TSTP Solution File: MGT039+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT039+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:22:08 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT039+2 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 02:53:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(in_environment_type, type, (
% 0.20/0.49 in_environment: ( $i * $i ) > $o)).
% 0.20/0.49 tff(critical_point_type, type, (
% 0.20/0.49 critical_point: $i > $i)).
% 0.20/0.49 tff(tptp_fun_E_0_type, type, (
% 0.20/0.49 tptp_fun_E_0: $i > $i)).
% 0.20/0.49 tff(tptp_fun_P_2_type, type, (
% 0.20/0.49 tptp_fun_P_2: $i)).
% 0.20/0.49 tff(start_time_type, type, (
% 0.20/0.49 start_time: $i > $i)).
% 0.20/0.49 tff(greater_type, type, (
% 0.20/0.49 greater: ( $i * $i ) > $o)).
% 0.20/0.49 tff(end_time_type, type, (
% 0.20/0.49 end_time: $i > $i)).
% 0.20/0.49 tff(greater_or_equal_type, type, (
% 0.20/0.49 greater_or_equal: ( $i * $i ) > $o)).
% 0.20/0.49 tff(zero_type, type, (
% 0.20/0.49 zero: $i)).
% 0.20/0.49 tff(cardinality_at_time_type, type, (
% 0.20/0.49 cardinality_at_time: ( $i * $i ) > $i)).
% 0.20/0.49 tff(first_movers_type, type, (
% 0.20/0.49 first_movers: $i)).
% 0.20/0.49 tff(environment_type, type, (
% 0.20/0.49 environment: $i > $o)).
% 0.20/0.49 tff(selection_favors_type, type, (
% 0.20/0.49 selection_favors: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(efficient_producers_type, type, (
% 0.20/0.49 efficient_producers: $i)).
% 0.20/0.49 tff(slow_change_type, type, (
% 0.20/0.49 slow_change: $i > $o)).
% 0.20/0.49 tff(observational_period_type, type, (
% 0.20/0.49 observational_period: $i > $o)).
% 0.20/0.49 tff(propagation_strategy_type, type, (
% 0.20/0.49 propagation_strategy: $i > $o)).
% 0.20/0.49 tff(appear_type, type, (
% 0.20/0.49 appear: ( $i * $i ) > $i)).
% 0.20/0.49 tff(tptp_fun_T_1_type, type, (
% 0.20/0.49 tptp_fun_T_1: $i > $i)).
% 0.20/0.49 tff(growth_rate_type, type, (
% 0.20/0.49 growth_rate: ( $i * $i ) > $i)).
% 0.20/0.49 tff(subpopulations_type, type, (
% 0.20/0.49 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.49 tff(subpopulation_type, type, (
% 0.20/0.49 subpopulation: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(1,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.49 tff(6,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal')).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.49 tff(9,plain,(
% 0.20/0.49 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[8])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 ((~![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)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 (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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (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))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.20/0.49 tff(15,assumption,(in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 ((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(18,axiom,(~![P: $i] : ((observational_period(P) & slow_change(P)) => selection_favors(efficient_producers, first_movers, P))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t8')).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[24, 16])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[25, 16])).
% 0.20/0.49 tff(27,plain,(
% 0.20/0.49 ~((~(observational_period(P!2) & slow_change(P!2))) | selection_favors(efficient_producers, first_movers, P!2))),
% 0.20/0.49 inference(skolemize,[status(sab)],[26])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (~selection_favors(efficient_producers, first_movers, P!2)),
% 0.20/0.49 inference(or_elim,[status(thm)],[27])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (observational_period(P!2) & slow_change(P!2)),
% 0.20/0.49 inference(or_elim,[status(thm)],[27])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 (observational_period(P!2)),
% 0.20/0.49 inference(and_elim,[status(thm)],[29])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (^[P: $i] : refl((selection_favors(efficient_producers, first_movers, P) | (~observational_period(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) | (~observational_period(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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(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)))))) <=> ![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(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))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 (^[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) | (~observational_period(P)) | (~((~(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) | (~observational_period(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)))))))), rewrite((selection_favors(efficient_producers, first_movers, P) | (~observational_period(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) | (~observational_period(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) | (~observational_period(P)) | (~((~(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) | (~observational_period(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))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(P)) | (~((~(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) | (~observational_period(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))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (^[P: $i] : rewrite((((~observational_period(P)) | (~((~(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) | (~observational_period(P)) | (~((~(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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (![P: $i] : (((~observational_period(P)) | (~((~(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) | (~observational_period(P)) | (~((~(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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (![P: $i] : ((~(observational_period(P) & ![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) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (^[P: $i] : 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) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (![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) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.50 tff(42,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/sandbox2/benchmark/theBenchmark.p','mp3_favoured_trategy')).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (![P: $i] : ((~(observational_period(P) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (![P: $i] : ((~(observational_period(P) & ![E: $i] : ((~(environment(E) & in_environment(P, E))) | selection_favors(efficient_producers, first_movers, end_time(E))))) | selection_favors(efficient_producers, first_movers, P))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.50 tff(46,plain,(
% 0.20/0.50 ![P: $i] : (((~observational_period(P)) | (~((~(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))),
% 0.20/0.50 inference(skolemize,[status(sab)],[45])).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(P)) | (~((~(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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[47, 34])).
% 0.20/0.50 tff(49,plain,
% 0.20/0.50 (![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[48, 32])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(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!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) | (~observational_period(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!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))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 ((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(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!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))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 ((~![P: $i] : (selection_favors(efficient_producers, first_movers, P) | (~observational_period(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!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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (~(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))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[52, 49, 30, 28])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 ((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))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (environment(tptp_fun_E_0(P!2))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (^[E: $i, T: $i] : refl((greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E))) <=> (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E))) <=> ![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (^[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) | (~in_environment(E, T)) | (~environment(E)))), (((~(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) | (~in_environment(E, T)) | (~environment(E)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 (![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) | (~in_environment(E, T)) | (~environment(E)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (^[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)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.50 tff(63,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(cardinality_at_time(first_movers, T), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_first_movers_exist')).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.50 tff(66,plain,(
% 0.20/0.50 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.20/0.50 inference(skolemize,[status(sab)],[65])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(cardinality_at_time(first_movers, 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)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(cardinality_at_time(first_movers, 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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 ((greater_or_equal(cardinality_at_time(first_movers, 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)))) | (~environment(tptp_fun_E_0(P!2)))) <=> ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(cardinality_at_time(first_movers, 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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(cardinality_at_time(first_movers, 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)))) | (~environment(tptp_fun_E_0(P!2))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(cardinality_at_time(first_movers, 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))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(cardinality_at_time(first_movers, 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)))) | (~environment(tptp_fun_E_0(P!2))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(cardinality_at_time(first_movers, 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)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[71, 69])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(cardinality_at_time(first_movers, 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)))) | (~environment(tptp_fun_E_0(P!2))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(cardinality_at_time(first_movers, 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))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (greater_or_equal(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[74, 68, 55, 15])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 ((~(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))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 ((~(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))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 ((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)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[77, 14])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 ((~![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)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 (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))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[79, 10])).
% 0.20/0.50 tff(81,assumption,(~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.20/0.50 tff(82,assumption,(greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 (slow_change(P!2)),
% 0.20/0.50 inference(and_elim,[status(thm)],[29])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(85,plain,
% 0.20/0.50 (![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))))))) <=> ![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)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 (![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))))))) <=> ![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)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (![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))))))) <=> ![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)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (^[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)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 (![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))))) <=> ![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)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (![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))))) <=> ![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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (![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))))) <=> ![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.50 tff(94,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/sandbox2/benchmark/theBenchmark.p','mp4_critical_point')).
% 0.20/0.50 tff(95,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.50 tff(97,plain,(
% 0.20/0.50 ![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)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[96])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (((~![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)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 ((~![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)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 ((~![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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[102, 99, 30, 83])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 ((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))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 (in_environment(P!2, tptp_fun_E_0(P!2))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[104, 53])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 (((~![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))))))) | ((~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)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 ((~![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))))))) | ((~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)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 ((~![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))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (~((~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)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[108, 55, 105, 103])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 (((~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)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (^[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)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (^[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)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.51 tff(118,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_transitivity')).
% 0.20/0.51 tff(119,plain,
% 0.20/0.51 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.20/0.51 tff(121,plain,(
% 0.20/0.51 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.20/0.51 inference(skolemize,[status(sab)],[120])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[122, 112])).
% 0.20/0.51 tff(124,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.51 ((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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(126,plain,
% 0.20/0.51 (((~![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)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[125])).
% 0.20/0.51 tff(127,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[126, 124])).
% 0.20/0.51 tff(128,plain,
% 0.20/0.51 ((~![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)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(129,plain,
% 0.20/0.51 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.51 tff(130,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[129, 123, 111, 82, 81])).
% 0.20/0.51 tff(131,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 (~greater(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[131, 81])).
% 0.20/0.51 tff(133,plain,
% 0.20/0.51 ((~![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)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(134,plain,
% 0.20/0.51 (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))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[133, 10])).
% 0.20/0.51 tff(135,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.51 tff(137,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(138,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(139,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.51 tff(140,axiom,(![E: $i] : (environment(E) => greater_or_equal(critical_point(E), appear(efficient_producers, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_critical_point_after_EP')).
% 0.20/0.51 tff(141,plain,
% 0.20/0.51 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.51 tff(142,plain,
% 0.20/0.51 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.20/0.51 tff(143,plain,(
% 0.20/0.51 ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[142])).
% 0.20/0.51 tff(144,plain,
% 0.20/0.51 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.20/0.51 tff(145,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(146,plain,
% 0.20/0.51 ((~![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))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(147,plain,
% 0.20/0.51 ((~![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)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.51 tff(148,plain,
% 0.20/0.51 (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[147, 144, 55])).
% 0.20/0.51 tff(149,plain,
% 0.20/0.51 ((~(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))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(150,plain,
% 0.20/0.51 ((~(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))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.51 tff(151,plain,
% 0.20/0.51 ((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)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[150, 134])).
% 0.20/0.51 tff(152,plain,
% 0.20/0.51 ((~((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)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 ((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)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 (critical_point(tptp_fun_E_0(P!2)) = appear(efficient_producers, tptp_fun_E_0(P!2))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[153, 132])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 (appear(efficient_producers, tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))),
% 0.20/0.51 inference(symmetry,[status(thm)],[154])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 (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)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.51 tff(157,plain,
% 0.20/0.51 (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)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[156])).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[111, 157])).
% 0.20/0.51 tff(159,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[81, 158])).
% 0.20/0.51 tff(160,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,[]))).
% 0.20/0.51 tff(161,assumption,(end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))), introduced(assumption)).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 (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)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.51 tff(163,plain,
% 0.20/0.51 (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)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[162])).
% 0.20/0.51 tff(164,assumption,(~selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.20/0.51 tff(165,plain,
% 0.20/0.51 (((~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)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(166,plain,
% 0.20/0.51 (in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[165, 109])).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 (^[E: $i, T: $i] : refl(((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(168,plain,
% 0.20/0.51 (![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.51 tff(169,plain,
% 0.20/0.51 (^[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))))) <=> ((~in_environment(E, T)) | (~environment(E)) | (~((~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))) <=> ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(170,plain,
% 0.20/0.51 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[169])).
% 0.20/0.51 tff(171,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[172])).
% 0.20/0.51 tff(174,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_subpopulations')).
% 0.20/0.51 tff(175,plain,
% 0.20/0.51 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.20/0.51 tff(177,plain,(
% 0.20/0.51 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[176])).
% 0.20/0.51 tff(178,plain,
% 0.20/0.51 (![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 (![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[178, 168])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 (((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~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] : ((~in_environment(E, T)) | (~environment(E)) | (~((~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)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 (((~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))) | (~((~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))))))) <=> ((~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)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 ((~((~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)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 (((~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))) | (~((~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))))))) <=> ((~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))) | (~((~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)))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[182])).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 (((~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))) | (~((~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))))))) <=> ((~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)))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[183, 181])).
% 0.20/0.51 tff(185,plain,
% 0.20/0.51 (((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~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))) | (~((~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] : ((~in_environment(E, T)) | (~environment(E)) | (~((~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))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[184])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 (((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~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))) | (~((~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] : ((~in_environment(E, T)) | (~environment(E)) | (~((~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)))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[185, 180])).
% 0.20/0.51 tff(187,plain,
% 0.20/0.51 ((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~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))) | (~((~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)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 ((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~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))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.52 tff(189,plain,
% 0.20/0.52 (~((~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)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[188, 179, 55, 166])).
% 0.20/0.52 tff(190,plain,
% 0.20/0.52 (((~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)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(191,plain,
% 0.20/0.52 (subpopulation(efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.20/0.52 tff(192,plain,
% 0.20/0.52 (((~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)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(193,plain,
% 0.20/0.52 (subpopulation(first_movers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.20/0.52 tff(194,plain,
% 0.20/0.52 ((~![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)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(195,plain,
% 0.20/0.52 (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))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[194, 10])).
% 0.20/0.52 tff(196,plain,
% 0.20/0.52 (((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))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 ((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)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[196, 160])).
% 0.20/0.52 tff(198,plain,
% 0.20/0.52 ((~(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)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(199,plain,
% 0.20/0.52 ((~(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)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.52 tff(200,plain,
% 0.20/0.52 (greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[199, 195])).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 (^[E: $i, T: $i] : refl((greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E)))) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(202,plain,
% 0.20/0.52 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E)))) <=> ![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[201])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 (^[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) | (~in_environment(E, T)) | (~environment(E)) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 (![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) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[203])).
% 0.20/0.52 tff(205,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 (^[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))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(207,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[206])).
% 0.20/0.52 tff(208,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/sandbox2/benchmark/theBenchmark.p','t6')).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.20/0.52 tff(211,plain,(
% 0.20/0.52 ![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))),
% 0.20/0.52 inference(skolemize,[status(sab)],[210])).
% 0.20/0.52 tff(212,plain,
% 0.20/0.52 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.20/0.52 tff(213,plain,
% 0.20/0.52 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[212, 202])).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~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)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(215,plain,
% 0.20/0.52 ((greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~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))) | (~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)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~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) | (~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))) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~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))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~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) | (~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))) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~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)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[216, 214])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~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) | (~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))) | (~greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~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))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 (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))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[219, 213, 55, 166])).
% 0.20/0.52 tff(221,plain,
% 0.20/0.52 (greater(cardinality_at_time(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[220, 200])).
% 0.20/0.52 tff(222,plain,
% 0.20/0.52 (^[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))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(223,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[222])).
% 0.20/0.52 tff(224,plain,
% 0.20/0.52 (^[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)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(225,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.52 tff(226,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(227,plain,
% 0.20/0.52 (^[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))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(228,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[227])).
% 0.20/0.52 tff(229,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/sandbox2/benchmark/theBenchmark.p','mp2_favour_members')).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.52 tff(231,plain,
% 0.20/0.52 (![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))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.20/0.52 tff(232,plain,(
% 0.20/0.52 ![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))),
% 0.20/0.52 inference(skolemize,[status(sab)],[231])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.20/0.52 tff(234,plain,
% 0.20/0.52 (![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)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[233, 223])).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 (((~![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))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 ((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))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(237,plain,
% 0.20/0.52 (((~![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)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[236])).
% 0.20/0.52 tff(238,plain,
% 0.20/0.52 (((~![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))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[237, 235])).
% 0.20/0.52 tff(239,plain,
% 0.20/0.52 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(240,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.20/0.53 tff(241,plain,
% 0.20/0.53 ((~(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)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[240, 234, 55, 221, 193, 191])).
% 0.20/0.53 tff(242,plain,
% 0.20/0.53 (~(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) = zero)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[241, 164])).
% 0.20/0.53 tff(243,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(244,plain,
% 0.20/0.53 (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))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[243, 10])).
% 0.20/0.53 tff(245,plain,
% 0.20/0.53 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(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_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) | (~in_environment(E, T)) | (~environment(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_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(246,plain,
% 0.20/0.53 ((greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~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)))) <=> ((~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))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(247,plain,
% 0.20/0.53 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~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))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(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_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[246])).
% 0.20/0.53 tff(248,plain,
% 0.20/0.53 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~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))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(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_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero))),
% 0.20/0.53 inference(transitivity,[status(thm)],[247, 245])).
% 0.20/0.53 tff(249,plain,
% 0.20/0.53 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero) | (~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))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(250,plain,
% 0.20/0.53 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~in_environment(E, T)) | (~environment(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_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.20/0.53 tff(251,plain,
% 0.20/0.53 (greater_or_equal(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[250, 68, 55, 166])).
% 0.20/0.53 tff(252,plain,
% 0.20/0.53 ((~(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))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(253,plain,
% 0.20/0.53 ((~(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))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.20/0.53 tff(254,plain,
% 0.20/0.53 ((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)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[253, 244])).
% 0.20/0.53 tff(255,plain,
% 0.20/0.53 ((~((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)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(256,plain,
% 0.20/0.53 ((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)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.20/0.53 tff(257,plain,
% 0.20/0.53 (greater(cardinality_at_time(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))), zero)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[256, 242])).
% 0.20/0.53 tff(258,plain,
% 0.20/0.53 (^[E: $i, T: $i] : refl((subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(259,plain,
% 0.20/0.53 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[258])).
% 0.20/0.53 tff(260,plain,
% 0.20/0.53 (^[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)) <=> (~((~in_environment(E, T)) | (~environment(E)) | (~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))) <=> (~(~((~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))))), rewrite((~(~((~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ((~in_environment(E, T)) | (~environment(E)) | (~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))) <=> ((~in_environment(E, T)) | (~environment(E)) | (~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)) <=> (((~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)))), rewrite((((~in_environment(E, T)) | (~environment(E)) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(261,plain,
% 0.20/0.53 (![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) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[260])).
% 0.20/0.53 tff(262,plain,
% 0.20/0.53 (![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))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(263,plain,
% 0.20/0.53 (^[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))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(264,plain,
% 0.20/0.53 (![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))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[263])).
% 0.20/0.53 tff(265,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/sandbox2/benchmark/theBenchmark.p','mp_contains_FM_and_EP')).
% 0.20/0.53 tff(266,plain,
% 0.20/0.53 (![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))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.20/0.53 tff(267,plain,
% 0.20/0.53 (![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))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.20/0.53 tff(268,plain,(
% 0.20/0.53 ![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))),
% 0.20/0.53 inference(skolemize,[status(sab)],[267])).
% 0.20/0.53 tff(269,plain,
% 0.20/0.53 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.20/0.53 tff(270,plain,
% 0.20/0.53 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[269, 259])).
% 0.20/0.53 tff(271,plain,
% 0.20/0.53 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(272,plain,
% 0.20/0.53 ((subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(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))) | (~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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(273,plain,
% 0.20/0.53 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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))) | (~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))) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~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))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[272])).
% 0.20/0.53 tff(274,plain,
% 0.20/0.53 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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))) | (~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))) | (~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) | (~in_environment(E, T)) | (~environment(E)) | (~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)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[273, 271])).
% 0.20/0.53 tff(275,plain,
% 0.20/0.53 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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))) | (~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))) | (~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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(276,plain,
% 0.20/0.53 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.20/0.53 tff(277,plain,
% 0.20/0.53 (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))),
% 0.46/0.53 inference(unit_resolution,[status(thm)],[276, 270, 55, 166])).
% 0.46/0.53 tff(278,plain,
% 0.46/0.53 (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))),
% 0.46/0.53 inference(unit_resolution,[status(thm)],[277, 221])).
% 0.46/0.53 tff(279,plain,
% 0.46/0.53 (subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.46/0.53 inference(unit_resolution,[status(thm)],[278, 257])).
% 0.46/0.53 tff(280,plain,
% 0.46/0.53 (^[E: $i, Tc: $i] : refl(((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))))),
% 0.46/0.53 inference(bind,[status(th)],[])).
% 0.46/0.53 tff(281,plain,
% 0.46/0.53 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.46/0.53 inference(quant_intro,[status(thm)],[280])).
% 0.46/0.53 tff(282,plain,
% 0.46/0.53 (^[E: $i, Tc: $i] : rewrite(((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))))),
% 0.46/0.53 inference(bind,[status(th)],[])).
% 0.46/0.53 tff(283,plain,
% 0.46/0.53 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.46/0.53 inference(quant_intro,[status(thm)],[282])).
% 0.46/0.53 tff(284,plain,
% 0.46/0.53 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.46/0.54 inference(transitivity,[status(thm)],[283, 281])).
% 0.46/0.54 tff(285,plain,
% 0.46/0.54 (^[E: $i, Tc: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & (Tc = critical_point(E))) <=> (~((~environment(E)) | (~(Tc = critical_point(E)))))), ((~(environment(E) & (Tc = critical_point(E)))) <=> (~(~((~environment(E)) | (~(Tc = critical_point(E)))))))), rewrite((~(~((~environment(E)) | (~(Tc = critical_point(E)))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))))), ((~(environment(E) & (Tc = critical_point(E)))) <=> ((~environment(E)) | (~(Tc = critical_point(E)))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), rewrite((((~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, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))), (((~(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, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))), (((~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] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))), rewrite(((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))) <=> (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))), (((~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] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))), (((~(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] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))))), rewrite((((~environment(E)) | (~(Tc = critical_point(E)))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))), (((~(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] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))))),
% 0.46/0.54 inference(bind,[status(th)],[])).
% 0.46/0.54 tff(286,plain,
% 0.46/0.54 (![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] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.46/0.54 inference(quant_intro,[status(thm)],[285])).
% 0.46/0.54 tff(287,plain,
% 0.46/0.54 (![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)))))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(288,plain,
% 0.46/0.54 (^[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)))))))),
% 0.46/0.54 inference(bind,[status(th)],[])).
% 0.46/0.54 tff(289,plain,
% 0.46/0.54 (![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)))))),
% 0.46/0.54 inference(quant_intro,[status(thm)],[288])).
% 0.46/0.54 tff(290,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/sandbox2/benchmark/theBenchmark.p','d1')).
% 0.46/0.54 tff(291,plain,
% 0.46/0.54 (![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)))))),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.46/0.54 tff(292,plain,
% 0.46/0.54 (![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)))))),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.46/0.54 tff(293,plain,(
% 0.46/0.54 ![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)))))),
% 0.46/0.54 inference(skolemize,[status(sab)],[292])).
% 0.46/0.54 tff(294,plain,
% 0.46/0.54 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[293, 286])).
% 0.46/0.54 tff(295,plain,
% 0.46/0.54 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[294, 284])).
% 0.46/0.54 tff(296,plain,
% 0.46/0.54 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~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, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | (~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)))))))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(297,plain,
% 0.46/0.54 (((~environment(tptp_fun_E_0(P!2))) | $false | (~((~![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))))))) <=> ((~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)))))))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(298,plain,
% 0.46/0.54 ((~(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)))))))) <=> (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), T)) | (~greater(T, critical_point(tptp_fun_E_0(P!2)))))) | greater(growth_rate(efficient_producers, critical_point(tptp_fun_E_0(P!2))), growth_rate(first_movers, critical_point(tptp_fun_E_0(P!2))))))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(299,plain,
% 0.46/0.54 ((~$true) <=> $false),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(300,plain,
% 0.46/0.54 ((critical_point(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) <=> $true),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(301,plain,
% 0.46/0.54 ((~(critical_point(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2)))) <=> (~$true)),
% 0.46/0.54 inference(monotonicity,[status(thm)],[300])).
% 0.46/0.54 tff(302,plain,
% 0.46/0.54 ((~(critical_point(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2)))) <=> $false),
% 0.46/0.54 inference(transitivity,[status(thm)],[301, 299])).
% 0.46/0.54 tff(303,plain,
% 0.46/0.54 (((~environment(tptp_fun_E_0(P!2))) | (~(critical_point(tptp_fun_E_0(P!2)) = 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))))))))) <=> ((~environment(tptp_fun_E_0(P!2))) | $false | (~((~![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)))))))),
% 0.46/0.54 inference(monotonicity,[status(thm)],[302, 298])).
% 0.46/0.54 tff(304,plain,
% 0.46/0.54 (((~environment(tptp_fun_E_0(P!2))) | (~(critical_point(tptp_fun_E_0(P!2)) = 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))))))))) <=> ((~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)))))))),
% 0.46/0.54 inference(transitivity,[status(thm)],[303, 297])).
% 0.46/0.54 tff(305,plain,
% 0.46/0.54 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~environment(tptp_fun_E_0(P!2))) | (~(critical_point(tptp_fun_E_0(P!2)) = 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)))))))))) <=> ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~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))))))))),
% 0.46/0.54 inference(monotonicity,[status(thm)],[304])).
% 0.46/0.54 tff(306,plain,
% 0.46/0.54 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~environment(tptp_fun_E_0(P!2))) | (~(critical_point(tptp_fun_E_0(P!2)) = 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)))))))))) <=> ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | (~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)))))))),
% 0.46/0.54 inference(transitivity,[status(thm)],[305, 296])).
% 0.46/0.54 tff(307,plain,
% 0.46/0.54 ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~environment(tptp_fun_E_0(P!2))) | (~(critical_point(tptp_fun_E_0(P!2)) = 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)))))))))),
% 0.46/0.54 inference(quant_inst,[status(thm)],[])).
% 0.46/0.54 tff(308,plain,
% 0.46/0.54 ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | (~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))))))),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.46/0.54 tff(309,plain,
% 0.46/0.54 (~((~![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)))))),
% 0.46/0.54 inference(unit_resolution,[status(thm)],[308, 295, 55])).
% 0.46/0.54 tff(310,plain,
% 0.46/0.54 (((~![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)))))),
% 0.46/0.54 inference(tautology,[status(thm)],[])).
% 0.46/0.54 tff(311,plain,
% 0.46/0.54 (![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)))))),
% 0.46/0.54 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.46/0.54 tff(312,plain,
% 0.46/0.54 (((~![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)))) | (~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)))))) <=> ((~![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)))) | (~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)))))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(313,plain,
% 0.46/0.54 ((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)))) | (~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)))))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(314,plain,
% 0.46/0.54 (((~![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)))) | (~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))))))),
% 0.46/0.54 inference(monotonicity,[status(thm)],[313])).
% 0.46/0.54 tff(315,plain,
% 0.46/0.54 (((~![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)))) | (~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)))))),
% 0.46/0.55 inference(transitivity,[status(thm)],[314, 312])).
% 0.46/0.55 tff(316,plain,
% 0.46/0.55 ((~![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)))))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(317,plain,
% 0.46/0.55 ((~![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)))) | (~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))))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.46/0.55 tff(318,plain,
% 0.46/0.55 ((~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))))),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[317, 111, 311])).
% 0.46/0.55 tff(319,plain,
% 0.46/0.55 (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))))),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[318, 279])).
% 0.46/0.55 tff(320,plain,
% 0.46/0.55 (^[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)))))),
% 0.46/0.55 inference(bind,[status(th)],[])).
% 0.46/0.55 tff(321,plain,
% 0.46/0.55 (![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))))),
% 0.46/0.55 inference(quant_intro,[status(thm)],[320])).
% 0.46/0.55 tff(322,plain,
% 0.46/0.55 (^[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))))))),
% 0.46/0.55 inference(bind,[status(th)],[])).
% 0.46/0.55 tff(323,plain,
% 0.46/0.55 (![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))))),
% 0.46/0.55 inference(quant_intro,[status(thm)],[322])).
% 0.46/0.55 tff(324,plain,
% 0.46/0.55 (![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))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(325,plain,
% 0.46/0.55 (^[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))))),
% 0.46/0.55 inference(bind,[status(th)],[])).
% 0.46/0.55 tff(326,plain,
% 0.46/0.55 (![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))),
% 0.46/0.55 inference(quant_intro,[status(thm)],[325])).
% 0.46/0.55 tff(327,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/sandbox2/benchmark/theBenchmark.p','mp1_high_growth_rates')).
% 0.46/0.55 tff(328,plain,
% 0.46/0.55 (![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))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.46/0.55 tff(329,plain,
% 0.46/0.55 (![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))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.46/0.55 tff(330,plain,(
% 0.46/0.55 ![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))),
% 0.46/0.55 inference(skolemize,[status(sab)],[329])).
% 0.46/0.55 tff(331,plain,
% 0.46/0.55 (![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))))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[330, 323])).
% 0.46/0.55 tff(332,plain,
% 0.46/0.55 (![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))))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[331, 321])).
% 0.46/0.55 tff(333,plain,
% 0.46/0.55 (((~![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))) | selection_favors(efficient_producers, 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(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))) | selection_favors(efficient_producers, 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(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))))))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(334,plain,
% 0.46/0.55 ((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))) | selection_favors(efficient_producers, 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(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))))))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(335,plain,
% 0.46/0.55 (((~![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))) | selection_favors(efficient_producers, 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(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)))))))),
% 0.48/0.55 inference(monotonicity,[status(thm)],[334])).
% 0.48/0.55 tff(336,plain,
% 0.48/0.55 (((~![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))) | selection_favors(efficient_producers, 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(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))))))),
% 0.48/0.55 inference(transitivity,[status(thm)],[335, 333])).
% 0.48/0.55 tff(337,plain,
% 0.48/0.55 ((~![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))))))),
% 0.48/0.55 inference(quant_inst,[status(thm)],[])).
% 0.48/0.55 tff(338,plain,
% 0.48/0.55 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (~environment(tptp_fun_E_0(P!2))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(tptp_fun_E_0(P!2))), growth_rate(first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.48/0.55 tff(339,plain,
% 0.48/0.55 ($false),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[338, 332, 55, 279, 319, 164])).
% 0.48/0.55 tff(340,plain,(selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.55 tff(341,plain,
% 0.48/0.55 (selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[340, 163])).
% 0.48/0.55 tff(342,plain,
% 0.48/0.55 ((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))))),
% 0.48/0.55 inference(tautology,[status(thm)],[])).
% 0.48/0.55 tff(343,plain,
% 0.48/0.55 (~selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2)))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[342, 53])).
% 0.48/0.55 tff(344,plain,
% 0.48/0.55 ($false),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[343, 341])).
% 0.48/0.55 tff(345,plain,(~(end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.55 tff(346,plain,
% 0.48/0.55 ((~![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)))))),
% 0.48/0.55 inference(quant_inst,[status(thm)],[])).
% 0.48/0.55 tff(347,plain,
% 0.48/0.55 (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))))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[346, 10])).
% 0.48/0.55 tff(348,plain,
% 0.48/0.55 (^[E: $i, T: $i] : refl((greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E))) <=> (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(349,plain,
% 0.48/0.55 (![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E))) <=> ![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[348])).
% 0.48/0.55 tff(350,plain,
% 0.48/0.55 (^[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) | (~in_environment(E, T)) | (~environment(E)))), (((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T)) <=> (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(351,plain,
% 0.48/0.55 (![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) | (~in_environment(E, T)) | (~environment(E)))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[350])).
% 0.48/0.55 tff(352,plain,
% 0.48/0.55 (![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))),
% 0.48/0.55 inference(rewrite,[status(thm)],[])).
% 0.48/0.55 tff(353,plain,
% 0.48/0.55 (^[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)))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(354,plain,
% 0.48/0.55 (![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))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[353])).
% 0.48/0.55 tff(355,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(end_time(E), T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_environment_end_point')).
% 0.48/0.55 tff(356,plain,
% 0.48/0.55 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.48/0.55 tff(357,plain,
% 0.48/0.55 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[356, 352])).
% 0.48/0.55 tff(358,plain,(
% 0.48/0.55 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.48/0.55 inference(skolemize,[status(sab)],[357])).
% 0.48/0.55 tff(359,plain,
% 0.48/0.55 (![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[358, 351])).
% 0.48/0.55 tff(360,plain,
% 0.48/0.55 (![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[359, 349])).
% 0.48/0.55 tff(361,plain,
% 0.48/0.55 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(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_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) | (~in_environment(E, T)) | (~environment(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_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.48/0.55 inference(rewrite,[status(thm)],[])).
% 0.48/0.55 tff(362,plain,
% 0.48/0.55 ((greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(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)))) <=> ((~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))))),
% 0.48/0.55 inference(rewrite,[status(thm)],[])).
% 0.48/0.55 tff(363,plain,
% 0.48/0.55 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(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))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(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_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.48/0.55 inference(monotonicity,[status(thm)],[362])).
% 0.48/0.55 tff(364,plain,
% 0.48/0.55 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(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))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(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_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.48/0.55 inference(transitivity,[status(thm)],[363, 361])).
% 0.48/0.55 tff(365,plain,
% 0.48/0.55 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(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))))),
% 0.48/0.55 inference(quant_inst,[status(thm)],[])).
% 0.48/0.55 tff(366,plain,
% 0.48/0.55 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(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_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.48/0.55 tff(367,plain,
% 0.48/0.55 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[366, 360, 55, 166])).
% 0.48/0.55 tff(368,plain,
% 0.48/0.55 ((~(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))))),
% 0.48/0.55 inference(tautology,[status(thm)],[])).
% 0.48/0.55 tff(369,plain,
% 0.48/0.55 ((~(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))))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[368, 367])).
% 0.48/0.55 tff(370,plain,
% 0.48/0.55 ((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)))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[369, 347])).
% 0.48/0.55 tff(371,plain,
% 0.48/0.55 ((~((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)))),
% 0.48/0.55 inference(tautology,[status(thm)],[])).
% 0.48/0.55 tff(372,plain,
% 0.48/0.55 ((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)))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[371, 370])).
% 0.48/0.55 tff(373,plain,
% 0.48/0.55 (greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[372, 345])).
% 0.48/0.55 tff(374,plain,
% 0.48/0.55 (((~![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(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)), 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(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)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.48/0.55 inference(rewrite,[status(thm)],[])).
% 0.48/0.55 tff(375,plain,
% 0.48/0.55 ((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(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)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.48/0.55 inference(rewrite,[status(thm)],[])).
% 0.48/0.55 tff(376,plain,
% 0.48/0.55 (((~![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(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)), appear(efficient_producers, tptp_fun_E_0(P!2)))))),
% 0.48/0.55 inference(monotonicity,[status(thm)],[375])).
% 0.48/0.55 tff(377,plain,
% 0.48/0.55 (((~![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(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)), appear(efficient_producers, tptp_fun_E_0(P!2))))),
% 0.48/0.55 inference(transitivity,[status(thm)],[376, 374])).
% 0.48/0.55 tff(378,plain,
% 0.48/0.55 ((~![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)))))),
% 0.48/0.56 inference(quant_inst,[status(thm)],[])).
% 0.48/0.56 tff(379,plain,
% 0.48/0.56 ((~![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(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)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.48/0.56 tff(380,plain,
% 0.48/0.56 (greater(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[379, 123, 373, 160])).
% 0.48/0.56 tff(381,plain,
% 0.48/0.56 (((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))))),
% 0.48/0.56 inference(tautology,[status(thm)],[])).
% 0.48/0.56 tff(382,plain,
% 0.48/0.56 ((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)))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[381, 380])).
% 0.48/0.56 tff(383,plain,
% 0.48/0.56 ((~(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)))))),
% 0.48/0.56 inference(tautology,[status(thm)],[])).
% 0.48/0.56 tff(384,plain,
% 0.48/0.56 ((~(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)))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[383, 382])).
% 0.48/0.56 tff(385,plain,
% 0.48/0.56 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[384, 80])).
% 0.48/0.56 tff(386,plain,
% 0.48/0.56 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | ((~environment(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)))) | 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)))))) <=> ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (~environment(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)))) | 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)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(387,plain,
% 0.48/0.56 ((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)))) | (~environment(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_or_equal(end_time(tptp_fun_E_0(P!2)), appear(efficient_producers, tptp_fun_E_0(P!2)))) | 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)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(388,plain,
% 0.48/0.56 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (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)))) | (~environment(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) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | ((~environment(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)))) | 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))))))),
% 0.48/0.56 inference(monotonicity,[status(thm)],[387])).
% 0.48/0.56 tff(389,plain,
% 0.48/0.56 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (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)))) | (~environment(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) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (~environment(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)))) | 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)))))),
% 0.48/0.56 inference(transitivity,[status(thm)],[388, 386])).
% 0.48/0.56 tff(390,plain,
% 0.48/0.56 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (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)))) | (~environment(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)))))),
% 0.48/0.56 inference(quant_inst,[status(thm)],[])).
% 0.48/0.56 tff(391,plain,
% 0.48/0.56 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~in_environment(E, T)) | (~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (~environment(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)))) | 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))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.48/0.56 tff(392,plain,
% 0.48/0.56 (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))))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[391, 213, 55, 385])).
% 0.48/0.56 tff(393,plain,
% 0.48/0.56 (greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[392, 15])).
% 0.48/0.56 tff(394,assumption,(subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.48/0.56 tff(395,assumption,(~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.48/0.56 tff(396,assumption,(greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.48/0.56 tff(397,plain,
% 0.48/0.56 (((~![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)), 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)))))) <=> ((~![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)), 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)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(398,plain,
% 0.48/0.56 ((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)), 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)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(399,plain,
% 0.48/0.56 (((~![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)), 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))))))),
% 0.48/0.56 inference(monotonicity,[status(thm)],[398])).
% 0.48/0.56 tff(400,plain,
% 0.48/0.56 (((~![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)), 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)))))),
% 0.48/0.56 inference(transitivity,[status(thm)],[399, 397])).
% 0.48/0.56 tff(401,plain,
% 0.48/0.56 ((~![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)))))),
% 0.48/0.56 inference(quant_inst,[status(thm)],[])).
% 0.48/0.56 tff(402,plain,
% 0.48/0.56 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.48/0.56 tff(403,plain,
% 0.48/0.56 ($false),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[402, 123, 111, 396, 395])).
% 0.48/0.56 tff(404,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.56 tff(405,plain,
% 0.48/0.56 (greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[404, 373])).
% 0.48/0.56 tff(406,plain,
% 0.48/0.56 (((~![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(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(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)))))) | (~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(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(407,plain,
% 0.48/0.56 ((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))))) <=> ((~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(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(408,plain,
% 0.48/0.56 (((~![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)))))) | ((~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(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))))),
% 0.48/0.56 inference(monotonicity,[status(thm)],[407])).
% 0.48/0.56 tff(409,plain,
% 0.48/0.56 (((~![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)))))) | (~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(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.56 inference(transitivity,[status(thm)],[408, 406])).
% 0.48/0.56 tff(410,plain,
% 0.48/0.56 ((~![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)))))),
% 0.48/0.56 inference(quant_inst,[status(thm)],[])).
% 0.48/0.56 tff(411,plain,
% 0.48/0.56 ((~![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(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(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.48/0.56 tff(412,plain,
% 0.48/0.56 ((~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))))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[411, 405, 311])).
% 0.48/0.56 tff(413,plain,
% 0.48/0.56 (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))))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[412, 394])).
% 0.48/0.56 tff(414,plain,
% 0.48/0.56 (((~![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))))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(415,plain,
% 0.48/0.56 ((~![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))))))),
% 0.48/0.56 inference(quant_inst,[status(thm)],[])).
% 0.48/0.56 tff(416,plain,
% 0.48/0.56 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(growth_rate(efficient_producers, end_time(tptp_fun_E_0(P!2))), growth_rate(first_movers, end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.48/0.56 tff(417,plain,
% 0.48/0.56 ($false),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[416, 332, 343, 55, 394, 413])).
% 0.48/0.56 tff(418,plain,(~subpopulations(first_movers, efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.56 tff(419,plain,
% 0.48/0.56 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | ((~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | subpopulations(first_movers, efficient_producers, 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)) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | subpopulations(first_movers, efficient_producers, 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)) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(420,plain,
% 0.48/0.56 ((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)))) | (~environment(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))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | subpopulations(first_movers, efficient_producers, 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)) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(421,plain,
% 0.48/0.56 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~environment(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) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | ((~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | subpopulations(first_movers, efficient_producers, 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)) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))))),
% 0.48/0.56 inference(monotonicity,[status(thm)],[420])).
% 0.48/0.56 tff(422,plain,
% 0.48/0.56 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~environment(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) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | subpopulations(first_movers, efficient_producers, 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)) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.56 inference(transitivity,[status(thm)],[421, 419])).
% 0.48/0.56 tff(423,plain,
% 0.48/0.56 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~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))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~environment(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)))),
% 0.48/0.56 inference(quant_inst,[status(thm)],[])).
% 0.48/0.56 tff(424,plain,
% 0.48/0.56 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)) | subpopulations(first_movers, efficient_producers, 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)) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.48/0.56 tff(425,plain,
% 0.48/0.56 ((~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)) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[424, 270, 55, 418])).
% 0.48/0.56 tff(426,plain,
% 0.48/0.56 (~greater(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))), zero)),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[425, 393, 15])).
% 0.48/0.56 tff(427,plain,
% 0.48/0.56 ((~((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)),
% 0.48/0.56 inference(tautology,[status(thm)],[])).
% 0.48/0.56 tff(428,plain,
% 0.48/0.56 ((~((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)),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[427, 426])).
% 0.48/0.56 tff(429,plain,
% 0.48/0.56 (cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[428, 78])).
% 0.48/0.56 tff(430,plain,
% 0.48/0.56 (((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(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)))))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(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)))))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(431,plain,
% 0.48/0.57 (((~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~environment(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))))))) <=> ((~environment(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)))))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(432,plain,
% 0.48/0.57 ((~((~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)))) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(433,plain,
% 0.48/0.57 (((~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~environment(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))))))) <=> ((~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~environment(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)))))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[432])).
% 0.48/0.57 tff(434,plain,
% 0.48/0.57 (((~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~environment(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))))))) <=> ((~environment(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)))))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.57 inference(transitivity,[status(thm)],[433, 431])).
% 0.48/0.57 tff(435,plain,
% 0.48/0.57 (((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, 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))) | (~((~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] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(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)))))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[434])).
% 0.48/0.57 tff(436,plain,
% 0.48/0.57 (((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, 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))) | (~((~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] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(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)))))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.57 inference(transitivity,[status(thm)],[435, 430])).
% 0.48/0.57 tff(437,plain,
% 0.48/0.57 ((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, 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))) | (~((~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)))))))),
% 0.48/0.57 inference(quant_inst,[status(thm)],[])).
% 0.48/0.57 tff(438,plain,
% 0.48/0.57 ((~![E: $i, T: $i] : ((~in_environment(E, T)) | (~environment(E)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(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)))))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.48/0.57 tff(439,plain,
% 0.48/0.57 (~((~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)))))),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[438, 179, 55, 15])).
% 0.48/0.57 tff(440,plain,
% 0.48/0.57 (((~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)))),
% 0.48/0.57 inference(tautology,[status(thm)],[])).
% 0.48/0.57 tff(441,plain,
% 0.48/0.57 (subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[440, 439])).
% 0.48/0.57 tff(442,plain,
% 0.48/0.57 (((~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)))),
% 0.48/0.57 inference(tautology,[status(thm)],[])).
% 0.48/0.57 tff(443,plain,
% 0.48/0.57 (subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[442, 439])).
% 0.48/0.57 tff(444,plain,
% 0.48/0.57 (((~![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))) | (~(cardinality_at_time(first_movers, 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)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(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)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~(cardinality_at_time(first_movers, 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)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(445,plain,
% 0.48/0.57 ((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))) | (~(cardinality_at_time(first_movers, 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)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(446,plain,
% 0.48/0.57 (((~![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))) | (~(cardinality_at_time(first_movers, 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)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[445])).
% 0.48/0.57 tff(447,plain,
% 0.48/0.57 (((~![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))) | (~(cardinality_at_time(first_movers, 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)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.57 inference(transitivity,[status(thm)],[446, 444])).
% 0.48/0.57 tff(448,plain,
% 0.48/0.57 ((~![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)))),
% 0.48/0.57 inference(quant_inst,[status(thm)],[])).
% 0.48/0.57 tff(449,plain,
% 0.48/0.57 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~(cardinality_at_time(first_movers, end_time(tptp_fun_E_0(P!2))) = zero)) | (~subpopulation(first_movers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))) | (~greater(cardinality_at_time(efficient_producers, end_time(tptp_fun_E_0(P!2))), zero)) | (~subpopulation(efficient_producers, tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.48/0.57 tff(450,plain,
% 0.48/0.57 ($false),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[449, 234, 343, 55, 393, 443, 441, 429])).
% 0.48/0.57 tff(451,plain,(~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.57 tff(452,assumption,(~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.48/0.57 tff(453,plain,
% 0.48/0.57 (((~![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))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(454,plain,
% 0.48/0.57 ((greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> $true) <=> greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(455,plain,
% 0.48/0.57 (($true | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))) <=> $true),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(456,plain,
% 0.48/0.57 ((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) <=> $true),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(457,plain,
% 0.48/0.57 (((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))) <=> ($true | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[456])).
% 0.48/0.57 tff(458,plain,
% 0.48/0.57 (((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),
% 0.48/0.57 inference(transitivity,[status(thm)],[457, 455])).
% 0.48/0.57 tff(459,plain,
% 0.48/0.57 ((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)),
% 0.48/0.57 inference(monotonicity,[status(thm)],[458])).
% 0.48/0.57 tff(460,plain,
% 0.48/0.57 ((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)))),
% 0.48/0.57 inference(transitivity,[status(thm)],[459, 454])).
% 0.48/0.57 tff(461,plain,
% 0.48/0.57 (((~![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))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[460])).
% 0.48/0.57 tff(462,plain,
% 0.48/0.57 (((~![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))))),
% 0.48/0.57 inference(transitivity,[status(thm)],[461, 453])).
% 0.48/0.57 tff(463,plain,
% 0.48/0.57 ((~![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)))))),
% 0.48/0.57 inference(quant_inst,[status(thm)],[])).
% 0.48/0.57 tff(464,plain,
% 0.48/0.57 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.48/0.57 tff(465,plain,
% 0.48/0.57 ($false),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[464, 10, 452])).
% 0.48/0.57 tff(466,plain,(greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.57 tff(467,plain,
% 0.48/0.57 (^[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))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(468,plain,
% 0.48/0.57 (![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)))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[467])).
% 0.48/0.57 tff(469,plain,
% 0.48/0.57 (^[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)))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(470,plain,
% 0.48/0.57 (![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)))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[469])).
% 0.48/0.57 tff(471,plain,
% 0.48/0.57 (![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))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(472,plain,
% 0.48/0.57 (^[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))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(473,plain,
% 0.48/0.57 (![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))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[472])).
% 0.48/0.57 tff(474,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/sandbox2/benchmark/theBenchmark.p','mp_time_in_environment')).
% 0.48/0.57 tff(475,plain,
% 0.48/0.57 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.48/0.57 tff(476,plain,
% 0.48/0.57 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[475, 471])).
% 0.48/0.57 tff(477,plain,(
% 0.48/0.57 ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.48/0.57 inference(skolemize,[status(sab)],[476])).
% 0.48/0.57 tff(478,plain,
% 0.48/0.57 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[477, 470])).
% 0.48/0.57 tff(479,plain,
% 0.48/0.57 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[478, 468])).
% 0.48/0.57 tff(480,plain,
% 0.48/0.57 (((~![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))) | (~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)))) | in_environment(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))) | (~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)))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(481,plain,
% 0.48/0.57 ((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))) | (~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)))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(482,plain,
% 0.48/0.57 (((~![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))) | (~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)))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[481])).
% 0.48/0.57 tff(483,plain,
% 0.48/0.57 (((~![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))) | (~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)))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.48/0.57 inference(transitivity,[status(thm)],[482, 480])).
% 0.48/0.57 tff(484,plain,
% 0.48/0.57 ((~![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)))))),
% 0.48/0.57 inference(quant_inst,[status(thm)],[])).
% 0.48/0.57 tff(485,plain,
% 0.48/0.57 ((~![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))) | (~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)))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.48/0.57 tff(486,plain,
% 0.48/0.57 ((~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), end_time(tptp_fun_E_0(P!2)))),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[485, 479, 55, 466])).
% 0.48/0.57 tff(487,plain,
% 0.48/0.57 (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[486, 451])).
% 0.48/0.57 tff(488,plain,
% 0.48/0.57 ((~(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)))))),
% 0.48/0.57 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(489,plain,
% 0.48/0.58 ((~(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)))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[488, 487])).
% 0.48/0.58 tff(490,plain,
% 0.48/0.58 (~((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))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[489, 12])).
% 0.48/0.58 tff(491,plain,
% 0.48/0.58 (((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))))),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(492,plain,
% 0.48/0.58 (~greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[491, 490])).
% 0.48/0.58 tff(493,assumption,(greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.48/0.58 tff(494,plain,
% 0.48/0.58 (((~![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))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(495,plain,
% 0.48/0.58 ((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))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(496,plain,
% 0.48/0.58 (((~![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)))))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[495])).
% 0.48/0.58 tff(497,plain,
% 0.48/0.58 (((~![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))))),
% 0.48/0.58 inference(transitivity,[status(thm)],[496, 494])).
% 0.48/0.58 tff(498,plain,
% 0.48/0.58 ((~![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)))))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(499,plain,
% 0.48/0.58 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.48/0.58 tff(500,plain,
% 0.48/0.58 ($false),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[499, 123, 493, 405, 492])).
% 0.48/0.58 tff(501,plain,(~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.58 tff(502,plain,
% 0.48/0.58 ((~![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)))))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(503,plain,
% 0.48/0.58 (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))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[502, 10])).
% 0.48/0.58 tff(504,plain,
% 0.48/0.58 (^[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))))),
% 0.48/0.58 inference(bind,[status(th)],[])).
% 0.48/0.58 tff(505,plain,
% 0.48/0.58 (![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)))),
% 0.48/0.58 inference(quant_intro,[status(thm)],[504])).
% 0.48/0.58 tff(506,plain,
% 0.48/0.58 (![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)))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(507,plain,
% 0.48/0.58 (^[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))))),
% 0.48/0.58 inference(bind,[status(th)],[])).
% 0.48/0.58 tff(508,plain,
% 0.48/0.58 (![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)))),
% 0.48/0.58 inference(quant_intro,[status(thm)],[507])).
% 0.48/0.58 tff(509,axiom,(![E: $i] : (environment(E) => greater_or_equal(critical_point(E), start_time(E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_time_of_critical_point')).
% 0.48/0.58 tff(510,plain,
% 0.48/0.58 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.48/0.58 tff(511,plain,
% 0.48/0.58 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[510, 506])).
% 0.48/0.58 tff(512,plain,(
% 0.48/0.58 ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.48/0.58 inference(skolemize,[status(sab)],[511])).
% 0.48/0.58 tff(513,plain,
% 0.48/0.58 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[512, 505])).
% 0.48/0.58 tff(514,plain,
% 0.48/0.58 (((~![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))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(515,plain,
% 0.48/0.58 ((~![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))))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(516,plain,
% 0.48/0.58 ((~![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)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.48/0.58 tff(517,plain,
% 0.48/0.58 (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[516, 513, 55])).
% 0.48/0.58 tff(518,plain,
% 0.48/0.58 ((~(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))))),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(519,plain,
% 0.48/0.58 ((~(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))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[518, 517])).
% 0.48/0.58 tff(520,plain,
% 0.48/0.58 ((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)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[519, 503])).
% 0.48/0.58 tff(521,plain,
% 0.48/0.58 ((~((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)))),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(522,plain,
% 0.48/0.58 ((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)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[521, 520])).
% 0.48/0.58 tff(523,plain,
% 0.48/0.58 (critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[522, 501])).
% 0.48/0.58 tff(524,plain,
% 0.48/0.58 (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)))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[523])).
% 0.48/0.58 tff(525,plain,
% 0.48/0.58 (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)))),
% 0.48/0.58 inference(symmetry,[status(thm)],[524])).
% 0.48/0.58 tff(526,plain,
% 0.48/0.58 ((~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))))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[525])).
% 0.48/0.58 tff(527,plain,
% 0.48/0.58 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(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))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(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))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(528,plain,
% 0.48/0.58 ((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)))) | (~environment(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)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(529,plain,
% 0.48/0.58 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (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)))) | (~environment(tptp_fun_E_0(P!2))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | ((~environment(tptp_fun_E_0(P!2))) | (~in_environment(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)))))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[528])).
% 0.48/0.58 tff(530,plain,
% 0.48/0.58 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (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)))) | (~environment(tptp_fun_E_0(P!2))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(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))))),
% 0.48/0.58 inference(transitivity,[status(thm)],[529, 527])).
% 0.48/0.58 tff(531,plain,
% 0.48/0.58 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (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)))) | (~environment(tptp_fun_E_0(P!2))))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(532,plain,
% 0.48/0.58 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(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)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.48/0.58 tff(533,plain,
% 0.48/0.58 (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[532, 360, 55, 487])).
% 0.48/0.58 tff(534,plain,
% 0.48/0.58 (~in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[533, 526])).
% 0.48/0.58 tff(535,plain,
% 0.48/0.58 ((~![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)))))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(536,plain,
% 0.48/0.58 (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))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[535, 10])).
% 0.48/0.58 tff(537,assumption,(~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.48/0.58 tff(538,plain,
% 0.48/0.58 ((~(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)))))),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(539,plain,
% 0.48/0.58 ((~(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)))))) | (~((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)))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[538, 537])).
% 0.48/0.58 tff(540,plain,
% 0.48/0.58 (~((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))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[539, 536])).
% 0.48/0.58 tff(541,plain,
% 0.48/0.58 (((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))))),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(542,plain,
% 0.48/0.58 (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[541, 540])).
% 0.48/0.58 tff(543,plain,
% 0.48/0.58 (~greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[404, 542])).
% 0.48/0.58 tff(544,plain,
% 0.48/0.58 (end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[372, 543])).
% 0.48/0.58 tff(545,plain,
% 0.48/0.58 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[544])).
% 0.48/0.58 tff(546,plain,
% 0.48/0.58 (greater_or_equal(tptp_fun_T_1(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)))),
% 0.48/0.58 inference(symmetry,[status(thm)],[545])).
% 0.48/0.58 tff(547,plain,
% 0.48/0.58 ((~![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)), critical_point(tptp_fun_E_0(P!2))) <=> ((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)))))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(548,plain,
% 0.48/0.58 (greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> ((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))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[547, 10])).
% 0.48/0.58 tff(549,plain,
% 0.48/0.58 (((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(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(550,plain,
% 0.48/0.58 ((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)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[549, 111])).
% 0.48/0.58 tff(551,plain,
% 0.48/0.58 ((~(greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> ((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_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) | (~((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)))))),
% 0.48/0.58 inference(tautology,[status(thm)],[])).
% 0.48/0.58 tff(552,plain,
% 0.48/0.58 ((~(greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> ((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_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[551, 550])).
% 0.48/0.58 tff(553,plain,
% 0.48/0.58 (greater_or_equal(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[552, 548])).
% 0.48/0.58 tff(554,plain,
% 0.48/0.58 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[553, 546])).
% 0.48/0.58 tff(555,plain,
% 0.48/0.58 ($false),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[537, 554])).
% 0.48/0.58 tff(556,plain,(greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.58 tff(557,plain,
% 0.48/0.58 (((~![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)))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(558,plain,
% 0.48/0.58 ((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)))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(559,plain,
% 0.48/0.58 (((~![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))))))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[558])).
% 0.48/0.58 tff(560,plain,
% 0.48/0.58 (((~![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)))))),
% 0.48/0.58 inference(transitivity,[status(thm)],[559, 557])).
% 0.48/0.58 tff(561,plain,
% 0.48/0.58 ((~![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)))))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(562,plain,
% 0.48/0.58 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.48/0.58 tff(563,plain,
% 0.48/0.58 (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[562, 479, 55, 517])).
% 0.48/0.58 tff(564,plain,
% 0.48/0.58 (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[563, 556])).
% 0.48/0.58 tff(565,plain,
% 0.48/0.58 ($false),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[564, 534])).
% 0.48/0.58 % SZS output end Proof
%------------------------------------------------------------------------------