TSTP Solution File: MGT039+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT039+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 05:22:07 EDT 2022
% Result : Theorem 0.15s 0.34s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : MGT039+1 : TPTP v8.1.0. Released v2.0.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n021.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri Sep 2 02:45:43 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.15/0.34 % SZS status Theorem
% 0.15/0.34 % SZS output start Proof
% 0.15/0.34 tff(in_environment_type, type, (
% 0.15/0.34 in_environment: ( $i * $i ) > $o)).
% 0.15/0.34 tff(critical_point_type, type, (
% 0.15/0.34 critical_point: $i > $i)).
% 0.15/0.34 tff(tptp_fun_E_0_type, type, (
% 0.15/0.34 tptp_fun_E_0: $i > $i)).
% 0.15/0.34 tff(tptp_fun_P_2_type, type, (
% 0.15/0.34 tptp_fun_P_2: $i)).
% 0.15/0.34 tff(start_time_type, type, (
% 0.15/0.34 start_time: $i > $i)).
% 0.15/0.34 tff(greater_type, type, (
% 0.15/0.34 greater: ( $i * $i ) > $o)).
% 0.15/0.34 tff(end_time_type, type, (
% 0.15/0.34 end_time: $i > $i)).
% 0.15/0.34 tff(greater_or_equal_type, type, (
% 0.15/0.34 greater_or_equal: ( $i * $i ) > $o)).
% 0.15/0.34 tff(tptp_fun_T_1_type, type, (
% 0.15/0.34 tptp_fun_T_1: $i > $i)).
% 0.15/0.34 tff(selection_favors_type, type, (
% 0.15/0.34 selection_favors: ( $i * $i * $i ) > $o)).
% 0.15/0.34 tff(first_movers_type, type, (
% 0.15/0.34 first_movers: $i)).
% 0.15/0.34 tff(efficient_producers_type, type, (
% 0.15/0.34 efficient_producers: $i)).
% 0.15/0.34 tff(environment_type, type, (
% 0.15/0.34 environment: $i > $o)).
% 0.15/0.34 tff(slow_change_type, type, (
% 0.15/0.34 slow_change: $i > $o)).
% 0.15/0.34 tff(observational_period_type, type, (
% 0.15/0.34 observational_period: $i > $o)).
% 0.15/0.34 tff(propagation_strategy_type, type, (
% 0.15/0.34 propagation_strategy: $i > $o)).
% 0.15/0.34 tff(1,plain,
% 0.15/0.34 (^[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))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(2,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.34 tff(3,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(4,plain,
% 0.15/0.34 (^[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))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(5,plain,
% 0.15/0.34 (![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)))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[4])).
% 0.15/0.34 tff(6,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal')).
% 0.15/0.34 tff(7,plain,
% 0.15/0.34 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.15/0.34 tff(8,plain,
% 0.15/0.34 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.15/0.34 tff(9,plain,(
% 0.15/0.34 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.15/0.34 inference(skolemize,[status(sab)],[8])).
% 0.15/0.34 tff(10,plain,
% 0.15/0.34 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.15/0.34 tff(11,plain,
% 0.15/0.34 ((~![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)))))),
% 0.15/0.34 inference(quant_inst,[status(thm)],[])).
% 0.15/0.34 tff(12,plain,
% 0.15/0.34 (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))))),
% 0.15/0.34 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.15/0.34 tff(13,assumption,(~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.15/0.34 tff(14,plain,
% 0.15/0.34 (((~![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))))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(15,plain,
% 0.15/0.34 ((greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))) <=> $true) <=> greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(16,plain,
% 0.15/0.35 (($true | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))) <=> $true),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(17,plain,
% 0.15/0.35 ((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) <=> $true),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(18,plain,
% 0.15/0.35 (((end_time(tptp_fun_E_0(P!2)) = end_time(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))) <=> ($true | greater(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))),
% 0.15/0.35 inference(monotonicity,[status(thm)],[17])).
% 0.15/0.35 tff(19,plain,
% 0.15/0.35 (((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),
% 0.15/0.35 inference(transitivity,[status(thm)],[18, 16])).
% 0.15/0.35 tff(20,plain,
% 0.15/0.35 ((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)),
% 0.15/0.35 inference(monotonicity,[status(thm)],[19])).
% 0.15/0.35 tff(21,plain,
% 0.15/0.35 ((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)))),
% 0.15/0.35 inference(transitivity,[status(thm)],[20, 15])).
% 0.15/0.35 tff(22,plain,
% 0.15/0.35 (((~![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))))),
% 0.15/0.35 inference(monotonicity,[status(thm)],[21])).
% 0.15/0.35 tff(23,plain,
% 0.15/0.35 (((~![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))))),
% 0.15/0.35 inference(transitivity,[status(thm)],[22, 14])).
% 0.15/0.35 tff(24,plain,
% 0.15/0.35 ((~![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)))))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(25,plain,
% 0.15/0.35 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.15/0.35 tff(26,plain,
% 0.15/0.35 ($false),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[25, 10, 13])).
% 0.15/0.35 tff(27,plain,(greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.35 tff(28,assumption,(end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2))), introduced(assumption)).
% 0.15/0.35 tff(29,plain,
% 0.15/0.35 (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)))),
% 0.15/0.35 inference(monotonicity,[status(thm)],[28])).
% 0.15/0.35 tff(30,plain,
% 0.15/0.35 (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)))),
% 0.15/0.35 inference(symmetry,[status(thm)],[29])).
% 0.15/0.35 tff(31,plain,
% 0.15/0.35 ((~![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)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(32,plain,
% 0.15/0.35 ((~![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)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(33,axiom,(~![P: $i] : ((observational_period(P) & slow_change(P)) => selection_favors(efficient_producers, first_movers, P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t8')).
% 0.15/0.35 tff(34,plain,
% 0.15/0.35 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.15/0.35 tff(35,plain,
% 0.15/0.35 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.15/0.35 tff(36,plain,
% 0.15/0.35 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.15/0.35 tff(37,plain,
% 0.15/0.35 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.15/0.35 tff(38,plain,
% 0.15/0.35 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.15/0.35 tff(39,plain,
% 0.15/0.35 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.15/0.35 tff(40,plain,
% 0.15/0.35 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.15/0.35 tff(41,plain,
% 0.15/0.35 (~![P: $i] : ((~(observational_period(P) & slow_change(P))) | selection_favors(efficient_producers, first_movers, P))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[40, 31])).
% 0.15/0.35 tff(42,plain,(
% 0.15/0.35 ~((~(observational_period(P!2) & slow_change(P!2))) | selection_favors(efficient_producers, first_movers, P!2))),
% 0.15/0.35 inference(skolemize,[status(sab)],[41])).
% 0.15/0.35 tff(43,plain,
% 0.15/0.35 (observational_period(P!2) & slow_change(P!2)),
% 0.15/0.35 inference(or_elim,[status(thm)],[42])).
% 0.15/0.35 tff(44,plain,
% 0.15/0.35 (slow_change(P!2)),
% 0.15/0.35 inference(and_elim,[status(thm)],[43])).
% 0.15/0.35 tff(45,plain,
% 0.15/0.35 (observational_period(P!2)),
% 0.15/0.35 inference(and_elim,[status(thm)],[43])).
% 0.15/0.35 tff(46,plain,
% 0.15/0.35 (^[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))))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(47,plain,
% 0.15/0.35 (![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)))))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[46])).
% 0.15/0.35 tff(48,plain,
% 0.15/0.35 (^[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))))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(49,plain,
% 0.15/0.35 (![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)))))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[48])).
% 0.15/0.35 tff(50,plain,
% 0.15/0.35 (![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)))))))),
% 0.15/0.35 inference(transitivity,[status(thm)],[49, 47])).
% 0.15/0.35 tff(51,plain,
% 0.15/0.35 (^[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)))))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(52,plain,
% 0.15/0.35 (![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)))))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[51])).
% 0.15/0.35 tff(53,plain,
% 0.15/0.35 (![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)))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(54,plain,
% 0.15/0.35 (^[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)))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(55,plain,
% 0.15/0.35 (![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)))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[54])).
% 0.15/0.35 tff(56,axiom,(![P: $i] : ((observational_period(P) & slow_change(P)) => ![E: $i] : ((environment(E) & in_environment(P, E)) => ?[T: $i] : (in_environment(E, T) & greater(T, critical_point(E)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp4_critical_point')).
% 0.15/0.35 tff(57,plain,
% 0.15/0.35 (![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)))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.15/0.35 tff(58,plain,
% 0.15/0.35 (![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)))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.15/0.35 tff(59,plain,(
% 0.15/0.35 ![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)))))),
% 0.15/0.35 inference(skolemize,[status(sab)],[58])).
% 0.15/0.35 tff(60,plain,
% 0.15/0.35 (![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)))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.15/0.35 tff(61,plain,
% 0.15/0.35 (![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)))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.15/0.35 tff(62,plain,
% 0.15/0.35 (((~![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)))))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(63,plain,
% 0.15/0.35 ((~![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)))))))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(64,plain,
% 0.15/0.35 ((~![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))))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.15/0.35 tff(65,plain,
% 0.15/0.35 (![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))))))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[64, 61, 45, 44])).
% 0.15/0.35 tff(66,plain,
% 0.15/0.35 (~selection_favors(efficient_producers, first_movers, P!2)),
% 0.15/0.35 inference(or_elim,[status(thm)],[42])).
% 0.15/0.35 tff(67,plain,
% 0.15/0.35 (^[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)))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(68,plain,
% 0.15/0.35 (![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))))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[67])).
% 0.15/0.35 tff(69,plain,
% 0.15/0.35 (^[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))))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(70,plain,
% 0.15/0.35 (![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))))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[69])).
% 0.15/0.35 tff(71,plain,
% 0.15/0.35 (^[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)))))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(72,plain,
% 0.15/0.35 (![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))))))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[71])).
% 0.15/0.35 tff(73,plain,
% 0.15/0.35 (![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))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(74,plain,
% 0.15/0.35 (^[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)))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(75,plain,
% 0.15/0.35 (![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))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[74])).
% 0.15/0.35 tff(76,plain,
% 0.15/0.35 (^[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))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(77,plain,
% 0.15/0.36 (![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))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[76])).
% 0.15/0.36 tff(78,axiom,(![P: $i] : ((((observational_period(P) & propagation_strategy(first_movers)) & propagation_strategy(efficient_producers)) & ![E: $i] : ((environment(E) & in_environment(P, E)) => selection_favors(efficient_producers, first_movers, end_time(E)))) => selection_favors(efficient_producers, first_movers, P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp3_favoured_trategy')).
% 0.15/0.36 tff(79,plain,
% 0.15/0.36 (![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))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.15/0.36 tff(80,plain,
% 0.15/0.36 (![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))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.15/0.36 tff(81,plain,
% 0.15/0.36 (![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))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.15/0.36 tff(82,plain,(
% 0.15/0.36 ![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))),
% 0.15/0.36 inference(skolemize,[status(sab)],[81])).
% 0.15/0.36 tff(83,plain,
% 0.15/0.36 (![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))))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.15/0.36 tff(84,plain,
% 0.15/0.36 (![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))))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[83, 70])).
% 0.15/0.36 tff(85,plain,
% 0.15/0.36 (![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))))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[84, 68])).
% 0.15/0.36 tff(86,plain,
% 0.15/0.36 (((~![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))))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(87,plain,
% 0.15/0.36 ((~![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))))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(88,plain,
% 0.15/0.36 ((~![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)))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.15/0.36 tff(89,plain,
% 0.15/0.36 (~(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))))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[88, 85, 45, 66])).
% 0.15/0.36 tff(90,plain,
% 0.15/0.36 ((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))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(91,plain,
% 0.15/0.36 (in_environment(P!2, tptp_fun_E_0(P!2))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.15/0.36 tff(92,plain,
% 0.15/0.36 ((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))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(93,plain,
% 0.15/0.36 (environment(tptp_fun_E_0(P!2))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.15/0.36 tff(94,plain,
% 0.15/0.36 (((~![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)))))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(95,plain,
% 0.15/0.36 ((~![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)))))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(96,plain,
% 0.15/0.36 ((~![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))))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.15/0.36 tff(97,plain,
% 0.15/0.36 (~((~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)))))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[96, 93, 91, 65])).
% 0.15/0.36 tff(98,plain,
% 0.15/0.36 (((~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)))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(99,plain,
% 0.15/0.36 (greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.15/0.36 tff(100,plain,
% 0.15/0.36 (((~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)))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(101,plain,
% 0.15/0.36 (in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.15/0.36 tff(102,plain,
% 0.15/0.36 (^[E: $i, T: $i] : refl((selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E)))) <=> (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E)))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(103,plain,
% 0.15/0.36 (![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E)))) <=> ![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[102])).
% 0.15/0.36 tff(104,plain,
% 0.15/0.36 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(T, critical_point(E))) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(T, critical_point(E)))))), ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(T, critical_point(E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(T, critical_point(E)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(T, critical_point(E))))), ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(T, critical_point(E)))))), (((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)) <=> (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))), (((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)) <=> (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(105,plain,
% 0.15/0.36 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)) <=> ![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[104])).
% 0.15/0.36 tff(106,plain,
% 0.15/0.36 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(107,plain,
% 0.15/0.36 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) <=> (environment(E) & in_environment(E, T) & greater(T, critical_point(E)))), ((((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T)) <=> ((environment(E) & in_environment(E, T) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T)))), rewrite(((environment(E) & in_environment(E, T) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T)) <=> ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))), ((((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T)) <=> ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(108,plain,
% 0.15/0.36 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[107])).
% 0.15/0.36 tff(109,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l8')).
% 0.15/0.36 tff(110,plain,
% 0.15/0.36 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.15/0.36 tff(111,plain,
% 0.15/0.36 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.15/0.36 tff(112,plain,(
% 0.15/0.36 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.15/0.36 inference(skolemize,[status(sab)],[111])).
% 0.15/0.36 tff(113,plain,
% 0.15/0.36 (![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.15/0.36 tff(114,plain,
% 0.15/0.36 (![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.15/0.36 tff(115,plain,
% 0.15/0.36 (((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(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(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))) <=> ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(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(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(116,plain,
% 0.15/0.36 ((selection_favors(efficient_producers, first_movers, 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(tptp_fun_T_1(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), 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)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(117,plain,
% 0.15/0.36 (((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (selection_favors(efficient_producers, first_movers, 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(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(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(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))))),
% 0.15/0.36 inference(monotonicity,[status(thm)],[116])).
% 0.15/0.36 tff(118,plain,
% 0.15/0.36 (((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (selection_favors(efficient_producers, first_movers, 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(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(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(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[117, 115])).
% 0.15/0.37 tff(119,plain,
% 0.15/0.37 ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (selection_favors(efficient_producers, first_movers, 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(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(120,plain,
% 0.15/0.37 ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), tptp_fun_T_1(tptp_fun_E_0(P!2)))) | (~greater(tptp_fun_T_1(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.15/0.37 tff(121,plain,
% 0.15/0.37 (selection_favors(efficient_producers, first_movers, tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[120, 114, 93, 101, 99])).
% 0.15/0.37 tff(122,plain,
% 0.15/0.37 (selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[121, 30])).
% 0.15/0.37 tff(123,plain,
% 0.15/0.37 ((selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~in_environment(P!2, tptp_fun_E_0(P!2)))) | (~selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))))),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(124,plain,
% 0.15/0.37 (~selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[123, 89])).
% 0.15/0.37 tff(125,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[124, 122])).
% 0.15/0.37 tff(126,plain,(~(end_time(tptp_fun_E_0(P!2)) = tptp_fun_T_1(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(127,plain,
% 0.15/0.37 ((~![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)))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(128,plain,
% 0.15/0.37 (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))))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[127, 10])).
% 0.15/0.37 tff(129,plain,
% 0.15/0.37 (^[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))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(130,plain,
% 0.15/0.37 (![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)))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[129])).
% 0.15/0.37 tff(131,plain,
% 0.15/0.37 (^[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)))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(132,plain,
% 0.15/0.37 (![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)))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[131])).
% 0.15/0.37 tff(133,plain,
% 0.15/0.37 (![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))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(134,plain,
% 0.15/0.37 (^[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)))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(135,plain,
% 0.15/0.37 (![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))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[134])).
% 0.15/0.37 tff(136,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(end_time(E), T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_environment_end_point')).
% 0.15/0.37 tff(137,plain,
% 0.15/0.37 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.15/0.37 tff(138,plain,
% 0.15/0.37 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.15/0.37 tff(139,plain,(
% 0.15/0.37 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(end_time(E), T))),
% 0.15/0.37 inference(skolemize,[status(sab)],[138])).
% 0.15/0.37 tff(140,plain,
% 0.15/0.37 (![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.15/0.37 tff(141,plain,
% 0.15/0.37 (![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.15/0.37 tff(142,plain,
% 0.15/0.37 (((~![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))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(143,plain,
% 0.15/0.37 ((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))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(144,plain,
% 0.15/0.37 (((~![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)))))),
% 0.15/0.37 inference(monotonicity,[status(thm)],[143])).
% 0.15/0.37 tff(145,plain,
% 0.15/0.37 (((~![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))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[144, 142])).
% 0.15/0.37 tff(146,plain,
% 0.15/0.37 ((~![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))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(147,plain,
% 0.15/0.37 ((~![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)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.15/0.37 tff(148,plain,
% 0.15/0.37 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[147, 141, 93, 101])).
% 0.15/0.37 tff(149,plain,
% 0.15/0.37 ((~(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))))),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(150,plain,
% 0.15/0.37 ((~(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))))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.15/0.37 tff(151,plain,
% 0.15/0.37 ((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)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[150, 128])).
% 0.15/0.37 tff(152,plain,
% 0.15/0.37 ((~((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)))),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(153,plain,
% 0.15/0.37 ((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)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.15/0.37 tff(154,plain,
% 0.15/0.37 (greater(end_time(tptp_fun_E_0(P!2)), tptp_fun_T_1(tptp_fun_E_0(P!2)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[153, 126])).
% 0.15/0.37 tff(155,plain,
% 0.15/0.37 (![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)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(156,plain,
% 0.15/0.37 (^[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)))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(157,plain,
% 0.15/0.37 (![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)))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[156])).
% 0.15/0.37 tff(158,plain,
% 0.15/0.37 (![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))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(159,plain,
% 0.15/0.37 (^[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)))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(160,plain,
% 0.15/0.37 (![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))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[159])).
% 0.15/0.37 tff(161,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_transitivity')).
% 0.15/0.37 tff(162,plain,
% 0.15/0.37 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.15/0.37 tff(163,plain,
% 0.15/0.37 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.15/0.37 tff(164,plain,(
% 0.15/0.37 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.15/0.37 inference(skolemize,[status(sab)],[163])).
% 0.15/0.37 tff(165,plain,
% 0.15/0.37 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.15/0.37 tff(166,plain,
% 0.15/0.37 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[165, 155])).
% 0.15/0.37 tff(167,plain,
% 0.15/0.37 (((~![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)))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(168,plain,
% 0.15/0.37 ((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)))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(169,plain,
% 0.15/0.37 (((~![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))))))),
% 0.15/0.37 inference(monotonicity,[status(thm)],[168])).
% 0.15/0.37 tff(170,plain,
% 0.15/0.37 (((~![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)))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[169, 167])).
% 0.15/0.37 tff(171,plain,
% 0.15/0.37 ((~![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)))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(172,plain,
% 0.15/0.37 ((~![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))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.15/0.37 tff(173,plain,
% 0.15/0.37 (greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[172, 166, 99, 154])).
% 0.15/0.37 tff(174,plain,
% 0.15/0.37 (((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(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] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(175,plain,
% 0.15/0.37 ((selection_favors(efficient_producers, first_movers, 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(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))) <=> (selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(176,plain,
% 0.15/0.37 (((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (selection_favors(efficient_producers, first_movers, 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(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))))),
% 0.15/0.38 inference(monotonicity,[status(thm)],[175])).
% 0.15/0.38 tff(177,plain,
% 0.15/0.38 (((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (selection_favors(efficient_producers, first_movers, 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(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.38 inference(transitivity,[status(thm)],[176, 174])).
% 0.15/0.38 tff(178,plain,
% 0.15/0.38 ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | (selection_favors(efficient_producers, first_movers, 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(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(179,plain,
% 0.15/0.38 ((~![E: $i, T: $i] : (selection_favors(efficient_producers, first_movers, T) | (~in_environment(E, T)) | (~environment(E)) | (~greater(T, critical_point(E))))) | selection_favors(efficient_producers, first_movers, end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.15/0.38 tff(180,plain,
% 0.15/0.38 (~in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2)))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[179, 114, 124, 93, 173])).
% 0.15/0.38 tff(181,plain,
% 0.15/0.38 (^[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))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(182,plain,
% 0.15/0.38 (![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)))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[181])).
% 0.15/0.38 tff(183,plain,
% 0.15/0.38 (^[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)))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(184,plain,
% 0.15/0.38 (![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)))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[183])).
% 0.15/0.38 tff(185,plain,
% 0.15/0.38 (![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))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(186,plain,
% 0.15/0.38 (^[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))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(187,plain,
% 0.15/0.38 (![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))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[186])).
% 0.15/0.38 tff(188,axiom,(![E: $i, T: $i] : (((environment(E) & greater_or_equal(T, start_time(E))) & greater_or_equal(end_time(E), T)) => in_environment(E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_time_in_environment')).
% 0.15/0.38 tff(189,plain,
% 0.15/0.38 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.15/0.38 tff(190,plain,
% 0.15/0.38 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.15/0.38 tff(191,plain,(
% 0.15/0.38 ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, start_time(E)) & greater_or_equal(end_time(E), T))) | in_environment(E, T))),
% 0.15/0.38 inference(skolemize,[status(sab)],[190])).
% 0.15/0.38 tff(192,plain,
% 0.15/0.38 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.15/0.38 tff(193,plain,
% 0.15/0.38 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[192, 182])).
% 0.15/0.38 tff(194,plain,
% 0.15/0.38 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(195,plain,
% 0.15/0.38 ((in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))) <=> ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(196,plain,
% 0.15/0.38 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | ((~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))))),
% 0.15/0.38 inference(monotonicity,[status(thm)],[195])).
% 0.15/0.38 tff(197,plain,
% 0.15/0.38 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~environment(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.38 inference(transitivity,[status(thm)],[196, 194])).
% 0.15/0.38 tff(198,plain,
% 0.15/0.38 ((~![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)))))),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(199,plain,
% 0.15/0.38 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), end_time(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), end_time(tptp_fun_E_0(P!2))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.15/0.38 tff(200,plain,
% 0.15/0.38 ((~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))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[199, 193, 93, 180])).
% 0.15/0.38 tff(201,plain,
% 0.15/0.38 (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[200, 27])).
% 0.15/0.38 tff(202,plain,
% 0.15/0.38 ((~(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)))))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(203,plain,
% 0.15/0.38 ((~(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)))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.15/0.38 tff(204,plain,
% 0.15/0.38 (~((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))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[203, 12])).
% 0.15/0.38 tff(205,plain,
% 0.15/0.38 (((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))))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(206,plain,
% 0.15/0.38 (~greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.15/0.38 tff(207,assumption,(greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), introduced(assumption)).
% 0.15/0.38 tff(208,plain,
% 0.15/0.38 (((~![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))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(209,plain,
% 0.15/0.38 ((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))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(210,plain,
% 0.15/0.38 (((~![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)))))),
% 0.15/0.38 inference(monotonicity,[status(thm)],[209])).
% 0.15/0.38 tff(211,plain,
% 0.15/0.38 (((~![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))))),
% 0.15/0.38 inference(transitivity,[status(thm)],[210, 208])).
% 0.15/0.38 tff(212,plain,
% 0.15/0.38 ((~![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)))))),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(213,plain,
% 0.15/0.38 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))) | greater(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.15/0.38 tff(214,plain,
% 0.15/0.38 ($false),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[213, 166, 207, 173, 206])).
% 0.15/0.38 tff(215,plain,(~greater(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.38 tff(216,plain,
% 0.15/0.38 ((~![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)))))),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(217,plain,
% 0.15/0.38 (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))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[216, 10])).
% 0.15/0.38 tff(218,plain,
% 0.15/0.38 (^[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))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(219,plain,
% 0.15/0.38 (![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)))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[218])).
% 0.15/0.38 tff(220,plain,
% 0.15/0.38 (![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)))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(221,plain,
% 0.15/0.38 (^[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))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(222,plain,
% 0.15/0.38 (![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)))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[221])).
% 0.15/0.38 tff(223,axiom,(![E: $i] : (environment(E) => greater_or_equal(critical_point(E), start_time(E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_time_of_critical_point')).
% 0.15/0.38 tff(224,plain,
% 0.15/0.38 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.15/0.38 tff(225,plain,
% 0.15/0.38 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.15/0.39 tff(226,plain,(
% 0.15/0.39 ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.15/0.39 inference(skolemize,[status(sab)],[225])).
% 0.15/0.39 tff(227,plain,
% 0.15/0.39 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), start_time(E)))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.15/0.39 tff(228,plain,
% 0.15/0.39 (((~![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))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(229,plain,
% 0.15/0.39 ((~![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))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(230,plain,
% 0.15/0.39 ((~![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)))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.15/0.39 tff(231,plain,
% 0.15/0.39 (greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[230, 227, 93])).
% 0.15/0.39 tff(232,plain,
% 0.15/0.39 ((~(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))))),
% 0.15/0.39 inference(tautology,[status(thm)],[])).
% 0.15/0.39 tff(233,plain,
% 0.15/0.39 ((~(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))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.15/0.39 tff(234,plain,
% 0.15/0.39 ((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)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[233, 217])).
% 0.15/0.39 tff(235,plain,
% 0.15/0.39 ((~((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)))),
% 0.15/0.39 inference(tautology,[status(thm)],[])).
% 0.15/0.39 tff(236,plain,
% 0.15/0.39 ((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)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.15/0.39 tff(237,plain,
% 0.15/0.39 (critical_point(tptp_fun_E_0(P!2)) = start_time(tptp_fun_E_0(P!2))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[236, 215])).
% 0.15/0.39 tff(238,plain,
% 0.15/0.39 (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)))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[237])).
% 0.15/0.39 tff(239,plain,
% 0.15/0.39 (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)))),
% 0.15/0.39 inference(symmetry,[status(thm)],[238])).
% 0.15/0.39 tff(240,plain,
% 0.15/0.39 ((~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))))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[239])).
% 0.15/0.39 tff(241,plain,
% 0.15/0.39 (((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | ((~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(242,plain,
% 0.15/0.39 ((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))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(243,plain,
% 0.15/0.39 (((~![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))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2))))))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[242])).
% 0.15/0.39 tff(244,plain,
% 0.15/0.39 (((~![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))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[243, 241])).
% 0.15/0.39 tff(245,plain,
% 0.15/0.39 ((~![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))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(246,plain,
% 0.15/0.39 ((~![E: $i, T: $i] : (greater_or_equal(end_time(E), T) | (~in_environment(E, T)) | (~environment(E)))) | (~environment(tptp_fun_E_0(P!2))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2))) | (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.15/0.39 tff(247,plain,
% 0.15/0.39 (~in_environment(tptp_fun_E_0(P!2), start_time(tptp_fun_E_0(P!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[246, 141, 93, 201])).
% 0.15/0.39 tff(248,plain,
% 0.15/0.39 (~in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2)))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[247, 240])).
% 0.15/0.39 tff(249,plain,
% 0.15/0.39 ((~![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)))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(250,plain,
% 0.15/0.39 (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))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[249, 10])).
% 0.15/0.39 tff(251,plain,
% 0.15/0.39 (((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))))),
% 0.15/0.39 inference(tautology,[status(thm)],[])).
% 0.15/0.39 tff(252,plain,
% 0.15/0.39 ((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)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[251, 173])).
% 0.15/0.39 tff(253,plain,
% 0.15/0.39 ((~(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)))))),
% 0.15/0.39 inference(tautology,[status(thm)],[])).
% 0.15/0.39 tff(254,plain,
% 0.15/0.39 ((~(greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))) <=> ((end_time(tptp_fun_E_0(P!2)) = critical_point(tptp_fun_E_0(P!2))) | greater(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))))) | greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.15/0.39 tff(255,plain,
% 0.15/0.39 (greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[254, 250])).
% 0.15/0.39 tff(256,plain,
% 0.15/0.39 (((~![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(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(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)))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(257,plain,
% 0.15/0.39 ((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(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)))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(258,plain,
% 0.15/0.39 (((~![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(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))))))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[257])).
% 0.15/0.39 tff(259,plain,
% 0.15/0.39 (((~![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(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)))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[258, 256])).
% 0.15/0.39 tff(260,plain,
% 0.15/0.39 ((~![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)))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(261,plain,
% 0.15/0.39 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~greater_or_equal(T, start_time(E))) | (~greater_or_equal(end_time(E), T)))) | (~environment(tptp_fun_E_0(P!2))) | in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(critical_point(tptp_fun_E_0(P!2)), start_time(tptp_fun_E_0(P!2)))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.15/0.39 tff(262,plain,
% 0.15/0.39 (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2))) | (~greater_or_equal(end_time(tptp_fun_E_0(P!2)), critical_point(tptp_fun_E_0(P!2))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[261, 193, 93, 231])).
% 0.15/0.39 tff(263,plain,
% 0.15/0.39 (in_environment(tptp_fun_E_0(P!2), critical_point(tptp_fun_E_0(P!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[262, 255])).
% 0.15/0.39 tff(264,plain,
% 0.15/0.39 ($false),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[263, 248])).
% 0.15/0.39 % SZS output end Proof
%------------------------------------------------------------------------------