%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT039+2 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n003.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 06:24:04 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT039+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : run_E %s %d THM
% 0.14/0.38 % Computer : n003.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 7 12:57:40 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.17/0.48 % SZS status Theorem
% 0.17/0.48 % SZS output start Proof
% 0.17/0.48 tff(greater_type, type, (
% 0.17/0.48 greater: ( $i * $i ) > $o)).
% 0.17/0.48 tff(growth_rate_type, type, (
% 0.17/0.48 growth_rate: ( $i * $i ) > $i)).
% 0.17/0.48 tff(end_time_type, type, (
% 0.17/0.48 end_time: $i > $i)).
% 0.17/0.48 tff(tptp_fun_E_0_type, type, (
% 0.17/0.48 tptp_fun_E_0: $i > $i)).
% 0.17/0.48 tff(tptp_fun_P_2_type, type, (
% 0.17/0.48 tptp_fun_P_2: $i)).
% 0.17/0.48 tff(first_movers_type, type, (
% 0.17/0.48 first_movers: $i)).
% 0.17/0.48 tff(efficient_producers_type, type, (
% 0.17/0.48 efficient_producers: $i)).
% 0.17/0.48 tff(subpopulations_type, type, (
% 0.17/0.48 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.17/0.48 tff(zero_type, type, (
% 0.17/0.48 zero: $i)).
% 0.17/0.48 tff(cardinality_at_time_type, type, (
% 0.17/0.48 cardinality_at_time: ( $i * $i ) > $i)).
% 0.17/0.48 tff(greater_or_equal_type, type, (
% 0.17/0.48 greater_or_equal: ( $i * $i ) > $o)).
% 0.17/0.48 tff(in_environment_type, type, (
% 0.17/0.48 in_environment: ( $i * $i ) > $o)).
% 0.17/0.48 tff(start_time_type, type, (
% 0.17/0.48 start_time: $i > $i)).
% 0.17/0.48 tff(critical_point_type, type, (
% 0.17/0.48 critical_point: $i > $i)).
% 0.17/0.48 tff(tptp_fun_T_1_type, type, (
% 0.17/0.48 tptp_fun_T_1: $i > $i)).
% 0.17/0.48 tff(selection_favors_type, type, (
% 0.17/0.48 selection_favors: ( $i * $i * $i ) > $o)).
% 0.17/0.48 tff(appear_type, type, (
% 0.17/0.48 appear: ( $i * $i ) > $i)).
% 0.17/0.48 tff(environment_type, type, (
% 0.17/0.48 environment: $i > $o)).
% 0.17/0.48 tff(slow_change_type, type, (
% 0.17/0.48 slow_change: $i > $o)).
% 0.17/0.48 tff(observational_period_type, type, (
% 0.17/0.48 observational_period: $i > $o)).
% 0.17/0.48 tff(propagation_strategy_type, type, (
% 0.17/0.48 propagation_strategy: $i > $o)).
% 0.17/0.48 tff(subpopulation_type, type, (
% 0.17/0.48 subpopulation: ( $i * $i * $i ) > $o)).
% 0.17/0.48 tff(1,plain,
% 0.17/0.48 (^[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))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(2,plain,
% 0.17/0.48 (![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)))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.48 tff(3,plain,
% 0.17/0.48 (![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)))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(4,plain,
% 0.17/0.48 (^[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))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(5,plain,
% 0.17/0.48 (![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)))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[4])).
% 0.17/0.48 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')).
% 0.17/0.48 tff(7,plain,
% 0.17/0.48 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.17/0.48 tff(8,plain,
% 0.17/0.48 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.17/0.48 tff(9,plain,(
% 0.17/0.48 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.17/0.48 inference(skolemize,[status(sab)],[8])).
% 0.17/0.48 tff(10,plain,
% 0.17/0.48 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.17/0.48 tff(11,plain,
% 0.17/0.48 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero) <=> ((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)))),
% 0.17/0.48 inference(quant_inst,[status(thm)],[])).
% 0.17/0.48 tff(12,plain,
% 0.17/0.48 (greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero) <=> ((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.17/0.48 tff(13,plain,
% 0.17/0.48 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.17/0.49 inference(quant_inst,[status(thm)],[])).
% 0.17/0.49 tff(14,plain,
% 0.17/0.49 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.17/0.49 tff(15,assumption,(~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.17/0.49 tff(16,plain,
% 0.17/0.49 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~((end_time(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.17/0.49 inference(tautology,[status(thm)],[])).
% 0.17/0.49 tff(17,plain,
% 0.17/0.49 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))) | (~((end_time(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.17/0.49 tff(18,plain,
% 0.17/0.49 (~((end_time(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.17/0.49 tff(19,plain,
% 0.17/0.49 (((end_time(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.17/0.49 inference(tautology,[status(thm)],[])).
% 0.17/0.49 tff(20,plain,
% 0.17/0.49 (~greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.17/0.49 tff(21,assumption,(~greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.17/0.49 tff(22,assumption,(end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))), introduced(assumption)).
% 0.17/0.49 tff(23,plain,
% 0.17/0.49 (selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) <=> selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.17/0.49 inference(monotonicity,[status(thm)],[22])).
% 0.17/0.49 tff(24,plain,
% 0.17/0.49 (selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) <=> selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2)))),
% 0.17/0.49 inference(symmetry,[status(thm)],[23])).
% 0.17/0.49 tff(25,plain,
% 0.17/0.49 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((tptp_fun_T_1(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.17/0.49 inference(quant_inst,[status(thm)],[])).
% 0.17/0.49 tff(26,plain,
% 0.17/0.49 (greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((tptp_fun_T_1(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[25, 10])).
% 0.17/0.49 tff(27,assumption,(~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.17/0.49 tff(28,assumption,(critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))), introduced(assumption)).
% 0.17/0.49 tff(29,plain,
% 0.17/0.49 (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.17/0.49 inference(monotonicity,[status(thm)],[28])).
% 0.17/0.49 tff(30,plain,
% 0.17/0.49 (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.17/0.49 inference(symmetry,[status(thm)],[29])).
% 0.17/0.49 tff(31,plain,
% 0.17/0.49 ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) <=> (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.17/0.49 inference(monotonicity,[status(thm)],[30])).
% 0.17/0.49 tff(32,plain,
% 0.17/0.49 (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[27, 31])).
% 0.17/0.49 tff(33,plain,
% 0.17/0.49 ((~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))) <=> (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P)))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(34,plain,
% 0.17/0.49 ((~![P: $i] : ((observational_period(P) & slow_change(P)) => selection_favors(efficient_producers, first_movers, P))) <=> (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P)))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(35,axiom,(~![P: $i] : ((observational_period(P) & slow_change(P)) => selection_favors(efficient_producers, first_movers, P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t8')).
% 0.17/0.49 tff(36,plain,
% 0.17/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.17/0.49 tff(37,plain,
% 0.17/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.17/0.49 tff(38,plain,
% 0.17/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.17/0.49 tff(39,plain,
% 0.17/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.17/0.49 tff(40,plain,(
% 0.17/0.49 ~((~(observational_period(P!2) & slow_change(P!2))) | selection_favors(efficient_producers, first_movers, P!2))),
% 0.17/0.49 inference(skolemize,[status(sab)],[39])).
% 0.17/0.49 tff(41,plain,
% 0.17/0.49 (observational_period(P!2) & slow_change(P!2)),
% 0.17/0.49 inference(or_elim,[status(thm)],[40])).
% 0.17/0.49 tff(42,plain,
% 0.17/0.49 (slow_change(P!2)),
% 0.17/0.49 inference(and_elim,[status(thm)],[41])).
% 0.17/0.49 tff(43,plain,
% 0.17/0.49 (observational_period(P!2)),
% 0.17/0.49 inference(and_elim,[status(thm)],[41])).
% 0.17/0.49 tff(44,plain,
% 0.17/0.49 (^[P: $i] : refl(((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) <=> ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))))),
% 0.17/0.49 inference(bind,[status(th)],[])).
% 0.17/0.49 tff(45,plain,
% 0.17/0.49 (![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) <=> ![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))),
% 0.17/0.49 inference(quant_intro,[status(thm)],[44])).
% 0.17/0.49 tff(46,plain,
% 0.17/0.49 (^[P: $i] : rewrite(((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) <=> ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))))),
% 0.17/0.49 inference(bind,[status(th)],[])).
% 0.17/0.49 tff(47,plain,
% 0.17/0.49 (![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) <=> ![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))),
% 0.17/0.49 inference(quant_intro,[status(thm)],[46])).
% 0.17/0.49 tff(48,plain,
% 0.17/0.49 (![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) <=> ![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))),
% 0.17/0.49 inference(transitivity,[status(thm)],[47, 45])).
% 0.17/0.49 tff(49,plain,
% 0.17/0.49 (^[P: $i] : trans(monotonicity(trans(monotonicity(rewrite((observational_period(P) & slow_change(P)) <=> (~((~observational_period(P)) | (~slow_change(P))))), ((~(observational_period(P) & slow_change(P))) <=> (~(~((~observational_period(P)) | (~slow_change(P))))))), rewrite((~(~((~observational_period(P)) | (~slow_change(P))))) <=> ((~observational_period(P)) | (~slow_change(P)))), ((~(observational_period(P) & slow_change(P))) <=> ((~observational_period(P)) | (~slow_change(P))))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(P, E)) <=> (~((~environment(E)) | (~in_environment(P, E))))), ((~(environment(E) & in_environment(P, E))) <=> (~(~((~environment(E)) | (~in_environment(P, E))))))), rewrite((~(~((~environment(E)) | (~in_environment(P, E))))) <=> ((~environment(E)) | (~in_environment(P, E)))), ((~(environment(E) & in_environment(P, E))) <=> ((~environment(E)) | (~in_environment(P, E))))), rewrite((in_environment(E, tptp_fun_T_1(E)) & greater(tptp_fun_T_1(E), critical_point(E))) <=> (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))), (((~(environment(E) & in_environment(P, E))) | (in_environment(E, tptp_fun_T_1(E)) & greater(tptp_fun_T_1(E), critical_point(E)))) <=> (((~environment(E)) | (~in_environment(P, E))) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))), rewrite((((~environment(E)) | (~in_environment(P, E))) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))) <=> ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))), (((~(environment(E) & in_environment(P, E))) | (in_environment(E, tptp_fun_T_1(E)) & greater(tptp_fun_T_1(E), critical_point(E)))) <=> ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))))), (![E: $i] : ((~(environment(E) & in_environment(P, E))) | (in_environment(E, tptp_fun_T_1(E)) & greater(tptp_fun_T_1(E), critical_point(E)))) <=> ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))), (((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | (in_environment(E, tptp_fun_T_1(E)) & greater(tptp_fun_T_1(E), critical_point(E))))) <=> (((~observational_period(P)) | (~slow_change(P))) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))))), rewrite((((~observational_period(P)) | (~slow_change(P))) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) <=> ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))), (((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | (in_environment(E, tptp_fun_T_1(E)) & greater(tptp_fun_T_1(E), critical_point(E))))) <=> ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))))),
% 0.17/0.49 inference(bind,[status(th)],[])).
% 0.17/0.49 tff(50,plain,
% 0.17/0.49 (![P: $i] : ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | (in_environment(E, tptp_fun_T_1(E)) & greater(tptp_fun_T_1(E), critical_point(E))))) <=> ![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))),
% 0.17/0.49 inference(quant_intro,[status(thm)],[49])).
% 0.17/0.49 tff(51,plain,
% 0.17/0.49 (![P: $i] : ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E))))) <=> ![P: $i] : ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(52,plain,
% 0.17/0.49 (^[P: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : rewrite(((environment(E) & in_environment(P, E)) => ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))) <=> ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))), (![E: $i] : ((environment(E) & in_environment(P, E)) => ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))) <=> ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))), (((observational_period(P) & slow_change(P)) => ![E: $i] : ((environment(E) & in_environment(P, E)) => ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E))))) <=> ((observational_period(P) & slow_change(P)) => ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E))))))), rewrite(((observational_period(P) & slow_change(P)) => ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E))))) <=> ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))), (((observational_period(P) & slow_change(P)) => ![E: $i] : ((environment(E) & in_environment(P, E)) => ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E))))) <=> ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))))),
% 0.17/0.49 inference(bind,[status(th)],[])).
% 0.17/0.49 tff(53,plain,
% 0.17/0.49 (![P: $i] : ((observational_period(P) & slow_change(P)) => ![E: $i] : ((environment(E) & in_environment(P, E)) => ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E))))) <=> ![P: $i] : ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))),
% 0.17/0.49 inference(quant_intro,[status(thm)],[52])).
% 0.17/0.49 tff(54,axiom,(![P: $i] : ((observational_period(P) & slow_change(P)) => ![E: $i] : ((environment(E) & in_environment(P, E)) => ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp4_critical_point')).
% 0.17/0.49 tff(55,plain,
% 0.17/0.49 (![P: $i] : ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.17/0.50 tff(56,plain,
% 0.17/0.50 (![P: $i] : ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.17/0.50 tff(57,plain,(
% 0.17/0.50 ![P: $i] : ((~(observational_period(P) & slow_change(P))) | ![E: $i] : ((~(environment(E) & in_environment(P, E))) | (in_environment(E, tptp_fun_T_1(E)) & greater(tptp_fun_T_1(E), critical_point(E)))))),
% 0.17/0.50 inference(skolemize,[status(sab)],[56])).
% 0.17/0.50 tff(58,plain,
% 0.17/0.50 (![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.17/0.50 tff(59,plain,
% 0.17/0.50 (![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.17/0.50 tff(60,plain,
% 0.17/0.50 (((~![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))) | ((~observational_period(P!2)) | (~slow_change(P!2)) | ![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))) <=> ((~![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))) | (~observational_period(P!2)) | (~slow_change(P!2)) | ![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))),
% 0.17/0.50 inference(rewrite,[status(thm)],[])).
% 0.17/0.50 tff(61,plain,
% 0.17/0.50 ((~![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))) | ((~observational_period(P!2)) | (~slow_change(P!2)) | ![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))),
% 0.17/0.50 inference(quant_inst,[status(thm)],[])).
% 0.17/0.50 tff(62,plain,
% 0.17/0.50 ((~![P: $i] : ((~observational_period(P)) | (~slow_change(P)) | ![E: $i] : ((~environment(E)) | (~in_environment(P, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E)))))))) | (~observational_period(P!2)) | (~slow_change(P!2)) | ![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.17/0.50 tff(63,plain,
% 0.17/0.50 (![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[62, 59, 43, 42])).
% 0.17/0.50 tff(64,plain,
% 0.17/0.50 (~selection_favors(efficient_producers, first_movers, P!2)),
% 0.17/0.50 inference(or_elim,[status(thm)],[40])).
% 0.17/0.50 tff(65,plain,
% 0.17/0.50 (propagation_strategy(efficient_producers) <=> propagation_strategy(efficient_producers)),
% 0.17/0.50 inference(rewrite,[status(thm)],[])).
% 0.17/0.50 tff(66,axiom,(propagation_strategy(efficient_producers)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_organizational_sets2')).
% 0.17/0.50 tff(67,plain,
% 0.17/0.50 (propagation_strategy(efficient_producers)),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.17/0.50 tff(68,plain,
% 0.17/0.50 (propagation_strategy(first_movers) <=> propagation_strategy(first_movers)),
% 0.17/0.50 inference(rewrite,[status(thm)],[])).
% 0.17/0.50 tff(69,axiom,(propagation_strategy(first_movers)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_organizational_sets1')).
% 0.25/0.50 tff(70,plain,
% 0.25/0.50 (propagation_strategy(first_movers)),
% 0.25/0.50 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.25/0.50 tff(71,plain,
% 0.25/0.50 (^[P: $i] : refl((selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P)))))) <=> (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P)))))))),
% 0.25/0.50 inference(bind,[status(th)],[])).
% 0.25/0.50 tff(72,plain,
% 0.25/0.50 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P)))))) <=> ![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))),
% 0.25/0.50 inference(quant_intro,[status(thm)],[71])).
% 0.25/0.50 tff(73,plain,
% 0.25/0.50 (^[P: $i] : trans(monotonicity(rewrite((~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))))) <=> (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P)))))), ((selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) <=> (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P)))))))), rewrite((selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P)))))) <=> (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))), ((selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) <=> (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))))),
% 0.25/0.50 inference(bind,[status(th)],[])).
% 0.25/0.50 tff(74,plain,
% 0.25/0.50 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) <=> ![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))),
% 0.25/0.50 inference(quant_intro,[status(thm)],[73])).
% 0.25/0.50 tff(75,plain,
% 0.25/0.50 (^[P: $i] : trans(monotonicity(rewrite(((~observational_period(P)) | (~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) <=> ((~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))))))), ((((~observational_period(P)) | (~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) | selection_favors(efficient_producers, first_movers, P)) <=> (((~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) | selection_favors(efficient_producers, first_movers, P)))), rewrite((((~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) | selection_favors(efficient_producers, first_movers, P)) <=> (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))))))), ((((~observational_period(P)) | (~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) | selection_favors(efficient_producers, first_movers, P)) <=> (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))))))))),
% 0.25/0.50 inference(bind,[status(th)],[])).
% 0.25/0.50 tff(76,plain,
% 0.25/0.50 (![P: $i] : (((~observational_period(P)) | (~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) | selection_favors(efficient_producers, first_movers, P)) <=> ![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))))))),
% 0.25/0.50 inference(quant_intro,[status(thm)],[75])).
% 0.25/0.50 tff(77,plain,
% 0.25/0.50 (![P: $i] : ((~(observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P)) <=> ![P: $i] : ((~(observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.25/0.50 inference(rewrite,[status(thm)],[])).
% 0.25/0.50 tff(78,plain,
% 0.25/0.50 (^[P: $i] : trans(monotonicity(trans(monotonicity(rewrite(((observational_period(P) & propagation_strategy(first_movers)) & propagation_strategy(efficient_producers)) <=> (observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers))), quant_intro(proof_bind(^[E: $i] : rewrite(((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E))) <=> ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))), (![E: $i] : ((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E))) <=> ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))), ((((observational_period(P) & propagation_strategy(first_movers)) & propagation_strategy(efficient_producers)) & ![E: $i] : ((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E)))) <=> ((observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers)) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E)))))), rewrite(((observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers)) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E)))) <=> (observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))), ((((observational_period(P) & propagation_strategy(first_movers)) & propagation_strategy(efficient_producers)) & ![E: $i] : ((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E)))) <=> (observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E)))))), (((((observational_period(P) & propagation_strategy(first_movers)) & propagation_strategy(efficient_producers)) & ![E: $i] : ((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E)))) => selection_favors(efficient_producers, first_movers, P)) <=> ((observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E)))) => selection_favors(efficient_producers, first_movers, P)))), rewrite(((observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E)))) => selection_favors(efficient_producers, first_movers, P)) <=> ((~(observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))), (((((observational_period(P) & propagation_strategy(first_movers)) & propagation_strategy(efficient_producers)) & ![E: $i] : ((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E)))) => selection_favors(efficient_producers, first_movers, P)) <=> ((~(observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))))),
% 0.25/0.51 inference(bind,[status(th)],[])).
% 0.25/0.51 tff(79,plain,
% 0.25/0.51 (![P: $i] : ((((observational_period(P) & propagation_strategy(first_movers)) & propagation_strategy(efficient_producers)) & ![E: $i] : ((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E)))) => selection_favors(efficient_producers, first_movers, P)) <=> ![P: $i] : ((~(observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.25/0.51 inference(quant_intro,[status(thm)],[78])).
% 0.25/0.51 tff(80,axiom,(![P: $i] : ((((observational_period(P) & propagation_strategy(first_movers)) & propagation_strategy(efficient_producers)) & ![E: $i] : ((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E)))) => selection_favors(efficient_producers, first_movers, P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp3_favoured_trategy')).
% 0.25/0.51 tff(81,plain,
% 0.25/0.51 (![P: $i] : ((~(observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.25/0.51 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.25/0.51 tff(82,plain,
% 0.25/0.51 (![P: $i] : ((~(observational_period(P) & propagation_strategy(first_movers) & propagation_strategy(efficient_producers) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.25/0.51 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.25/0.51 tff(83,plain,(
% 0.25/0.51 ![P: $i] : (((~observational_period(P)) | (~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P)))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.25/0.51 inference(skolemize,[status(sab)],[82])).
% 0.25/0.51 tff(84,plain,
% 0.25/0.51 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~((~(environment(tptp_fun_E_0(P)) & in_environment(P, tptp_fun_E_0(P)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))))))),
% 0.25/0.51 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.25/0.51 tff(85,plain,
% 0.25/0.51 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))),
% 0.25/0.51 inference(modus_ponens,[status(thm)],[84, 74])).
% 0.25/0.51 tff(86,plain,
% 0.25/0.51 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))),
% 0.25/0.51 inference(modus_ponens,[status(thm)],[85, 72])).
% 0.25/0.51 tff(87,plain,
% 0.25/0.51 (((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))) | ((~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | selection_favors(efficient_producers, first_movers, P!2) | (~observational_period(P!2)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))) <=> ((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))) | (~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | selection_favors(efficient_producers, first_movers, P!2) | (~observational_period(P!2)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))),
% 0.25/0.51 inference(rewrite,[status(thm)],[])).
% 0.25/0.51 tff(88,plain,
% 0.25/0.51 ((selection_favors(efficient_producers, first_movers, P!2) | (~propagation_strategy(first_movers)) | (~observational_period(P!2)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))))) <=> ((~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | selection_favors(efficient_producers, first_movers, P!2) | (~observational_period(P!2)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))),
% 0.25/0.51 inference(rewrite,[status(thm)],[])).
% 0.25/0.51 tff(89,plain,
% 0.25/0.51 ((~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))) <=> (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))))),
% 0.25/0.51 inference(rewrite,[status(thm)],[])).
% 0.25/0.51 tff(90,plain,
% 0.25/0.51 ((selection_favors(efficient_producers, first_movers, P!2) | (~propagation_strategy(first_movers)) | (~observational_period(P!2)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))))) <=> (selection_favors(efficient_producers, first_movers, P!2) | (~propagation_strategy(first_movers)) | (~observational_period(P!2)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))),
% 0.25/0.51 inference(monotonicity,[status(thm)],[89])).
% 0.25/0.51 tff(91,plain,
% 0.25/0.51 ((selection_favors(efficient_producers, first_movers, P!2) | (~propagation_strategy(first_movers)) | (~observational_period(P!2)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))))) <=> ((~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | selection_favors(efficient_producers, first_movers, P!2) | (~observational_period(P!2)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))),
% 0.25/0.51 inference(transitivity,[status(thm)],[90, 88])).
% 0.25/0.51 tff(92,plain,
% 0.25/0.51 (((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))) | (selection_favors(efficient_producers, first_movers, P!2) | (~propagation_strategy(first_movers)) | (~observational_period(P!2)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))) <=> ((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))) | ((~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | selection_favors(efficient_producers, first_movers, P!2) | (~observational_period(P!2)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))))))),
% 0.25/0.51 inference(monotonicity,[status(thm)],[91])).
% 0.25/0.51 tff(93,plain,
% 0.25/0.51 (((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))) | (selection_favors(efficient_producers, first_movers, P!2) | (~propagation_strategy(first_movers)) | (~observational_period(P!2)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))) <=> ((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))) | (~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | selection_favors(efficient_producers, first_movers, P!2) | (~observational_period(P!2)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))),
% 0.25/0.51 inference(transitivity,[status(thm)],[92, 87])).
% 0.25/0.51 tff(94,plain,
% 0.25/0.51 ((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))) | (selection_favors(efficient_producers, first_movers, P!2) | (~propagation_strategy(first_movers)) | (~observational_period(P!2)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))))),
% 0.25/0.51 inference(quant_inst,[status(thm)],[])).
% 0.25/0.51 tff(95,plain,
% 0.25/0.51 ((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~propagation_strategy(first_movers)) | (~observational_period(P)) | (~propagation_strategy(efficient_producers)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P))) | (~environment(tptp_fun_E_0(P))) | (~in_environment(P, tptp_fun_E_0(P))))))) | (~propagation_strategy(first_movers)) | (~propagation_strategy(efficient_producers)) | selection_favors(efficient_producers, first_movers, P!2) | (~observational_period(P!2)) | (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))))),
% 0.25/0.52 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.25/0.52 tff(96,plain,
% 0.25/0.52 (~(selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[95, 86, 70, 67, 43, 64])).
% 0.25/0.52 tff(97,plain,
% 0.25/0.52 ((selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))) | in_environment(P!2, tptp_fun_E_0(P!2))),
% 0.25/0.52 inference(tautology,[status(thm)],[])).
% 0.25/0.52 tff(98,plain,
% 0.25/0.52 (in_environment(P!2, tptp_fun_E_0(P!2))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.25/0.52 tff(99,plain,
% 0.25/0.52 ((selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))) | environment(tptp_fun_E_0(P!2))),
% 0.25/0.52 inference(tautology,[status(thm)],[])).
% 0.25/0.52 tff(100,plain,
% 0.25/0.52 (environment(tptp_fun_E_0(P!2))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.25/0.52 tff(101,plain,
% 0.25/0.52 (((~![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))) | (~((~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))))) <=> ((~![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))) | (~((~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))))),
% 0.25/0.52 inference(rewrite,[status(thm)],[])).
% 0.25/0.52 tff(102,plain,
% 0.25/0.52 ((~![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))) | (~((~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))))),
% 0.25/0.52 inference(quant_inst,[status(thm)],[])).
% 0.25/0.52 tff(103,plain,
% 0.25/0.52 ((~![E: $i] : ((~environment(E)) | (~in_environment(P!2, E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater(tptp_fun_T_1(E), critical_point(E))))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2))) | (~((~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))))),
% 0.25/0.52 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.25/0.52 tff(104,plain,
% 0.25/0.52 (~((~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[103, 100, 98, 63])).
% 0.25/0.52 tff(105,plain,
% 0.25/0.52 (((~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(tautology,[status(thm)],[])).
% 0.25/0.52 tff(106,plain,
% 0.25/0.52 (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.25/0.52 tff(107,plain,
% 0.25/0.52 ($false),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[106, 32])).
% 0.25/0.52 tff(108,plain,((~(critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2)))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.25/0.52 tff(109,plain,
% 0.25/0.52 (~(critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[108, 27])).
% 0.25/0.52 tff(110,plain,
% 0.25/0.52 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.25/0.52 inference(quant_inst,[status(thm)],[])).
% 0.25/0.52 tff(111,plain,
% 0.25/0.52 (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[110, 10])).
% 0.25/0.52 tff(112,plain,
% 0.25/0.52 (^[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))))),
% 0.25/0.52 inference(bind,[status(th)],[])).
% 0.25/0.52 tff(113,plain,
% 0.25/0.52 (![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)))),
% 0.25/0.52 inference(quant_intro,[status(thm)],[112])).
% 0.25/0.52 tff(114,plain,
% 0.25/0.52 (![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)))),
% 0.25/0.52 inference(rewrite,[status(thm)],[])).
% 0.25/0.52 tff(115,plain,
% 0.25/0.52 (^[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))))),
% 0.25/0.52 inference(bind,[status(th)],[])).
% 0.25/0.52 tff(116,plain,
% 0.25/0.52 (![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)))),
% 0.25/0.52 inference(quant_intro,[status(thm)],[115])).
% 0.25/0.52 tff(117,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')).
% 0.25/0.52 tff(118,plain,
% 0.25/0.52 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.25/0.52 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.25/0.52 tff(119,plain,
% 0.25/0.52 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.25/0.52 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.25/0.52 tff(120,plain,(
% 0.25/0.52 ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.25/0.52 inference(skolemize,[status(sab)],[119])).
% 0.25/0.52 tff(121,plain,
% 0.25/0.52 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.25/0.52 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.25/0.52 tff(122,plain,
% 0.25/0.52 (((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))) <=> ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.52 inference(rewrite,[status(thm)],[])).
% 0.25/0.52 tff(123,plain,
% 0.25/0.52 ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.52 inference(quant_inst,[status(thm)],[])).
% 0.25/0.52 tff(124,plain,
% 0.25/0.52 ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.25/0.52 tff(125,plain,
% 0.25/0.52 (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[124, 121, 100])).
% 0.25/0.52 tff(126,plain,
% 0.25/0.52 ((~(greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | ((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.52 inference(tautology,[status(thm)],[])).
% 0.25/0.52 tff(127,plain,
% 0.25/0.52 ((~(greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) | ((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.25/0.52 tff(128,plain,
% 0.25/0.52 ((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[127, 111])).
% 0.25/0.52 tff(129,plain,
% 0.25/0.52 ((~((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))) | (critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(tautology,[status(thm)],[])).
% 0.25/0.52 tff(130,plain,
% 0.25/0.52 ((critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.25/0.52 tff(131,plain,
% 0.25/0.52 (greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.52 inference(unit_resolution,[status(thm)],[130, 109])).
% 0.25/0.52 tff(132,plain,
% 0.25/0.52 (![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)))),
% 0.25/0.52 inference(rewrite,[status(thm)],[])).
% 0.25/0.52 tff(133,plain,
% 0.25/0.52 (^[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)))))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(134,plain,
% 0.25/0.53 (![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)))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[133])).
% 0.25/0.53 tff(135,plain,
% 0.25/0.53 (![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))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(136,plain,
% 0.25/0.53 (^[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)))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(137,plain,
% 0.25/0.53 (![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))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[136])).
% 0.25/0.53 tff(138,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')).
% 0.25/0.53 tff(139,plain,
% 0.25/0.53 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.25/0.53 tff(140,plain,
% 0.25/0.53 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.25/0.53 tff(141,plain,(
% 0.25/0.53 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.25/0.53 inference(skolemize,[status(sab)],[140])).
% 0.25/0.53 tff(142,plain,
% 0.25/0.53 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.25/0.53 tff(143,plain,
% 0.25/0.53 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.25/0.53 tff(144,plain,
% 0.25/0.53 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(145,plain,
% 0.25/0.53 ((greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))) <=> ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(146,plain,
% 0.25/0.53 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.25/0.53 inference(monotonicity,[status(thm)],[145])).
% 0.25/0.53 tff(147,plain,
% 0.25/0.53 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.53 inference(transitivity,[status(thm)],[146, 144])).
% 0.25/0.53 tff(148,plain,
% 0.25/0.53 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.25/0.53 inference(quant_inst,[status(thm)],[])).
% 0.25/0.53 tff(149,plain,
% 0.25/0.53 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.25/0.53 tff(150,plain,
% 0.25/0.53 ($false),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[149, 143, 106, 131, 27])).
% 0.25/0.53 tff(151,plain,(greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.25/0.53 tff(152,plain,
% 0.25/0.53 (((tptp_fun_T_1(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.53 inference(tautology,[status(thm)],[])).
% 0.25/0.53 tff(153,plain,
% 0.25/0.53 ((tptp_fun_T_1(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.25/0.53 tff(154,plain,
% 0.25/0.53 ((~(greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((tptp_fun_T_1(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) | greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~((tptp_fun_T_1(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.25/0.53 inference(tautology,[status(thm)],[])).
% 0.25/0.53 tff(155,plain,
% 0.25/0.53 ((~(greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((tptp_fun_T_1(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) | greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.25/0.53 tff(156,plain,
% 0.25/0.53 (greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[155, 26])).
% 0.25/0.53 tff(157,plain,
% 0.25/0.53 (((~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))) | in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.25/0.53 inference(tautology,[status(thm)],[])).
% 0.25/0.53 tff(158,plain,
% 0.25/0.53 (in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[157, 104])).
% 0.25/0.53 tff(159,plain,
% 0.25/0.53 (^[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)))))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(160,plain,
% 0.25/0.53 (![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))))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[159])).
% 0.25/0.53 tff(161,plain,
% 0.25/0.53 (^[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))))))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(162,plain,
% 0.25/0.53 (![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))))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[161])).
% 0.25/0.53 tff(163,plain,
% 0.25/0.53 (![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))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(164,plain,
% 0.25/0.53 (^[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))))),
% 0.25/0.54 inference(bind,[status(th)],[])).
% 0.25/0.54 tff(165,plain,
% 0.25/0.54 (![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))),
% 0.25/0.54 inference(quant_intro,[status(thm)],[164])).
% 0.25/0.54 tff(166,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')).
% 0.25/0.54 tff(167,plain,
% 0.25/0.54 (![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))),
% 0.25/0.54 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.25/0.54 tff(168,plain,
% 0.25/0.54 (![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))),
% 0.25/0.54 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.25/0.54 tff(169,plain,(
% 0.25/0.54 ![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))),
% 0.25/0.54 inference(skolemize,[status(sab)],[168])).
% 0.25/0.54 tff(170,plain,
% 0.25/0.54 (![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))))),
% 0.25/0.54 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.25/0.54 tff(171,plain,
% 0.25/0.54 (![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))))),
% 0.25/0.54 inference(modus_ponens,[status(thm)],[170, 160])).
% 0.25/0.54 tff(172,plain,
% 0.25/0.54 (((~![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))))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![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))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.25/0.54 inference(rewrite,[status(thm)],[])).
% 0.25/0.54 tff(173,plain,
% 0.25/0.54 ((greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.25/0.54 inference(rewrite,[status(thm)],[])).
% 0.25/0.54 tff(174,plain,
% 0.25/0.54 (((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![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))))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))))),
% 0.25/0.54 inference(monotonicity,[status(thm)],[173])).
% 0.25/0.54 tff(175,plain,
% 0.25/0.54 (((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![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))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.25/0.54 inference(transitivity,[status(thm)],[174, 172])).
% 0.25/0.54 tff(176,plain,
% 0.25/0.54 ((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.25/0.54 inference(quant_inst,[status(thm)],[])).
% 0.25/0.54 tff(177,plain,
% 0.25/0.54 ((~![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))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.54 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.25/0.54 tff(178,plain,
% 0.25/0.54 (greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.25/0.54 inference(unit_resolution,[status(thm)],[177, 171, 100, 158])).
% 0.25/0.54 tff(179,plain,
% 0.25/0.54 (greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.25/0.54 inference(unit_resolution,[status(thm)],[178, 156])).
% 0.25/0.54 tff(180,assumption,(~selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.25/0.54 tff(181,assumption,(greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)), introduced(assumption)).
% 0.25/0.54 tff(182,plain,
% 0.25/0.54 (^[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))))))),
% 0.25/0.54 inference(bind,[status(th)],[])).
% 0.25/0.54 tff(183,plain,
% 0.25/0.54 (![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)))))),
% 0.25/0.54 inference(quant_intro,[status(thm)],[182])).
% 0.25/0.54 tff(184,plain,
% 0.25/0.54 (^[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)))))))),
% 0.25/0.54 inference(bind,[status(th)],[])).
% 0.25/0.54 tff(185,plain,
% 0.25/0.54 (![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)))))),
% 0.25/0.54 inference(quant_intro,[status(thm)],[184])).
% 0.25/0.54 tff(186,plain,
% 0.25/0.54 (![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)))),
% 0.25/0.54 inference(rewrite,[status(thm)],[])).
% 0.25/0.54 tff(187,plain,
% 0.25/0.54 (^[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))))),
% 0.25/0.54 inference(bind,[status(th)],[])).
% 0.25/0.54 tff(188,plain,
% 0.25/0.54 (![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)))),
% 0.25/0.55 inference(quant_intro,[status(thm)],[187])).
% 0.25/0.55 tff(189,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')).
% 0.25/0.55 tff(190,plain,
% 0.25/0.55 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.25/0.55 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.25/0.55 tff(191,plain,
% 0.25/0.55 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.25/0.55 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.25/0.55 tff(192,plain,(
% 0.25/0.55 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.25/0.55 inference(skolemize,[status(sab)],[191])).
% 0.25/0.55 tff(193,plain,
% 0.25/0.55 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.25/0.55 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.25/0.55 tff(194,plain,
% 0.25/0.55 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.25/0.55 inference(modus_ponens,[status(thm)],[193, 183])).
% 0.25/0.55 tff(195,plain,
% 0.25/0.55 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))))),
% 0.25/0.55 inference(rewrite,[status(thm)],[])).
% 0.25/0.55 tff(196,plain,
% 0.25/0.55 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))))),
% 0.25/0.55 inference(quant_inst,[status(thm)],[])).
% 0.25/0.55 tff(197,plain,
% 0.25/0.55 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))))),
% 0.25/0.55 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.25/0.55 tff(198,plain,
% 0.25/0.55 (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.25/0.55 inference(unit_resolution,[status(thm)],[197, 194, 100, 158])).
% 0.25/0.55 tff(199,plain,
% 0.25/0.55 (((~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))) | subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.25/0.55 inference(tautology,[status(thm)],[])).
% 0.25/0.55 tff(200,plain,
% 0.25/0.55 (subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.25/0.55 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.25/0.55 tff(201,plain,
% 0.25/0.55 (((~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))) | subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.25/0.55 inference(tautology,[status(thm)],[])).
% 0.25/0.55 tff(202,plain,
% 0.25/0.55 (subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.25/0.55 inference(unit_resolution,[status(thm)],[201, 198])).
% 0.25/0.55 tff(203,plain,
% 0.25/0.55 (^[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))))),
% 0.25/0.55 inference(bind,[status(th)],[])).
% 0.25/0.55 tff(204,plain,
% 0.25/0.55 (![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)))),
% 0.25/0.55 inference(quant_intro,[status(thm)],[203])).
% 0.25/0.55 tff(205,plain,
% 0.25/0.55 (^[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)))))),
% 0.25/0.55 inference(bind,[status(th)],[])).
% 0.25/0.55 tff(206,plain,
% 0.25/0.55 (![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)))),
% 0.25/0.55 inference(quant_intro,[status(thm)],[205])).
% 0.25/0.55 tff(207,plain,
% 0.25/0.55 (![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))),
% 0.25/0.55 inference(rewrite,[status(thm)],[])).
% 0.25/0.55 tff(208,plain,
% 0.25/0.55 (^[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))))),
% 0.25/0.55 inference(bind,[status(th)],[])).
% 0.25/0.55 tff(209,plain,
% 0.25/0.55 (![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))),
% 0.25/0.55 inference(quant_intro,[status(thm)],[208])).
% 0.25/0.55 tff(210,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')).
% 0.25/0.55 tff(211,plain,
% 0.25/0.55 (![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))),
% 0.25/0.55 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.25/0.55 tff(212,plain,
% 0.25/0.55 (![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))),
% 0.25/0.55 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.25/0.55 tff(213,plain,(
% 0.25/0.55 ![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))),
% 0.25/0.55 inference(skolemize,[status(sab)],[212])).
% 0.25/0.55 tff(214,plain,
% 0.25/0.55 (![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)))),
% 0.25/0.56 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.25/0.56 tff(215,plain,
% 0.25/0.56 (![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)))),
% 0.25/0.56 inference(modus_ponens,[status(thm)],[214, 204])).
% 0.25/0.56 tff(216,plain,
% 0.25/0.56 (((~![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)))) | ((~environment(tptp_fun_E_0(P!2))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))) <=> ((~![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)))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.25/0.56 inference(rewrite,[status(thm)],[])).
% 0.25/0.56 tff(217,plain,
% 0.25/0.56 ((selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero))) <=> ((~environment(tptp_fun_E_0(P!2))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.25/0.56 inference(rewrite,[status(thm)],[])).
% 0.25/0.56 tff(218,plain,
% 0.25/0.56 (((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = 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)))) | ((~environment(tptp_fun_E_0(P!2))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.25/0.56 inference(monotonicity,[status(thm)],[217])).
% 0.25/0.56 tff(219,plain,
% 0.25/0.56 (((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = 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)))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.25/0.56 inference(transitivity,[status(thm)],[218, 216])).
% 0.25/0.56 tff(220,plain,
% 0.25/0.56 ((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)))),
% 0.25/0.56 inference(quant_inst,[status(thm)],[])).
% 0.25/0.56 tff(221,plain,
% 0.25/0.56 ((~![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)))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.25/0.56 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.25/0.56 tff(222,plain,
% 0.25/0.56 ((~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.25/0.56 inference(unit_resolution,[status(thm)],[221, 215, 100, 202, 200])).
% 0.25/0.56 tff(223,plain,
% 0.25/0.56 (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)),
% 0.25/0.56 inference(unit_resolution,[status(thm)],[222, 181, 180])).
% 0.25/0.56 tff(224,assumption,(subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.25/0.56 tff(225,plain,
% 0.25/0.56 (^[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)))))))))),
% 0.25/0.56 inference(bind,[status(th)],[])).
% 0.25/0.56 tff(226,plain,
% 0.25/0.56 (![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))))))))),
% 0.25/0.56 inference(quant_intro,[status(thm)],[225])).
% 0.25/0.56 tff(227,plain,
% 0.25/0.56 (^[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)))))))))),
% 0.25/0.57 inference(bind,[status(th)],[])).
% 0.25/0.57 tff(228,plain,
% 0.25/0.57 (![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))))))))),
% 0.25/0.57 inference(quant_intro,[status(thm)],[227])).
% 0.25/0.57 tff(229,plain,
% 0.25/0.57 (![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))))))))),
% 0.25/0.57 inference(transitivity,[status(thm)],[228, 226])).
% 0.25/0.57 tff(230,plain,
% 0.25/0.57 (^[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)))))))))),
% 0.25/0.57 inference(bind,[status(th)],[])).
% 0.25/0.57 tff(231,plain,
% 0.25/0.57 (![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))))))))),
% 0.25/0.57 inference(quant_intro,[status(thm)],[230])).
% 0.25/0.57 tff(232,plain,
% 0.25/0.57 (![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)))))),
% 0.25/0.57 inference(rewrite,[status(thm)],[])).
% 0.25/0.57 tff(233,plain,
% 0.25/0.57 (^[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)))))))),
% 0.25/0.57 inference(bind,[status(th)],[])).
% 0.25/0.57 tff(234,plain,
% 0.25/0.57 (![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)))))),
% 0.25/0.57 inference(quant_intro,[status(thm)],[233])).
% 0.25/0.57 tff(235,plain,
% 0.25/0.57 (![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)))),
% 0.25/0.57 inference(elim_unused_vars,[status(thm)],[])).
% 0.25/0.57 tff(236,plain,
% 0.25/0.57 (![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)))),
% 0.25/0.57 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.25/0.57 tff(237,plain,
% 0.25/0.57 (![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)))),
% 0.25/0.57 inference(transitivity,[status(thm)],[236, 235])).
% 0.25/0.57 tff(238,plain,
% 0.25/0.57 (![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)))))),
% 0.25/0.57 inference(transitivity,[status(thm)],[237, 234])).
% 0.25/0.57 tff(239,plain,
% 0.25/0.57 (^[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)))))))),
% 0.25/0.58 inference(bind,[status(th)],[])).
% 0.25/0.58 tff(240,plain,
% 0.25/0.58 (![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)))))),
% 0.25/0.58 inference(quant_intro,[status(thm)],[239])).
% 0.25/0.58 tff(241,plain,
% 0.25/0.58 (![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)))))),
% 0.25/0.58 inference(transitivity,[status(thm)],[240, 238])).
% 0.25/0.58 tff(242,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')).
% 0.25/0.58 tff(243,plain,
% 0.25/0.58 (![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)))))),
% 0.25/0.58 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.25/0.58 tff(244,plain,
% 0.25/0.58 (![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)))))),
% 0.25/0.58 inference(modus_ponens,[status(thm)],[243, 232])).
% 0.25/0.58 tff(245,plain,(
% 0.25/0.58 ![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)))))),
% 0.25/0.58 inference(skolemize,[status(sab)],[244])).
% 0.25/0.58 tff(246,plain,
% 0.25/0.58 (![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))))))))),
% 0.25/0.58 inference(modus_ponens,[status(thm)],[245, 231])).
% 0.25/0.58 tff(247,plain,
% 0.25/0.58 (![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))))))))),
% 0.25/0.58 inference(modus_ponens,[status(thm)],[246, 229])).
% 0.25/0.58 tff(248,plain,
% 0.25/0.58 (((~![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(tptp_fun_E_0(P!2))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))))))) <=> ((~![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(tptp_fun_E_0(P!2))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))))))),
% 0.25/0.58 inference(rewrite,[status(thm)],[])).
% 0.25/0.58 tff(249,plain,
% 0.25/0.58 (((~environment(tptp_fun_E_0(P!2))) | (~(greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2))))))))) <=> ((~environment(tptp_fun_E_0(P!2))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))))))),
% 0.25/0.58 inference(rewrite,[status(thm)],[])).
% 0.25/0.58 tff(250,plain,
% 0.25/0.58 (((~![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(tptp_fun_E_0(P!2))) | (~(greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))))))) <=> ((~![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(tptp_fun_E_0(P!2))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2))))))))),
% 0.25/0.58 inference(monotonicity,[status(thm)],[249])).
% 0.25/0.58 tff(251,plain,
% 0.25/0.58 (((~![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(tptp_fun_E_0(P!2))) | (~(greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))))))) <=> ((~![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(tptp_fun_E_0(P!2))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))))))),
% 0.25/0.58 inference(transitivity,[status(thm)],[250, 248])).
% 0.25/0.58 tff(252,plain,
% 0.25/0.58 ((~![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(tptp_fun_E_0(P!2))) | (~(greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))))))),
% 0.25/0.58 inference(quant_inst,[status(thm)],[])).
% 0.25/0.58 tff(253,plain,
% 0.25/0.58 ((~![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(tptp_fun_E_0(P!2))) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2))))))),
% 0.25/0.58 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.25/0.58 tff(254,plain,
% 0.25/0.58 (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2)))))),
% 0.25/0.58 inference(unit_resolution,[status(thm)],[253, 247, 100])).
% 0.25/0.58 tff(255,plain,
% 0.25/0.58 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2))))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))),
% 0.25/0.59 inference(tautology,[status(thm)],[])).
% 0.25/0.59 tff(256,plain,
% 0.25/0.59 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))),
% 0.25/0.59 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.25/0.59 tff(257,plain,
% 0.25/0.59 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.25/0.59 inference(rewrite,[status(thm)],[])).
% 0.25/0.59 tff(258,plain,
% 0.25/0.59 ((greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))) <=> ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.25/0.59 inference(rewrite,[status(thm)],[])).
% 0.25/0.59 tff(259,plain,
% 0.25/0.59 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))))),
% 0.25/0.59 inference(monotonicity,[status(thm)],[258])).
% 0.25/0.59 tff(260,plain,
% 0.25/0.59 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.25/0.59 inference(transitivity,[status(thm)],[259, 257])).
% 0.25/0.59 tff(261,plain,
% 0.25/0.59 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.25/0.59 inference(quant_inst,[status(thm)],[])).
% 0.25/0.59 tff(262,plain,
% 0.25/0.59 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.25/0.59 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.25/0.59 tff(263,plain,
% 0.25/0.59 (greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.25/0.59 inference(unit_resolution,[status(thm)],[262, 106, 256])).
% 0.25/0.59 tff(264,plain,
% 0.25/0.59 (greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.25/0.59 inference(unit_resolution,[status(thm)],[263, 224])).
% 0.25/0.59 tff(265,plain,
% 0.25/0.59 (^[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)))))),
% 0.25/0.59 inference(bind,[status(th)],[])).
% 0.25/0.59 tff(266,plain,
% 0.25/0.59 (![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))))),
% 0.25/0.59 inference(quant_intro,[status(thm)],[265])).
% 0.25/0.59 tff(267,plain,
% 0.25/0.59 (^[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))))))),
% 0.25/0.59 inference(bind,[status(th)],[])).
% 0.25/0.59 tff(268,plain,
% 0.25/0.59 (![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))))),
% 0.25/0.59 inference(quant_intro,[status(thm)],[267])).
% 0.25/0.59 tff(269,plain,
% 0.25/0.59 (![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))),
% 0.25/0.59 inference(rewrite,[status(thm)],[])).
% 0.25/0.59 tff(270,plain,
% 0.25/0.59 (^[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))))),
% 0.25/0.59 inference(bind,[status(th)],[])).
% 0.25/0.59 tff(271,plain,
% 0.25/0.59 (![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))),
% 0.25/0.59 inference(quant_intro,[status(thm)],[270])).
% 0.25/0.59 tff(272,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')).
% 0.25/0.59 tff(273,plain,
% 0.25/0.59 (![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))),
% 0.25/0.59 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.25/0.59 tff(274,plain,
% 0.25/0.59 (![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))),
% 0.25/0.60 inference(modus_ponens,[status(thm)],[273, 269])).
% 0.25/0.60 tff(275,plain,(
% 0.25/0.60 ![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))),
% 0.25/0.60 inference(skolemize,[status(sab)],[274])).
% 0.25/0.60 tff(276,plain,
% 0.25/0.60 (![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))))),
% 0.25/0.60 inference(modus_ponens,[status(thm)],[275, 268])).
% 0.25/0.60 tff(277,plain,
% 0.25/0.60 (![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))))),
% 0.25/0.60 inference(modus_ponens,[status(thm)],[276, 266])).
% 0.25/0.60 tff(278,plain,
% 0.25/0.60 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | ((~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))))),
% 0.25/0.60 inference(rewrite,[status(thm)],[])).
% 0.25/0.60 tff(279,plain,
% 0.25/0.60 ((selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))))) <=> ((~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))))),
% 0.25/0.60 inference(rewrite,[status(thm)],[])).
% 0.25/0.60 tff(280,plain,
% 0.25/0.60 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | ((~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))))))),
% 0.25/0.60 inference(monotonicity,[status(thm)],[279])).
% 0.25/0.60 tff(281,plain,
% 0.25/0.60 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))))),
% 0.35/0.60 inference(transitivity,[status(thm)],[280, 278])).
% 0.35/0.60 tff(282,plain,
% 0.35/0.60 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))))),
% 0.35/0.60 inference(quant_inst,[status(thm)],[])).
% 0.35/0.60 tff(283,plain,
% 0.35/0.60 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.35/0.60 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.35/0.60 tff(284,plain,
% 0.35/0.60 ($false),
% 0.35/0.60 inference(unit_resolution,[status(thm)],[283, 277, 100, 264, 224, 180])).
% 0.35/0.60 tff(285,plain,((~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.60 tff(286,plain,
% 0.35/0.60 (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.35/0.60 inference(unit_resolution,[status(thm)],[285, 180])).
% 0.35/0.60 tff(287,plain,
% 0.35/0.60 (^[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))))),
% 0.35/0.60 inference(bind,[status(th)],[])).
% 0.35/0.60 tff(288,plain,
% 0.35/0.60 (![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)))),
% 0.35/0.60 inference(quant_intro,[status(thm)],[287])).
% 0.35/0.60 tff(289,plain,
% 0.35/0.60 (^[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)))))),
% 0.35/0.60 inference(bind,[status(th)],[])).
% 0.35/0.60 tff(290,plain,
% 0.35/0.60 (![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)))),
% 0.35/0.60 inference(quant_intro,[status(thm)],[289])).
% 0.35/0.60 tff(291,plain,
% 0.35/0.60 (![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))),
% 0.35/0.60 inference(rewrite,[status(thm)],[])).
% 0.35/0.60 tff(292,plain,
% 0.35/0.60 (^[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))))),
% 0.35/0.61 inference(bind,[status(th)],[])).
% 0.35/0.61 tff(293,plain,
% 0.35/0.61 (![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))),
% 0.35/0.61 inference(quant_intro,[status(thm)],[292])).
% 0.35/0.61 tff(294,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_contains_FM_and_EP')).
% 0.35/0.61 tff(295,plain,
% 0.35/0.61 (![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))),
% 0.35/0.61 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.35/0.61 tff(296,plain,
% 0.35/0.61 (![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))),
% 0.35/0.61 inference(modus_ponens,[status(thm)],[295, 291])).
% 0.35/0.61 tff(297,plain,(
% 0.35/0.61 ![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))),
% 0.35/0.61 inference(skolemize,[status(sab)],[296])).
% 0.35/0.61 tff(298,plain,
% 0.35/0.61 (![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)))),
% 0.35/0.61 inference(modus_ponens,[status(thm)],[297, 290])).
% 0.35/0.61 tff(299,plain,
% 0.35/0.61 (![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)))),
% 0.35/0.61 inference(modus_ponens,[status(thm)],[298, 288])).
% 0.35/0.61 tff(300,plain,
% 0.35/0.61 (((~![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(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), 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(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))),
% 0.35/0.61 inference(rewrite,[status(thm)],[])).
% 0.35/0.61 tff(301,plain,
% 0.35/0.61 ((subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))) <=> ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))),
% 0.35/0.61 inference(rewrite,[status(thm)],[])).
% 0.35/0.61 tff(302,plain,
% 0.35/0.61 (((~![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, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), 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(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))))),
% 0.35/0.61 inference(monotonicity,[status(thm)],[301])).
% 0.35/0.61 tff(303,plain,
% 0.35/0.61 (((~![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, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), 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(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))),
% 0.35/0.61 inference(transitivity,[status(thm)],[302, 300])).
% 0.35/0.61 tff(304,plain,
% 0.35/0.61 ((~![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, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))),
% 0.35/0.61 inference(quant_inst,[status(thm)],[])).
% 0.35/0.61 tff(305,plain,
% 0.35/0.61 ((~![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(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.35/0.61 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.35/0.61 tff(306,plain,
% 0.35/0.61 (subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.35/0.61 inference(unit_resolution,[status(thm)],[305, 299, 100, 158])).
% 0.35/0.61 tff(307,plain,
% 0.35/0.61 (~greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.35/0.61 inference(unit_resolution,[status(thm)],[306, 181, 286])).
% 0.35/0.61 tff(308,plain,
% 0.35/0.61 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) <=> ((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))),
% 0.35/0.61 inference(quant_inst,[status(thm)],[])).
% 0.35/0.61 tff(309,plain,
% 0.35/0.61 (greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) <=> ((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[308, 10])).
% 0.35/0.62 tff(310,plain,
% 0.35/0.62 (^[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))))),
% 0.35/0.62 inference(bind,[status(th)],[])).
% 0.35/0.62 tff(311,plain,
% 0.35/0.62 (![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)))),
% 0.35/0.62 inference(quant_intro,[status(thm)],[310])).
% 0.35/0.62 tff(312,plain,
% 0.35/0.62 (^[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)))))),
% 0.35/0.62 inference(bind,[status(th)],[])).
% 0.35/0.62 tff(313,plain,
% 0.35/0.62 (![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)))),
% 0.35/0.62 inference(quant_intro,[status(thm)],[312])).
% 0.35/0.62 tff(314,plain,
% 0.35/0.62 (![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))),
% 0.35/0.62 inference(rewrite,[status(thm)],[])).
% 0.35/0.62 tff(315,plain,
% 0.35/0.62 (^[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)))),
% 0.35/0.62 inference(bind,[status(th)],[])).
% 0.35/0.62 tff(316,plain,
% 0.35/0.62 (![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))),
% 0.35/0.62 inference(quant_intro,[status(thm)],[315])).
% 0.35/0.62 tff(317,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')).
% 0.35/0.62 tff(318,plain,
% 0.35/0.62 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.35/0.62 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.35/0.62 tff(319,plain,
% 0.35/0.62 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.35/0.62 inference(modus_ponens,[status(thm)],[318, 314])).
% 0.35/0.62 tff(320,plain,(
% 0.35/0.62 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.35/0.62 inference(skolemize,[status(sab)],[319])).
% 0.35/0.62 tff(321,plain,
% 0.35/0.62 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.35/0.62 inference(modus_ponens,[status(thm)],[320, 313])).
% 0.35/0.62 tff(322,plain,
% 0.35/0.62 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.35/0.62 inference(modus_ponens,[status(thm)],[321, 311])).
% 0.35/0.62 tff(323,plain,
% 0.35/0.62 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.35/0.62 inference(rewrite,[status(thm)],[])).
% 0.35/0.62 tff(324,plain,
% 0.35/0.62 ((greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.35/0.62 inference(rewrite,[status(thm)],[])).
% 0.35/0.62 tff(325,plain,
% 0.35/0.62 (((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))),
% 0.35/0.62 inference(monotonicity,[status(thm)],[324])).
% 0.35/0.62 tff(326,plain,
% 0.35/0.62 (((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.35/0.62 inference(transitivity,[status(thm)],[325, 323])).
% 0.35/0.62 tff(327,plain,
% 0.35/0.62 ((~![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, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.35/0.62 inference(quant_inst,[status(thm)],[])).
% 0.35/0.62 tff(328,plain,
% 0.35/0.62 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.35/0.62 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.35/0.62 tff(329,plain,
% 0.35/0.62 (greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[328, 322, 100, 158])).
% 0.35/0.62 tff(330,plain,
% 0.35/0.62 ((~(greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) <=> ((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))) | (~greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | ((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.35/0.62 inference(tautology,[status(thm)],[])).
% 0.35/0.62 tff(331,plain,
% 0.35/0.62 ((~(greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) <=> ((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))) | ((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[330, 329])).
% 0.35/0.62 tff(332,plain,
% 0.35/0.62 ((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[331, 309])).
% 0.35/0.62 tff(333,plain,
% 0.35/0.62 ((~((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))) | (cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.35/0.62 inference(tautology,[status(thm)],[])).
% 0.35/0.62 tff(334,plain,
% 0.35/0.62 ((cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[333, 332])).
% 0.35/0.62 tff(335,plain,
% 0.35/0.62 ($false),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[334, 307, 223])).
% 0.35/0.62 tff(336,plain,((~greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.62 tff(337,plain,
% 0.35/0.62 (selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[336, 179])).
% 0.35/0.62 tff(338,plain,
% 0.35/0.62 (selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2)))),
% 0.35/0.62 inference(modus_ponens,[status(thm)],[337, 24])).
% 0.35/0.62 tff(339,plain,
% 0.35/0.62 ((selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))) | (~selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))))),
% 0.35/0.62 inference(tautology,[status(thm)],[])).
% 0.35/0.62 tff(340,plain,
% 0.35/0.62 (~selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2)))),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[339, 96])).
% 0.35/0.62 tff(341,plain,
% 0.35/0.62 ($false),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[340, 338])).
% 0.35/0.62 tff(342,plain,(~(end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.62 tff(343,plain,
% 0.35/0.62 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.35/0.62 inference(quant_inst,[status(thm)],[])).
% 0.35/0.62 tff(344,plain,
% 0.35/0.62 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.35/0.62 inference(unit_resolution,[status(thm)],[343, 10])).
% 0.35/0.62 tff(345,plain,
% 0.35/0.62 (^[E: $i, T: $i] : refl((greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T))) <=> (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T))))),
% 0.35/0.63 inference(bind,[status(th)],[])).
% 0.35/0.63 tff(346,plain,
% 0.35/0.63 (![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T))) <=> ![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))),
% 0.35/0.63 inference(quant_intro,[status(thm)],[345])).
% 0.35/0.63 tff(347,plain,
% 0.35/0.63 (^[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(end_time(E), T)) <=> (((~environment(E)) | (~in_environment(E, T))) | greater_or_equal(end_time(E), T)))), rewrite((((~environment(E)) | (~in_environment(E, T))) | greater_or_equal(end_time(E), T)) <=> (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))), (((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T)) <=> (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))))),
% 0.35/0.63 inference(bind,[status(th)],[])).
% 0.35/0.63 tff(348,plain,
% 0.35/0.63 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T)) <=> ![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))),
% 0.35/0.63 inference(quant_intro,[status(thm)],[347])).
% 0.35/0.63 tff(349,plain,
% 0.35/0.63 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.35/0.63 inference(rewrite,[status(thm)],[])).
% 0.35/0.63 tff(350,plain,
% 0.35/0.63 (^[E: $i, T: $i] : rewrite(((environment(E) & in_environment(E, T)) => greater_or_equal(end_time(E), T)) <=> ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T)))),
% 0.35/0.63 inference(bind,[status(th)],[])).
% 0.35/0.63 tff(351,plain,
% 0.35/0.63 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(end_time(E), T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.35/0.63 inference(quant_intro,[status(thm)],[350])).
% 0.35/0.63 tff(352,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(end_time(E), T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_environment_end_point')).
% 0.35/0.63 tff(353,plain,
% 0.35/0.63 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.35/0.63 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.35/0.63 tff(354,plain,
% 0.35/0.63 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.35/0.63 inference(modus_ponens,[status(thm)],[353, 349])).
% 0.35/0.63 tff(355,plain,(
% 0.35/0.63 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.35/0.63 inference(skolemize,[status(sab)],[354])).
% 0.35/0.63 tff(356,plain,
% 0.35/0.63 (![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))),
% 0.35/0.63 inference(modus_ponens,[status(thm)],[355, 348])).
% 0.35/0.63 tff(357,plain,
% 0.35/0.63 (![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))),
% 0.35/0.63 inference(modus_ponens,[status(thm)],[356, 346])).
% 0.35/0.63 tff(358,plain,
% 0.35/0.63 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.35/0.63 inference(rewrite,[status(thm)],[])).
% 0.35/0.63 tff(359,plain,
% 0.35/0.63 ((greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.35/0.63 inference(rewrite,[status(thm)],[])).
% 0.35/0.63 tff(360,plain,
% 0.35/0.63 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.35/0.63 inference(monotonicity,[status(thm)],[359])).
% 0.35/0.63 tff(361,plain,
% 0.35/0.63 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.35/0.63 inference(transitivity,[status(thm)],[360, 358])).
% 0.35/0.63 tff(362,plain,
% 0.35/0.63 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.35/0.63 inference(quant_inst,[status(thm)],[])).
% 0.35/0.63 tff(363,plain,
% 0.35/0.63 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.35/0.63 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.35/0.63 tff(364,plain,
% 0.35/0.63 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.35/0.63 inference(unit_resolution,[status(thm)],[363, 357, 100, 158])).
% 0.35/0.63 tff(365,plain,
% 0.35/0.63 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | ((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.35/0.63 inference(tautology,[status(thm)],[])).
% 0.35/0.63 tff(366,plain,
% 0.35/0.63 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))))) | ((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.35/0.63 inference(unit_resolution,[status(thm)],[365, 364])).
% 0.35/0.63 tff(367,plain,
% 0.35/0.63 ((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.35/0.63 inference(unit_resolution,[status(thm)],[366, 344])).
% 0.35/0.63 tff(368,plain,
% 0.35/0.63 ((~((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))) | (end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.35/0.63 inference(tautology,[status(thm)],[])).
% 0.35/0.63 tff(369,plain,
% 0.35/0.63 ((end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.35/0.63 inference(unit_resolution,[status(thm)],[368, 367])).
% 0.35/0.63 tff(370,plain,
% 0.35/0.63 (greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.35/0.63 inference(unit_resolution,[status(thm)],[369, 342])).
% 0.35/0.63 tff(371,plain,
% 0.35/0.63 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.35/0.63 inference(rewrite,[status(thm)],[])).
% 0.35/0.63 tff(372,plain,
% 0.35/0.63 ((greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))) <=> ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.35/0.63 inference(rewrite,[status(thm)],[])).
% 0.35/0.63 tff(373,plain,
% 0.35/0.63 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.35/0.63 inference(monotonicity,[status(thm)],[372])).
% 0.35/0.63 tff(374,plain,
% 0.35/0.63 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.35/0.63 inference(transitivity,[status(thm)],[373, 371])).
% 0.35/0.63 tff(375,plain,
% 0.35/0.63 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.35/0.63 inference(quant_inst,[status(thm)],[])).
% 0.35/0.63 tff(376,plain,
% 0.35/0.63 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.35/0.63 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.35/0.63 tff(377,plain,
% 0.35/0.63 (greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.35/0.63 inference(unit_resolution,[status(thm)],[376, 143, 106, 370])).
% 0.35/0.64 tff(378,assumption,(greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.35/0.64 tff(379,plain,
% 0.35/0.64 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(rewrite,[status(thm)],[])).
% 0.35/0.64 tff(380,plain,
% 0.35/0.64 ((greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))) <=> ((~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(rewrite,[status(thm)],[])).
% 0.35/0.64 tff(381,plain,
% 0.35/0.64 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.35/0.64 inference(monotonicity,[status(thm)],[380])).
% 0.35/0.64 tff(382,plain,
% 0.35/0.64 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(transitivity,[status(thm)],[381, 379])).
% 0.35/0.64 tff(383,plain,
% 0.35/0.64 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.35/0.64 inference(quant_inst,[status(thm)],[])).
% 0.35/0.64 tff(384,plain,
% 0.35/0.64 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.35/0.64 tff(385,plain,
% 0.35/0.64 ($false),
% 0.35/0.64 inference(unit_resolution,[status(thm)],[384, 143, 378, 377, 21])).
% 0.35/0.64 tff(386,plain,((~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.64 tff(387,plain,
% 0.35/0.64 (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(unit_resolution,[status(thm)],[386, 20])).
% 0.35/0.64 tff(388,plain,
% 0.35/0.64 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) <=> ((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.35/0.64 inference(quant_inst,[status(thm)],[])).
% 0.35/0.64 tff(389,plain,
% 0.35/0.64 (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) <=> ((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(unit_resolution,[status(thm)],[388, 10])).
% 0.35/0.64 tff(390,plain,
% 0.35/0.64 (^[E: $i] : refl(((~environment(E)) | greater_or_equal(critical_point(E), start_time(E))) <=> ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E))))),
% 0.35/0.64 inference(bind,[status(th)],[])).
% 0.35/0.64 tff(391,plain,
% 0.35/0.64 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.35/0.64 inference(quant_intro,[status(thm)],[390])).
% 0.35/0.64 tff(392,plain,
% 0.35/0.64 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.35/0.64 inference(rewrite,[status(thm)],[])).
% 0.35/0.64 tff(393,plain,
% 0.35/0.64 (^[E: $i] : rewrite((environment(E) => greater_or_equal(critical_point(E), start_time(E))) <=> ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E))))),
% 0.35/0.64 inference(bind,[status(th)],[])).
% 0.35/0.64 tff(394,plain,
% 0.35/0.64 (![E: $i] : (environment(E) => greater_or_equal(critical_point(E), start_time(E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.35/0.64 inference(quant_intro,[status(thm)],[393])).
% 0.35/0.64 tff(395,axiom,(![E: $i] : (environment(E) => greater_or_equal(critical_point(E), start_time(E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_time_of_critical_point')).
% 0.35/0.64 tff(396,plain,
% 0.35/0.64 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.35/0.64 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.35/0.64 tff(397,plain,
% 0.35/0.64 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.35/0.64 inference(modus_ponens,[status(thm)],[396, 392])).
% 0.35/0.64 tff(398,plain,(
% 0.35/0.64 ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.35/0.64 inference(skolemize,[status(sab)],[397])).
% 0.35/0.64 tff(399,plain,
% 0.35/0.64 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.35/0.64 inference(modus_ponens,[status(thm)],[398, 391])).
% 0.35/0.64 tff(400,plain,
% 0.35/0.64 (((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))) <=> ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(rewrite,[status(thm)],[])).
% 0.35/0.64 tff(401,plain,
% 0.35/0.64 ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(quant_inst,[status(thm)],[])).
% 0.35/0.64 tff(402,plain,
% 0.35/0.64 ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.35/0.64 tff(403,plain,
% 0.35/0.64 (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(unit_resolution,[status(thm)],[402, 399, 100])).
% 0.35/0.64 tff(404,plain,
% 0.35/0.64 ((~(greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) <=> ((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | ((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(tautology,[status(thm)],[])).
% 0.35/0.64 tff(405,plain,
% 0.35/0.64 ((~(greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) <=> ((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))) | ((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(unit_resolution,[status(thm)],[404, 403])).
% 0.35/0.64 tff(406,plain,
% 0.35/0.64 ((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(unit_resolution,[status(thm)],[405, 389])).
% 0.35/0.64 tff(407,plain,
% 0.35/0.64 ((~((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))) | (critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(tautology,[status(thm)],[])).
% 0.35/0.64 tff(408,plain,
% 0.35/0.64 ((critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))) | greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(unit_resolution,[status(thm)],[407, 406])).
% 0.35/0.64 tff(409,plain,
% 0.35/0.64 (critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))),
% 0.35/0.64 inference(unit_resolution,[status(thm)],[408, 387])).
% 0.35/0.64 tff(410,plain,
% 0.35/0.64 (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) <=> in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(monotonicity,[status(thm)],[409])).
% 0.35/0.64 tff(411,plain,
% 0.35/0.64 (in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2))) <=> in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2)))),
% 0.35/0.64 inference(symmetry,[status(thm)],[410])).
% 0.35/0.64 tff(412,plain,
% 0.35/0.64 ((~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))) <=> (~in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))))),
% 0.35/0.64 inference(monotonicity,[status(thm)],[411])).
% 0.35/0.64 tff(413,plain,
% 0.35/0.64 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))),
% 0.35/0.64 inference(rewrite,[status(thm)],[])).
% 0.35/0.64 tff(414,plain,
% 0.35/0.64 ((greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))),
% 0.35/0.64 inference(rewrite,[status(thm)],[])).
% 0.35/0.64 tff(415,plain,
% 0.35/0.64 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2))))))),
% 0.35/0.64 inference(monotonicity,[status(thm)],[414])).
% 0.35/0.64 tff(416,plain,
% 0.35/0.64 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.65 inference(transitivity,[status(thm)],[415, 413])).
% 0.40/0.65 tff(417,plain,
% 0.40/0.65 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.65 inference(quant_inst,[status(thm)],[])).
% 0.40/0.65 tff(418,plain,
% 0.40/0.65 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2))))),
% 0.40/0.65 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.40/0.65 tff(419,plain,
% 0.40/0.65 (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))),
% 0.40/0.65 inference(unit_resolution,[status(thm)],[418, 357, 100, 15])).
% 0.40/0.65 tff(420,plain,
% 0.40/0.65 (~in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2)))),
% 0.40/0.65 inference(modus_ponens,[status(thm)],[419, 412])).
% 0.40/0.65 tff(421,plain,
% 0.40/0.65 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.40/0.65 inference(quant_inst,[status(thm)],[])).
% 0.40/0.65 tff(422,plain,
% 0.40/0.65 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.40/0.65 inference(unit_resolution,[status(thm)],[421, 10])).
% 0.40/0.65 tff(423,plain,
% 0.40/0.65 (((end_time(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.40/0.65 inference(tautology,[status(thm)],[])).
% 0.40/0.65 tff(424,plain,
% 0.40/0.65 ((end_time(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.40/0.65 inference(unit_resolution,[status(thm)],[423, 377])).
% 0.40/0.65 tff(425,plain,
% 0.40/0.65 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) | (~((end_time(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.40/0.65 inference(tautology,[status(thm)],[])).
% 0.40/0.65 tff(426,plain,
% 0.40/0.65 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.40/0.65 inference(unit_resolution,[status(thm)],[425, 424])).
% 0.40/0.65 tff(427,plain,
% 0.40/0.65 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.40/0.65 inference(unit_resolution,[status(thm)],[426, 422])).
% 0.40/0.65 tff(428,plain,
% 0.40/0.65 (^[E: $i, T: $i] : refl((in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))) <=> (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))))),
% 0.40/0.65 inference(bind,[status(th)],[])).
% 0.40/0.65 tff(429,plain,
% 0.40/0.65 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))),
% 0.40/0.65 inference(quant_intro,[status(thm)],[428])).
% 0.40/0.65 tff(430,plain,
% 0.40/0.65 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T)) <=> (~((~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))))), ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) <=> (~(~((~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))))))), rewrite((~(~((~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))))) <=> ((~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))), ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) <=> ((~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))))), (((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T)) <=> (((~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))) | in_environment(E, T)))), rewrite((((~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))), (((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))))),
% 0.40/0.65 inference(bind,[status(th)],[])).
% 0.40/0.65 tff(431,plain,
% 0.40/0.65 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))),
% 0.40/0.65 inference(quant_intro,[status(thm)],[430])).
% 0.40/0.65 tff(432,plain,
% 0.40/0.65 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.40/0.65 inference(rewrite,[status(thm)],[])).
% 0.40/0.65 tff(433,plain,
% 0.40/0.65 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & greater_or_equal(T, start_time(E))) & greater_or_equal(end_time(E), T)) <=> (environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))), ((((environment(E) & greater_or_equal(T, start_time(E))) & greater_or_equal(end_time(E), T)) => in_environment(E, T)) <=> ((environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T)) => in_environment(E, T)))), rewrite(((environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T)) => in_environment(E, T)) <=> ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))), ((((environment(E) & greater_or_equal(T, start_time(E))) & greater_or_equal(end_time(E), T)) => in_environment(E, T)) <=> ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))))),
% 0.40/0.65 inference(bind,[status(th)],[])).
% 0.40/0.65 tff(434,plain,
% 0.40/0.65 (![E: $i, T: $i] : (((environment(E) & greater_or_equal(T, start_time(E))) & greater_or_equal(end_time(E), T)) => in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.40/0.65 inference(quant_intro,[status(thm)],[433])).
% 0.40/0.65 tff(435,axiom,(![E: $i, T: $i] : (((environment(E) & greater_or_equal(T, start_time(E))) & greater_or_equal(end_time(E), T)) => in_environment(E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_time_in_environment')).
% 0.40/0.65 tff(436,plain,
% 0.40/0.65 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.40/0.65 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.40/0.65 tff(437,plain,
% 0.40/0.65 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.40/0.65 inference(modus_ponens,[status(thm)],[436, 432])).
% 0.40/0.65 tff(438,plain,(
% 0.40/0.65 ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.40/0.65 inference(skolemize,[status(sab)],[437])).
% 0.40/0.65 tff(439,plain,
% 0.40/0.65 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))),
% 0.40/0.65 inference(modus_ponens,[status(thm)],[438, 431])).
% 0.40/0.65 tff(440,plain,
% 0.40/0.65 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))),
% 0.40/0.65 inference(modus_ponens,[status(thm)],[439, 429])).
% 0.40/0.65 tff(441,plain,
% 0.40/0.65 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.65 inference(rewrite,[status(thm)],[])).
% 0.40/0.65 tff(442,plain,
% 0.40/0.65 ((in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.65 inference(rewrite,[status(thm)],[])).
% 0.40/0.65 tff(443,plain,
% 0.40/0.65 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))))),
% 0.40/0.65 inference(monotonicity,[status(thm)],[442])).
% 0.40/0.65 tff(444,plain,
% 0.40/0.65 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.65 inference(transitivity,[status(thm)],[443, 441])).
% 0.40/0.65 tff(445,plain,
% 0.40/0.65 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.40/0.65 inference(quant_inst,[status(thm)],[])).
% 0.40/0.65 tff(446,plain,
% 0.40/0.65 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.40/0.65 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.40/0.65 tff(447,plain,
% 0.40/0.65 (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.40/0.65 inference(unit_resolution,[status(thm)],[446, 440, 100, 403])).
% 0.40/0.65 tff(448,plain,
% 0.40/0.65 (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2)))),
% 0.40/0.65 inference(unit_resolution,[status(thm)],[447, 427])).
% 0.40/0.65 tff(449,plain,
% 0.40/0.65 ($false),
% 0.40/0.65 inference(unit_resolution,[status(thm)],[448, 420])).
% 0.40/0.65 tff(450,plain,(greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.65 tff(451,assumption,(~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.40/0.65 tff(452,plain,
% 0.40/0.65 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))),
% 0.40/0.65 inference(rewrite,[status(thm)],[])).
% 0.40/0.65 tff(453,plain,
% 0.40/0.65 ((greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> $true) <=> greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.65 inference(rewrite,[status(thm)],[])).
% 0.40/0.65 tff(454,plain,
% 0.40/0.65 (($true | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))) <=> $true),
% 0.40/0.65 inference(rewrite,[status(thm)],[])).
% 0.40/0.65 tff(455,plain,
% 0.40/0.65 ((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) <=> $true),
% 0.40/0.65 inference(rewrite,[status(thm)],[])).
% 0.40/0.65 tff(456,plain,
% 0.40/0.65 (((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))) <=> ($true | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))),
% 0.40/0.65 inference(monotonicity,[status(thm)],[455])).
% 0.40/0.65 tff(457,plain,
% 0.40/0.65 (((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))) <=> $true),
% 0.40/0.65 inference(transitivity,[status(thm)],[456, 454])).
% 0.40/0.65 tff(458,plain,
% 0.40/0.65 ((greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))) <=> (greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> $true)),
% 0.40/0.66 inference(monotonicity,[status(thm)],[457])).
% 0.40/0.66 tff(459,plain,
% 0.40/0.66 ((greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))) <=> greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.66 inference(transitivity,[status(thm)],[458, 453])).
% 0.40/0.66 tff(460,plain,
% 0.40/0.66 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))),
% 0.40/0.66 inference(monotonicity,[status(thm)],[459])).
% 0.40/0.66 tff(461,plain,
% 0.40/0.66 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))),
% 0.40/0.66 inference(transitivity,[status(thm)],[460, 452])).
% 0.40/0.66 tff(462,plain,
% 0.40/0.66 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.66 inference(quant_inst,[status(thm)],[])).
% 0.40/0.66 tff(463,plain,
% 0.40/0.66 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.66 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.40/0.66 tff(464,plain,
% 0.40/0.66 ($false),
% 0.40/0.66 inference(unit_resolution,[status(thm)],[463, 10, 451])).
% 0.40/0.66 tff(465,plain,(greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.66 tff(466,plain,
% 0.40/0.66 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.66 inference(rewrite,[status(thm)],[])).
% 0.40/0.66 tff(467,plain,
% 0.40/0.66 ((in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.66 inference(rewrite,[status(thm)],[])).
% 0.40/0.66 tff(468,plain,
% 0.40/0.66 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))))),
% 0.40/0.66 inference(monotonicity,[status(thm)],[467])).
% 0.40/0.66 tff(469,plain,
% 0.40/0.66 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.66 inference(transitivity,[status(thm)],[468, 466])).
% 0.40/0.66 tff(470,plain,
% 0.40/0.66 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.66 inference(quant_inst,[status(thm)],[])).
% 0.40/0.66 tff(471,plain,
% 0.40/0.66 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))),
% 0.40/0.66 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.40/0.66 tff(472,plain,
% 0.40/0.66 (in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.40/0.66 inference(unit_resolution,[status(thm)],[471, 440, 100, 465])).
% 0.40/0.66 tff(473,plain,
% 0.40/0.66 (in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.66 inference(unit_resolution,[status(thm)],[472, 450])).
% 0.40/0.66 tff(474,plain,
% 0.40/0.66 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))),
% 0.40/0.66 inference(rewrite,[status(thm)],[])).
% 0.40/0.66 tff(475,plain,
% 0.40/0.66 ((greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))),
% 0.40/0.66 inference(rewrite,[status(thm)],[])).
% 0.40/0.66 tff(476,plain,
% 0.40/0.66 (((~![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, end_time(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)))),
% 0.40/0.66 inference(monotonicity,[status(thm)],[475])).
% 0.40/0.66 tff(477,plain,
% 0.40/0.66 (((~![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, end_time(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))),
% 0.40/0.66 inference(transitivity,[status(thm)],[476, 474])).
% 0.40/0.66 tff(478,plain,
% 0.40/0.66 ((~![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, end_time(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.66 inference(quant_inst,[status(thm)],[])).
% 0.40/0.66 tff(479,plain,
% 0.40/0.66 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.40/0.66 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.40/0.66 tff(480,plain,
% 0.40/0.66 (greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.40/0.66 inference(unit_resolution,[status(thm)],[479, 322, 100, 473])).
% 0.40/0.66 tff(481,plain,
% 0.40/0.66 ((~(greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero) <=> ((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)))) | (~greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | ((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))),
% 0.40/0.66 inference(tautology,[status(thm)],[])).
% 0.40/0.66 tff(482,plain,
% 0.40/0.66 ((~(greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero) <=> ((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)))) | ((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))),
% 0.40/0.66 inference(unit_resolution,[status(thm)],[481, 480])).
% 0.40/0.66 tff(483,plain,
% 0.40/0.66 ((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.40/0.66 inference(unit_resolution,[status(thm)],[482, 12])).
% 0.40/0.66 tff(484,plain,
% 0.40/0.66 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))))),
% 0.40/0.67 inference(rewrite,[status(thm)],[])).
% 0.40/0.67 tff(485,plain,
% 0.40/0.67 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))))),
% 0.40/0.67 inference(quant_inst,[status(thm)],[])).
% 0.40/0.67 tff(486,plain,
% 0.40/0.67 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))))),
% 0.40/0.67 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.40/0.67 tff(487,plain,
% 0.40/0.67 (~((~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(unit_resolution,[status(thm)],[486, 194, 100, 473])).
% 0.40/0.67 tff(488,plain,
% 0.40/0.67 (((~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))) | subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.67 inference(tautology,[status(thm)],[])).
% 0.40/0.67 tff(489,plain,
% 0.40/0.67 (subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.67 inference(unit_resolution,[status(thm)],[488, 487])).
% 0.40/0.67 tff(490,plain,
% 0.40/0.67 (((~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))) | subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.67 inference(tautology,[status(thm)],[])).
% 0.40/0.67 tff(491,plain,
% 0.40/0.67 (subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.67 inference(unit_resolution,[status(thm)],[490, 487])).
% 0.40/0.67 tff(492,plain,
% 0.40/0.67 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(quant_inst,[status(thm)],[])).
% 0.40/0.67 tff(493,plain,
% 0.40/0.67 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.40/0.67 inference(unit_resolution,[status(thm)],[492, 10])).
% 0.40/0.67 tff(494,plain,
% 0.40/0.67 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(rewrite,[status(thm)],[])).
% 0.40/0.67 tff(495,plain,
% 0.40/0.67 ((greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))) <=> ((~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(rewrite,[status(thm)],[])).
% 0.40/0.67 tff(496,plain,
% 0.40/0.67 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))))),
% 0.40/0.67 inference(monotonicity,[status(thm)],[495])).
% 0.40/0.67 tff(497,plain,
% 0.40/0.67 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(transitivity,[status(thm)],[496, 494])).
% 0.40/0.67 tff(498,plain,
% 0.40/0.67 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(quant_inst,[status(thm)],[])).
% 0.40/0.67 tff(499,plain,
% 0.40/0.67 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.40/0.67 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.40/0.67 tff(500,plain,
% 0.40/0.67 (greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.40/0.67 inference(unit_resolution,[status(thm)],[499, 143, 370, 151])).
% 0.40/0.67 tff(501,plain,
% 0.40/0.67 (((end_time(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.40/0.67 inference(tautology,[status(thm)],[])).
% 0.40/0.67 tff(502,plain,
% 0.40/0.67 ((end_time(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.40/0.67 inference(unit_resolution,[status(thm)],[501, 500])).
% 0.40/0.67 tff(503,plain,
% 0.40/0.67 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) | (~((end_time(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(tautology,[status(thm)],[])).
% 0.40/0.67 tff(504,plain,
% 0.40/0.67 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.40/0.67 inference(unit_resolution,[status(thm)],[503, 502])).
% 0.40/0.67 tff(505,plain,
% 0.40/0.67 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.40/0.67 inference(unit_resolution,[status(thm)],[504, 493])).
% 0.40/0.67 tff(506,plain,
% 0.40/0.67 (((~![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))))) | ((~environment(tptp_fun_E_0(P!2))) | greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![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))))) | (~environment(tptp_fun_E_0(P!2))) | greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(rewrite,[status(thm)],[])).
% 0.40/0.67 tff(507,plain,
% 0.40/0.67 ((greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.67 inference(rewrite,[status(thm)],[])).
% 0.40/0.67 tff(508,plain,
% 0.40/0.67 (((~![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, end_time(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![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))))) | ((~environment(tptp_fun_E_0(P!2))) | greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))))),
% 0.40/0.67 inference(monotonicity,[status(thm)],[507])).
% 0.40/0.67 tff(509,plain,
% 0.40/0.67 (((~![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, end_time(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))) <=> ((~![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))))) | (~environment(tptp_fun_E_0(P!2))) | greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.68 inference(transitivity,[status(thm)],[508, 506])).
% 0.40/0.68 tff(510,plain,
% 0.40/0.68 ((~![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, end_time(tptp_fun_E_0(P!2))), zero) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.40/0.68 inference(quant_inst,[status(thm)],[])).
% 0.40/0.68 tff(511,plain,
% 0.40/0.68 ((~![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))))) | (~environment(tptp_fun_E_0(P!2))) | greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.40/0.68 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.40/0.68 tff(512,plain,
% 0.40/0.68 (greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.40/0.68 inference(unit_resolution,[status(thm)],[511, 171, 100, 505])).
% 0.40/0.68 tff(513,plain,
% 0.40/0.68 (greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.40/0.68 inference(unit_resolution,[status(thm)],[512, 473])).
% 0.40/0.68 tff(514,plain,
% 0.40/0.68 (((~![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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = 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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero)))),
% 0.40/0.68 inference(rewrite,[status(thm)],[])).
% 0.40/0.68 tff(515,plain,
% 0.40/0.68 ((selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero))) <=> (selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero)))),
% 0.40/0.68 inference(rewrite,[status(thm)],[])).
% 0.40/0.68 tff(516,plain,
% 0.40/0.68 (((~![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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = 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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero))))),
% 0.40/0.68 inference(monotonicity,[status(thm)],[515])).
% 0.40/0.68 tff(517,plain,
% 0.40/0.68 (((~![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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = 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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero)))),
% 0.40/0.68 inference(transitivity,[status(thm)],[516, 514])).
% 0.40/0.68 tff(518,plain,
% 0.40/0.68 ((~![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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero)))),
% 0.40/0.69 inference(quant_inst,[status(thm)],[])).
% 0.40/0.69 tff(519,plain,
% 0.40/0.69 ((~![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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero))),
% 0.40/0.69 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.40/0.69 tff(520,plain,
% 0.40/0.69 (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero)),
% 0.40/0.69 inference(unit_resolution,[status(thm)],[519, 215, 340, 100, 513, 491, 489])).
% 0.40/0.69 tff(521,plain,
% 0.40/0.69 ((~((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))) | (cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.40/0.69 inference(tautology,[status(thm)],[])).
% 0.40/0.69 tff(522,plain,
% 0.40/0.69 ((~((cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))) | greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.40/0.69 inference(unit_resolution,[status(thm)],[521, 520])).
% 0.40/0.69 tff(523,plain,
% 0.40/0.69 (greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.40/0.69 inference(unit_resolution,[status(thm)],[522, 483])).
% 0.40/0.69 tff(524,plain,
% 0.40/0.69 (((~![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(tptp_fun_E_0(P!2))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), 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(tptp_fun_E_0(P!2))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)))),
% 0.40/0.69 inference(rewrite,[status(thm)],[])).
% 0.40/0.69 tff(525,plain,
% 0.40/0.69 ((subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero))) <=> ((~environment(tptp_fun_E_0(P!2))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)))),
% 0.40/0.69 inference(rewrite,[status(thm)],[])).
% 0.40/0.69 tff(526,plain,
% 0.40/0.69 (((~![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, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), 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(tptp_fun_E_0(P!2))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero))))),
% 0.40/0.69 inference(monotonicity,[status(thm)],[525])).
% 0.40/0.69 tff(527,plain,
% 0.40/0.69 (((~![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, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), 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(tptp_fun_E_0(P!2))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)))),
% 0.40/0.69 inference(transitivity,[status(thm)],[526, 524])).
% 0.40/0.69 tff(528,plain,
% 0.40/0.69 ((~![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, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)))),
% 0.40/0.69 inference(quant_inst,[status(thm)],[])).
% 0.40/0.69 tff(529,plain,
% 0.40/0.69 ((~![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(tptp_fun_E_0(P!2))) | subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero))),
% 0.40/0.69 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.40/0.69 tff(530,plain,
% 0.40/0.69 (subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero))),
% 0.40/0.69 inference(unit_resolution,[status(thm)],[529, 299, 100, 513, 473])).
% 0.40/0.69 tff(531,plain,
% 0.40/0.69 (subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.40/0.69 inference(unit_resolution,[status(thm)],[530, 523])).
% 0.40/0.69 tff(532,plain,
% 0.40/0.69 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | ((~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.69 inference(rewrite,[status(thm)],[])).
% 0.40/0.69 tff(533,plain,
% 0.40/0.69 ((greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))) <=> ((~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))),
% 0.40/0.69 inference(rewrite,[status(thm)],[])).
% 0.40/0.69 tff(534,plain,
% 0.40/0.69 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | ((~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))))),
% 0.40/0.69 inference(monotonicity,[status(thm)],[533])).
% 0.40/0.69 tff(535,plain,
% 0.40/0.69 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))),
% 0.46/0.70 inference(transitivity,[status(thm)],[534, 532])).
% 0.46/0.70 tff(536,plain,
% 0.46/0.70 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(537,plain,
% 0.46/0.70 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.46/0.70 tff(538,plain,
% 0.46/0.70 ((~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[537, 256, 377])).
% 0.46/0.70 tff(539,plain,
% 0.46/0.70 (greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[538, 531])).
% 0.46/0.70 tff(540,plain,
% 0.46/0.70 (((~![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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))))) <=> ((~![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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(541,plain,
% 0.46/0.70 ((~![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, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(542,plain,
% 0.46/0.70 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.46/0.70 tff(543,plain,
% 0.46/0.70 ($false),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[542, 277, 340, 100, 531, 539])).
% 0.46/0.70 % SZS output end Proof
% 0.46/0.71 % E exiting
%------------------------------------------------------------------------------