0.44 tff(161,plain,
% 0.14/0.44 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(162,plain,
% 0.14/0.44 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero)),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.14/0.44 tff(163,plain,
% 0.14/0.44 (greater_or_equal(cardinality_at_time(first_movers, T!0), zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[162, 156, 48, 80])).
% 0.14/0.44 tff(164,plain,
% 0.14/0.44 ((~(greater_or_equal(cardinality_at_time(first_movers, T!0), zero) <=> ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)))) | (~greater_or_equal(cardinality_at_time(first_movers, T!0), zero)) | ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero))),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(165,plain,
% 0.14/0.44 ((~(greater_or_equal(cardinality_at_time(first_movers, T!0), zero) <=> ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)))) | ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero))),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.14/0.44 tff(166,plain,
% 0.14/0.44 ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[165, 143])).
% 0.14/0.44 tff(167,plain,
% 0.14/0.44 ((~((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero))) | (cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.14/0.44 inference(tautology,[status(thm)],[])).
% 0.14/0.44 tff(168,plain,
% 0.14/0.44 ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.14/0.44 tff(169,plain,
% 0.14/0.44 (greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[168, 141])).
% 0.14/0.44 tff(170,plain,
% 0.14/0.44 (^[E: $i, T: $i] : refl((subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(171,plain,
% 0.14/0.44 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[170])).
% 0.14/0.44 tff(172,plain,
% 0.14/0.44 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))), ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))), ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))), (((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))), (((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(173,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[172])).
% 0.14/0.44 tff(174,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(175,plain,
% 0.14/0.44 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))), (((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)))), rewrite(((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))), (((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(176,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[175])).
% 0.14/0.44 tff(177,axiom,(![E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_non_empty_fm_and_ep')).
% 0.14/0.44 tff(178,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.14/0.44 tff(179,plain,
% 0.14/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.14/0.44 tff(180,plain,(
% 0.14/0.44 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.14/0.44 inference(skolemize,[status(sab)],[179])).
% 0.14/0.44 tff(181,plain,
% 0.14/0.44 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.14/0.44 tff(182,plain,
% 0.14/0.44 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.14/0.44 inference(modus_ponens,[status(thm)],[181, 171])).
% 0.14/0.44 tff(183,plain,
% 0.14/0.44 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(184,plain,
% 0.14/0.44 ((subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) <=> ((~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.14/0.44 inference(rewrite,[status(thm)],[])).
% 0.14/0.44 tff(185,plain,
% 0.14/0.44 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))))),
% 0.14/0.45 inference(monotonicity,[status(thm)],[184])).
% 0.14/0.45 tff(186,plain,
% 0.14/0.45 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.14/0.45 inference(transitivity,[status(thm)],[185, 183])).
% 0.14/0.45 tff(187,plain,
% 0.14/0.45 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.14/0.45 inference(quant_inst,[status(thm)],[])).
% 0.14/0.45 tff(188,plain,
% 0.14/0.45 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.14/0.45 tff(189,plain,
% 0.14/0.45 (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[188, 182, 48, 80])).
% 0.14/0.45 tff(190,plain,
% 0.14/0.45 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.14/0.45 inference(unit_resolution,[status(thm)],[189, 169, 98])).
% 0.14/0.45 tff(191,plain,
% 0.14/0.45 (^[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)))))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(192,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[191])).
% 0.14/0.45 tff(193,plain,
% 0.14/0.45 (^[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)))))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(194,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[193])).
% 0.14/0.45 tff(195,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(transitivity,[status(thm)],[194, 192])).
% 0.14/0.45 tff(196,plain,
% 0.14/0.45 (^[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)))))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(197,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[196])).
% 0.14/0.45 tff(198,plain,
% 0.14/0.45 (![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)))))),
% 0.14/0.45 inference(rewrite,[status(thm)],[])).
% 0.14/0.45 tff(199,plain,
% 0.14/0.45 (^[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)))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(200,plain,
% 0.14/0.45 (![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)))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[199])).
% 0.14/0.45 tff(201,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.14/0.45 tff(202,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.14/0.45 tff(203,plain,
% 0.14/0.45 (![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)))),
% 0.14/0.45 inference(transitivity,[status(thm)],[202, 201])).
% 0.14/0.45 tff(204,plain,
% 0.14/0.45 (![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)))))),
% 0.14/0.45 inference(transitivity,[status(thm)],[203, 200])).
% 0.14/0.45 tff(205,plain,
% 0.14/0.45 (^[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)))))))),
% 0.14/0.45 inference(bind,[status(th)],[])).
% 0.14/0.45 tff(206,plain,
% 0.14/0.45 (![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)))))),
% 0.14/0.45 inference(quant_intro,[status(thm)],[205])).
% 0.14/0.45 tff(207,plain,
% 0.14/0.45 (![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)))))),
% 0.14/0.45 inference(transitivity,[status(thm)],[206, 204])).
% 0.14/0.45 tff(208,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')).
% 0.14/0.45 tff(209,plain,
% 0.14/0.45 (![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)))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.14/0.45 tff(210,plain,
% 0.14/0.45 (![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)))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[209, 198])).
% 0.14/0.45 tff(211,plain,(
% 0.14/0.45 ![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)))))),
% 0.14/0.45 inference(skolemize,[status(sab)],[210])).
% 0.14/0.45 tff(212,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[211, 197])).
% 0.14/0.45 tff(213,plain,
% 0.14/0.45 (![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))))))))),
% 0.14/0.45 inference(modus_ponens,[status(thm)],[212, 195])).
% 0.14/0.45 tff(214,plain,
% 0.14/0.45 (((~![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))))))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(215,plain,
% 0.14/0.46 (((~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))))))),
% 0.14/0.46 inference(rewrite,[status(thm)],[])).
% 0.14/0.46 tff(216,plain,
% 0.14/0.46 (((~![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)))))))),
% 0.14/0.46 inference(monotonicity,[status(thm)],[215])).
% 0.14/0.46 tff(217,plain,
% 0.14/0.46 (((~![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))))))),
% 0.14/0.46 inference(transitivity,[status(thm)],[216, 214])).
% 0.14/0.46 tff(218,plain,
% 0.14/0.46 ((~![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))))))))),
% 0.14/0.46 inference(quant_inst,[status(thm)],[])).
% 0.14/0.46 tff(219,plain,
% 0.14/0.46 ((~![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)))))),
% 0.14/0.46 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.14/0.46 tff(220,plain,
% 0.14/0.46 (~((~![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))))),
% 0.14/0.46 inference(unit_resolution,[status(thm)],[219, 213, 48])).
% 0.14/0.46 tff(221,plain,
% 0.14/0.46 (((~![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)))) | ![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))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(222,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.22/0.46 tff(223,plain,
% 0.22/0.46 (((~![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(T!0, critical_point(E!1))) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![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(T!0, critical_point(E!1))) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(224,plain,
% 0.22/0.46 ((greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(T!0, critical_point(E!1)))) <=> ((~greater(T!0, critical_point(E!1))) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(225,plain,
% 0.22/0.46 (((~![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, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(T!0, 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))))) | ((~greater(T!0, critical_point(E!1))) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[224])).
% 0.22/0.46 tff(226,plain,
% 0.22/0.46 (((~![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, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(T!0, 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))))) | (~greater(T!0, critical_point(E!1))) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[225, 223])).
% 0.22/0.46 tff(227,plain,
% 0.22/0.46 ((~![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, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(T!0, critical_point(E!1))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(228,plain,
% 0.22/0.46 ((~![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(T!0, critical_point(E!1))) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.22/0.46 tff(229,plain,
% 0.22/0.46 (greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[228, 24, 222])).
% 0.22/0.46 tff(230,plain,
% 0.22/0.46 (greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[229, 190])).
% 0.22/0.46 tff(231,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(232,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[231])).
% 0.22/0.46 tff(233,plain,
% 0.22/0.46 (^[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))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(234,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[233])).
% 0.22/0.46 tff(235,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(236,plain,
% 0.22/0.46 (^[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))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(237,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[236])).
% 0.22/0.46 tff(238,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')).
% 0.22/0.46 tff(239,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.22/0.46 tff(240,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[239, 235])).
% 0.22/0.46 tff(241,plain,(
% 0.22/0.46 ![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))),
% 0.22/0.46 inference(skolemize,[status(sab)],[240])).
% 0.22/0.46 tff(242,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[241, 234])).
% 0.22/0.46 tff(243,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[242, 232])).
% 0.22/0.46 tff(244,plain,
% 0.22/0.46 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, 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(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(245,plain,
% 0.22/0.46 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(246,plain,
% 0.22/0.47 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.22/0.47 tff(247,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[246, 243, 48, 120, 190, 230])).
% 0.22/0.47 % SZS output end Proof
% 0.22/0.47 % E exiting
%------------------------------------------------------------------------------