TSTP Solution File: MGT034+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT034+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 05:22:02 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT034+2 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:57:16 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(greater_type, type, (
% 0.19/0.41 greater: ( $i * $i ) > $o)).
% 0.19/0.41 tff(growth_rate_type, type, (
% 0.19/0.41 growth_rate: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_T_0_type, type, (
% 0.19/0.41 tptp_fun_T_0: $i)).
% 0.19/0.41 tff(efficient_producers_type, type, (
% 0.19/0.41 efficient_producers: $i)).
% 0.19/0.41 tff(first_movers_type, type, (
% 0.19/0.41 first_movers: $i)).
% 0.19/0.41 tff(subpopulations_type, type, (
% 0.19/0.41 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_E_1_type, type, (
% 0.19/0.41 tptp_fun_E_1: $i)).
% 0.19/0.41 tff(appear_type, type, (
% 0.19/0.41 appear: ( $i * $i ) > $i)).
% 0.19/0.41 tff(in_environment_type, type, (
% 0.19/0.41 in_environment: ( $i * $i ) > $o)).
% 0.19/0.41 tff(critical_point_type, type, (
% 0.19/0.41 critical_point: $i > $i)).
% 0.19/0.41 tff(greater_or_equal_type, type, (
% 0.19/0.41 greater_or_equal: ( $i * $i ) > $o)).
% 0.19/0.41 tff(environment_type, type, (
% 0.19/0.41 environment: $i > $o)).
% 0.19/0.41 tff(selection_favors_type, type, (
% 0.19/0.41 selection_favors: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(zero_type, type, (
% 0.19/0.41 zero: $i)).
% 0.19/0.41 tff(difference_type, type, (
% 0.19/0.41 difference: ( $i * $i ) > $i)).
% 0.19/0.41 tff(decreases_type, type, (
% 0.19/0.41 decreases: $i > $o)).
% 0.19/0.41 tff(disbanding_rate_type, type, (
% 0.19/0.41 disbanding_rate: ( $i * $i ) > $i)).
% 0.19/0.41 tff(founding_rate_type, type, (
% 0.19/0.41 founding_rate: ( $i * $i ) > $i)).
% 0.19/0.41 tff(1,assumption,(~in_environment(E!1, appear(efficient_producers, E!1))), introduced(assumption)).
% 0.19/0.41 tff(2,assumption,(~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))), introduced(assumption)).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl((greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : rewrite((greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.41 tff(8,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal')).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.41 tff(11,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> $true) <=> greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (($true | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) <=> $true),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) <=> $true),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) <=> ($true | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) <=> $true),
% 0.19/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ((greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))) <=> (greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> $true)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 ((greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))) <=> greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))),
% 0.19/0.41 inference(transitivity,[status(thm)],[19, 14])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))) <=> ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[21, 13])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)) <=> ((appear(efficient_producers, E!1) = appear(efficient_producers, E!1)) | greater(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[24, 12, 2])).
% 0.19/0.41 tff(26,plain,(greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 ((~![E: $i, T: $i] : ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => selection_favors(first_movers, efficient_producers, T))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(29,axiom,(~![E: $i, T: $i] : ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => selection_favors(first_movers, efficient_producers, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t3')).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | selection_favors(first_movers, efficient_producers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 27])).
% 0.19/0.41 tff(37,plain,(
% 0.19/0.41 ~((~(environment(E!1) & in_environment(E!1, critical_point(E!1)) & greater_or_equal(T!0, appear(efficient_producers, E!1)) & greater(critical_point(E!1), T!0))) | selection_favors(first_movers, efficient_producers, T!0))),
% 0.19/0.41 inference(skolemize,[status(sab)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (environment(E!1) & in_environment(E!1, critical_point(E!1)) & greater_or_equal(T!0, appear(efficient_producers, E!1)) & greater(critical_point(E!1), T!0)),
% 0.19/0.41 inference(or_elim,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (in_environment(E!1, critical_point(E!1))),
% 0.19/0.41 inference(and_elim,[status(thm)],[38])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (environment(E!1)),
% 0.19/0.41 inference(and_elim,[status(thm)],[38])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (^[E: $i, T: $i] : refl((in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))) <=> (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T)) <=> (~((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))), ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) <=> (~(~((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))) <=> ((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))), ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) <=> ((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))))), (((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T)) <=> (((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))) | in_environment(E, T)))), rewrite((((~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))), (((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)))), ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) <=> ((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)))), rewrite(((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) <=> (environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))), ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) <=> (environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T)))), (((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => in_environment(E, T)) <=> ((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T)) => in_environment(E, T)))), rewrite(((environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T)) => in_environment(E, T)) <=> ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))), (((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => in_environment(E, T)) <=> ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (![E: $i, T: $i] : ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.42 tff(48,axiom,(![E: $i, T: $i] : ((((environment(E) & in_environment(E, critical_point(E))) & greater_or_equal(T, appear(efficient_producers, E))) & greater(critical_point(E), T)) => in_environment(E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_critical_time_points')).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.19/0.42 tff(51,plain,(
% 0.19/0.42 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, critical_point(E)) & greater_or_equal(T, appear(efficient_producers, E)) & greater(critical_point(E), T))) | in_environment(E, T))),
% 0.19/0.42 inference(skolemize,[status(sab)],[50])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((in_environment(E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1)))) <=> ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (in_environment(E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (in_environment(E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[56, 54])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (in_environment(E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~in_environment(E, critical_point(E))) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(critical_point(E), T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | (~greater_or_equal(appear(efficient_producers, E!1), appear(efficient_producers, E!1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (in_environment(E!1, appear(efficient_producers, E!1)) | (~greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[59, 53, 40, 39, 26])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (~greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[60, 1])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[62, 12])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (^[E: $i] : refl((subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E)))) <=> (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E)))) <=> ![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, critical_point(E))) <=> (~((~environment(E)) | (~in_environment(E, critical_point(E)))))), ((~(environment(E) & in_environment(E, critical_point(E)))) <=> (~(~((~environment(E)) | (~in_environment(E, critical_point(E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, critical_point(E)))))) <=> ((~environment(E)) | (~in_environment(E, critical_point(E))))), ((~(environment(E) & in_environment(E, critical_point(E)))) <=> ((~environment(E)) | (~in_environment(E, critical_point(E)))))), (((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> (((~environment(E)) | (~in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))))), rewrite((((~environment(E)) | (~in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))), (((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> ![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> ![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (^[E: $i] : rewrite(((environment(E) & in_environment(E, critical_point(E))) => subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (![E: $i] : ((environment(E) & in_environment(E, critical_point(E))) => subpopulations(first_movers, efficient_producers, E, critical_point(E))) <=> ![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.42 tff(71,axiom,(![E: $i] : ((environment(E) & in_environment(E, critical_point(E))) => subpopulations(first_movers, efficient_producers, E, critical_point(E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_critical_point_means_FM_and_EP')).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.42 tff(74,plain,(
% 0.19/0.42 ![E: $i] : ((~(environment(E) & in_environment(E, critical_point(E)))) | subpopulations(first_movers, efficient_producers, E, critical_point(E)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[73])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))) | (subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))))) <=> ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))) | subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))) | (subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, critical_point(E)) | (~environment(E)) | (~in_environment(E, critical_point(E))))) | subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[79, 76, 40, 39])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (^[E: $i, T: $i] : refl((greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> ![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater_or_equal(T, appear(efficient_producers, E))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater_or_equal(T, appear(efficient_producers, E))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.43 tff(88,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater_or_equal(T, appear(efficient_producers, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_FM_and_EP_members_EP_appeared')).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.43 tff(91,plain,(
% 0.19/0.43 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater_or_equal(T, appear(efficient_producers, E)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[90])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))) <=> ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 ((greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 (((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 ((~![E: $i, T: $i] : (greater_or_equal(T, appear(efficient_producers, E)) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[99, 93, 40, 80])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 ((~(greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))) | (~greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))) | ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 ((~(greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))) | ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[102, 63])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 ((~((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))) | (critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (critical_point(E!1) = appear(efficient_producers, E!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[105, 61])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (in_environment(E!1, critical_point(E!1)) <=> in_environment(E!1, appear(efficient_producers, E!1))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (in_environment(E!1, appear(efficient_producers, E!1)) <=> in_environment(E!1, critical_point(E!1))),
% 0.21/0.43 inference(symmetry,[status(thm)],[107])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 ((~in_environment(E!1, appear(efficient_producers, E!1))) <=> (~in_environment(E!1, critical_point(E!1)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (~in_environment(E!1, critical_point(E!1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[1, 109])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[39, 110])).
% 0.21/0.43 tff(112,plain,(in_environment(E!1, appear(efficient_producers, E!1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (^[E: $i] : refl((subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))) <=> (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))) <=> ![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, appear(efficient_producers, E))) <=> (~((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))), ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) <=> (~(~((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))) <=> ((~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))), ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) <=> ((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))))), (((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> (((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))))), rewrite((((~environment(E)) | (~in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))), (((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> ![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 (![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> ![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 (^[E: $i] : rewrite(((environment(E) & in_environment(E, appear(efficient_producers, E))) => subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (![E: $i] : ((environment(E) & in_environment(E, appear(efficient_producers, E))) => subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E))) <=> ![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.43 tff(120,axiom,(![E: $i] : ((environment(E) & in_environment(E, appear(efficient_producers, E))) => subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_FM_and_EP_when_EP_appears')).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 (![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 (![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.21/0.43 tff(123,plain,(
% 0.21/0.43 ![E: $i] : ((~(environment(E) & in_environment(E, appear(efficient_producers, E)))) | subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[122])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[124, 114])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | ((~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))) <=> ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 ((subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1)))) <=> ((~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))) <=> ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | ((~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))) <=> ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~environment(E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~![E: $i] : (subpopulations(first_movers, efficient_producers, E, appear(efficient_producers, E)) | (~environment(E)) | (~in_environment(E, appear(efficient_producers, E))))) | (~environment(E!1)) | subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)) | (~in_environment(E!1, appear(efficient_producers, E!1)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[131, 125, 40])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[132, 112])).
% 0.21/0.44 tff(134,assumption,(~subpopulations(first_movers, efficient_producers, E!1, T!0)), introduced(assumption)).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(critical_point(E!1), T!0) <=> ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (greater_or_equal(critical_point(E!1), T!0) <=> ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[135, 12])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (greater(critical_point(E!1), T!0)),
% 0.21/0.44 inference(and_elim,[status(thm)],[38])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)) | (~greater(critical_point(E!1), T!0))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 ((~(greater_or_equal(critical_point(E!1), T!0) <=> ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)))) | greater_or_equal(critical_point(E!1), T!0) | (~((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~(greater_or_equal(critical_point(E!1), T!0) <=> ((critical_point(E!1) = T!0) | greater(critical_point(E!1), T!0)))) | greater_or_equal(critical_point(E!1), T!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (greater_or_equal(critical_point(E!1), T!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[141, 136])).
% 0.21/0.44 tff(143,assumption,(subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))), introduced(assumption)).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (greater_or_equal(T!0, appear(efficient_producers, E!1))),
% 0.21/0.44 inference(and_elim,[status(thm)],[38])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (^[E: $i, T1: $i, T2: $i, T: $i] : refl((subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))) <=> ![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[145])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (^[E: $i, T1: $i, T2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T)) <=> (~((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) <=> (~(~((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))))), rewrite((~(~((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))) <=> ((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) <=> ((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))) | subpopulations(first_movers, efficient_producers, E, T)))), rewrite((((~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 (^[E: $i, T1: $i, T2: $i, T: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1)))), (((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))), (((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T)))), ((((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))), ((((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 (![E: $i, T1: $i, T2: $i, T: $i] : (((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.44 tff(152,axiom,(![E: $i, T1: $i, T2: $i, T: $i] : (((((environment(E) & subpopulations(first_movers, efficient_producers, E, T1)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) => subpopulations(first_movers, efficient_producers, E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a10')).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 (![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 (![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.21/0.44 tff(155,plain,(
% 0.21/0.44 ![E: $i, T1: $i, T2: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T1) & subpopulations(first_movers, efficient_producers, E, T2) & greater_or_equal(T, T1) & greater_or_equal(T2, T))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.21/0.44 inference(skolemize,[status(sab)],[154])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 (![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[156, 146])).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 (((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | ((~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))))) <=> ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 ((subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~greater_or_equal(critical_point(E!1), T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)))) <=> ((~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 (((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~greater_or_equal(critical_point(E!1), T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | ((~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[159])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 (((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~greater_or_equal(critical_point(E!1), T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[160, 158])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~greater_or_equal(critical_point(E!1), T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 ((~![E: $i, T1: $i, T2: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~greater_or_equal(T2, T)) | (~greater_or_equal(T, T1)) | (~subpopulations(first_movers, efficient_producers, E, T1)) | (~subpopulations(first_movers, efficient_producers, E, T2)))) | (~environment(E!1)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | (~greater_or_equal(critical_point(E!1), T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[163, 157, 40, 144, 80, 143, 142, 134])).
% 0.21/0.45 tff(165,plain,(subpopulations(first_movers, efficient_producers, E!1, T!0) | (~subpopulations(first_movers, efficient_producers, E!1, appear(efficient_producers, E!1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[165, 133])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 (^[E: $i, T: $i] : refl((subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[167])).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[169])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[172])).
% 0.21/0.45 tff(174,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_symmetry_of_subpopulations')).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.45 tff(176,plain,
% 0.21/0.45 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.21/0.45 tff(177,plain,(
% 0.21/0.45 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.21/0.45 inference(skolemize,[status(sab)],[176])).
% 0.21/0.45 tff(178,plain,
% 0.21/0.45 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.21/0.45 tff(179,plain,
% 0.21/0.45 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[178, 168])).
% 0.21/0.45 tff(180,plain,
% 0.21/0.45 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(181,plain,
% 0.21/0.45 ((subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(182,plain,
% 0.21/0.46 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[181])).
% 0.21/0.46 tff(183,plain,
% 0.21/0.46 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.21/0.46 inference(transitivity,[status(thm)],[182, 180])).
% 0.21/0.46 tff(184,plain,
% 0.21/0.46 ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(185,plain,
% 0.21/0.46 ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.46 tff(186,plain,
% 0.21/0.46 (subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[185, 179, 40, 166])).
% 0.21/0.46 tff(187,plain,
% 0.21/0.46 (~selection_favors(first_movers, efficient_producers, T!0)),
% 0.21/0.46 inference(or_elim,[status(thm)],[37])).
% 0.21/0.46 tff(188,plain,
% 0.21/0.46 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(189,plain,
% 0.21/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[188])).
% 0.21/0.46 tff(190,plain,
% 0.21/0.46 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(191,plain,
% 0.21/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[190])).
% 0.21/0.46 tff(192,plain,
% 0.21/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(193,plain,
% 0.21/0.46 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) <=> (environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)))), rewrite(((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(194,plain,
% 0.21/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[193])).
% 0.21/0.46 tff(195,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp1_high_growth_rates')).
% 0.21/0.46 tff(196,plain,
% 0.21/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.46 tff(197,plain,
% 0.21/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.21/0.46 tff(198,plain,(
% 0.21/0.46 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.21/0.46 inference(skolemize,[status(sab)],[197])).
% 0.21/0.46 tff(199,plain,
% 0.21/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.21/0.46 tff(200,plain,
% 0.21/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[199, 189])).
% 0.21/0.46 tff(201,plain,
% 0.21/0.46 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(first_movers, efficient_producers, T!0) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(first_movers, efficient_producers, T!0) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(202,plain,
% 0.21/0.46 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(first_movers, efficient_producers, T!0) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(203,plain,
% 0.21/0.46 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(first_movers, efficient_producers, T!0) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.46 tff(204,plain,
% 0.21/0.46 (~greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[203, 200, 40, 187, 186])).
% 0.21/0.46 tff(205,plain,
% 0.21/0.46 (^[E: $i, T: $i] : refl(((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(206,plain,
% 0.21/0.46 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[205])).
% 0.21/0.46 tff(207,plain,
% 0.21/0.46 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(208,plain,
% 0.21/0.46 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[207])).
% 0.21/0.46 tff(209,plain,
% 0.21/0.46 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(210,plain,
% 0.21/0.46 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(211,plain,
% 0.21/0.46 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[210])).
% 0.21/0.46 tff(212,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3')).
% 0.21/0.46 tff(213,plain,
% 0.21/0.46 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.21/0.46 tff(214,plain,
% 0.21/0.46 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.21/0.46 tff(215,plain,(
% 0.21/0.46 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[214])).
% 0.21/0.46 tff(216,plain,
% 0.21/0.46 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.21/0.46 tff(217,plain,
% 0.21/0.46 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[216, 206])).
% 0.21/0.46 tff(218,plain,
% 0.21/0.46 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(219,plain,
% 0.21/0.46 (((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(220,plain,
% 0.21/0.46 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[219])).
% 0.21/0.46 tff(221,plain,
% 0.21/0.46 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[220, 218])).
% 0.21/0.47 tff(222,plain,
% 0.21/0.47 ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(223,plain,
% 0.21/0.47 ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.21/0.47 tff(224,plain,
% 0.21/0.47 (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[223, 217, 40, 166])).
% 0.21/0.47 tff(225,plain,
% 0.21/0.47 (^[E: $i, T: $i] : refl((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(226,plain,
% 0.21/0.47 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[225])).
% 0.21/0.47 tff(227,plain,
% 0.21/0.47 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))), rewrite((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(228,plain,
% 0.21/0.47 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))) <=> ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[227])).
% 0.21/0.47 tff(229,plain,
% 0.21/0.47 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))) <=> ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(230,plain,
% 0.21/0.47 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))) <=> (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(231,plain,
% 0.21/0.47 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))) <=> ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[230])).
% 0.21/0.47 tff(232,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a12')).
% 0.21/0.47 tff(233,plain,
% 0.21/0.47 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.21/0.47 tff(234,plain,
% 0.21/0.47 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.21/0.47 tff(235,plain,(
% 0.21/0.47 ![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[234])).
% 0.21/0.47 tff(236,plain,
% 0.21/0.47 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.21/0.47 tff(237,plain,
% 0.21/0.47 (![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[236, 226])).
% 0.21/0.47 tff(238,plain,
% 0.21/0.47 (((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))) <=> ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(239,plain,
% 0.21/0.47 ((decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(240,plain,
% 0.21/0.47 (((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[239])).
% 0.21/0.47 tff(241,plain,
% 0.21/0.47 (((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[240, 238])).
% 0.21/0.47 tff(242,plain,
% 0.21/0.47 ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(243,plain,
% 0.21/0.47 ((~![E: $i, T: $i] : (decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.21/0.47 tff(244,plain,
% 0.21/0.47 (decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[243, 237, 40, 166])).
% 0.21/0.47 tff(245,plain,
% 0.21/0.47 (^[T: $i] : refl((decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(246,plain,
% 0.21/0.47 (![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))) <=> ![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[245])).
% 0.21/0.47 tff(247,plain,
% 0.21/0.47 (^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> (~(decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))), ((~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))) <=> (~(~(decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))))), rewrite((~(~(decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))), ((~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))))))), ((decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))))), rewrite((decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))), ((decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(248,plain,
% 0.21/0.47 (![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[247])).
% 0.21/0.47 tff(249,plain,
% 0.21/0.47 (![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(250,plain,
% 0.21/0.47 (^[T: $i] : rewrite(((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) => decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) <=> (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(251,plain,
% 0.21/0.47 (![T: $i] : ((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) => decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) <=> ![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[250])).
% 0.21/0.47 tff(252,axiom,(![T: $i] : ((decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) => decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_difference_between_founding_rates')).
% 0.21/0.47 tff(253,plain,
% 0.21/0.47 (![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.21/0.47 tff(254,plain,
% 0.21/0.47 (![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.21/0.47 tff(255,plain,(
% 0.21/0.47 ![T: $i] : (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~(decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T))) & (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[254])).
% 0.21/0.47 tff(256,plain,
% 0.21/0.47 (![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.21/0.47 tff(257,plain,
% 0.21/0.47 (![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[256, 246])).
% 0.21/0.47 tff(258,plain,
% 0.21/0.47 (((~![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) | (decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))) | (~decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))))) <=> ((~![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) | decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))) | (~decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(259,plain,
% 0.21/0.47 ((~![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) | (decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))) | (~decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(260,plain,
% 0.21/0.47 ((~![T: $i] : (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | (~decreases(difference(founding_rate(first_movers, T), founding_rate(efficient_producers, T)))))) | decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))) | (~decreases(difference(founding_rate(first_movers, T!0), founding_rate(efficient_producers, T!0))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.21/0.47 tff(261,plain,
% 0.21/0.47 (decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[260, 257, 244, 224])).
% 0.21/0.47 tff(262,plain,
% 0.21/0.47 (^[T: $i] : refl((greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(263,plain,
% 0.21/0.47 (![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[262])).
% 0.21/0.47 tff(264,plain,
% 0.21/0.47 (![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(265,axiom,(![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_negative_growth_rate_difference')).
% 0.21/0.47 tff(266,plain,
% 0.21/0.47 (![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.21/0.47 tff(267,plain,(
% 0.21/0.47 ![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[266])).
% 0.21/0.47 tff(268,plain,
% 0.21/0.47 (![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.21/0.47 tff(269,plain,
% 0.21/0.47 ((~![T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) | (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) <=> greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(270,plain,
% 0.21/0.47 (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) <=> greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[269, 268])).
% 0.21/0.47 tff(271,plain,
% 0.21/0.47 (^[E: $i, Tc: $i] : refl(((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(272,plain,
% 0.21/0.47 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[271])).
% 0.21/0.48 tff(273,plain,
% 0.21/0.48 (^[E: $i, Tc: $i] : rewrite(((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(274,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[273])).
% 0.21/0.48 tff(275,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[274, 272])).
% 0.21/0.48 tff(276,plain,
% 0.21/0.48 (^[E: $i, Tc: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & (Tc = critical_point(E))) <=> (~((~environment(E)) | (~(Tc = critical_point(E)))))), ((~(environment(E) & (Tc = critical_point(E)))) <=> (~(~((~environment(E)) | (~(Tc = critical_point(E)))))))), rewrite((~(~((~environment(E)) | (~(Tc = critical_point(E)))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))))), ((~(environment(E) & (Tc = critical_point(E)))) <=> ((~environment(E)) | (~(Tc = critical_point(E)))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) <=> (~((~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) <=> (~(~((~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) <=> ((~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (((~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), rewrite((((~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))), rewrite(((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))) <=> (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), (((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))), (((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~(Tc = critical_point(E)))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))))), rewrite((((~environment(E)) | (~(Tc = critical_point(E)))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))), (((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(277,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[276])).
% 0.21/0.48 tff(278,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(279,plain,
% 0.21/0.48 (^[E: $i, Tc: $i] : trans(monotonicity(rewrite(((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), (((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))), rewrite(((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(280,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[279])).
% 0.21/0.48 tff(281,axiom,(![E: $i, Tc: $i] : ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1')).
% 0.21/0.48 tff(282,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.21/0.48 tff(283,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.21/0.48 tff(284,plain,(
% 0.21/0.48 ![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[283])).
% 0.21/0.48 tff(285,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[284, 277])).
% 0.21/0.48 tff(286,plain,
% 0.21/0.48 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[285, 275])).
% 0.21/0.48 tff(287,plain,
% 0.21/0.48 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))) | ((~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))) <=> ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))) | (~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(288,plain,
% 0.21/0.48 (((~environment(E!1)) | $false | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T))))))) <=> ((~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(289,plain,
% 0.21/0.48 ((~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))) <=> (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(290,plain,
% 0.21/0.48 ((~$true) <=> $false),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(291,plain,
% 0.21/0.48 ((critical_point(E!1) = critical_point(E!1)) <=> $true),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(292,plain,
% 0.21/0.48 ((~(critical_point(E!1) = critical_point(E!1))) <=> (~$true)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[291])).
% 0.21/0.48 tff(293,plain,
% 0.21/0.48 ((~(critical_point(E!1) = critical_point(E!1))) <=> $false),
% 0.21/0.48 inference(transitivity,[status(thm)],[292, 290])).
% 0.21/0.48 tff(294,plain,
% 0.21/0.48 (((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T))))))) <=> ((~environment(E!1)) | $false | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[293, 289])).
% 0.21/0.48 tff(295,plain,
% 0.21/0.48 (((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T))))))) <=> ((~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[294, 288])).
% 0.21/0.48 tff(296,plain,
% 0.21/0.48 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))) | ((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))) <=> ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))) | ((~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[295])).
% 0.21/0.48 tff(297,plain,
% 0.21/0.48 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))) | ((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))) <=> ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))) | (~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[296, 287])).
% 0.21/0.48 tff(298,plain,
% 0.21/0.48 ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))) | ((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(299,plain,
% 0.21/0.48 ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, Tc)) | (~subpopulations(first_movers, efficient_producers, E, T)))))))) | (~environment(E!1)) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.21/0.48 tff(300,plain,
% 0.21/0.48 (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[299, 286, 40])).
% 0.21/0.48 tff(301,plain,
% 0.21/0.48 ((greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~greater(T, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T))))) | (~greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(302,plain,
% 0.21/0.48 (~greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[301, 300])).
% 0.21/0.48 tff(303,plain,
% 0.21/0.48 ((~(greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) <=> greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))) | (~greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(304,plain,
% 0.21/0.48 (~greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[303, 302, 270])).
% 0.21/0.48 tff(305,plain,
% 0.21/0.48 (^[E: $i, T: $i] : refl((greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(306,plain,
% 0.21/0.48 (![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[305])).
% 0.21/0.48 tff(307,plain,
% 0.21/0.48 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(308,plain,
% 0.21/0.49 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[307])).
% 0.21/0.49 tff(309,plain,
% 0.21/0.49 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(310,plain,
% 0.21/0.49 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(311,plain,
% 0.21/0.49 (![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[310])).
% 0.21/0.49 tff(312,axiom,(![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))) => greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_relationship_of_growth_rates')).
% 0.21/0.49 tff(313,plain,
% 0.21/0.49 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.21/0.49 tff(314,plain,
% 0.21/0.49 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.21/0.49 tff(315,plain,(
% 0.21/0.49 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & (~greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))),
% 0.21/0.49 inference(skolemize,[status(sab)],[314])).
% 0.21/0.49 tff(316,plain,
% 0.21/0.49 (![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[315, 308])).
% 0.21/0.49 tff(317,plain,
% 0.21/0.49 (![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[316, 306])).
% 0.21/0.49 tff(318,plain,
% 0.21/0.49 (((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))) <=> ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(319,plain,
% 0.21/0.49 ((greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1)))) <=> ((~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(320,plain,
% 0.21/0.49 (((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[319])).
% 0.21/0.49 tff(321,plain,
% 0.21/0.49 (((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))) <=> ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[320, 318])).
% 0.21/0.49 tff(322,plain,
% 0.21/0.49 ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1)))) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(323,plain,
% 0.21/0.49 ((~![E: $i, T: $i] : (greater(zero, difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) | greater_or_equal(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | (~subpopulations(first_movers, efficient_producers, E!1, critical_point(E!1))) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.21/0.49 tff(324,plain,
% 0.21/0.49 (greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[323, 317, 40, 80])).
% 0.21/0.49 tff(325,plain,
% 0.21/0.49 (greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[324, 304])).
% 0.21/0.49 tff(326,plain,
% 0.21/0.49 (^[E: $i, T: $i, To: $i] : refl((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(327,plain,
% 0.21/0.49 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))) <=> ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[326])).
% 0.21/0.49 tff(328,plain,
% 0.21/0.49 (^[E: $i, T: $i, To: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)) <=> (~((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))), ((~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))) <=> (~(~((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))) <=> ((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))), ((~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))) <=> ((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T))))), ((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | ((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))))), rewrite((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | ((~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))), ((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(329,plain,
% 0.21/0.49 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))) <=> ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[328])).
% 0.21/0.49 tff(330,plain,
% 0.21/0.49 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))) <=> ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(331,plain,
% 0.21/0.49 (^[E: $i, T: $i, To: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero))), ((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) <=> ((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))))), rewrite(((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)))), ((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E))))), (((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) <=> ((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)))), rewrite(((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))), (((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) <=> (environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)))), rewrite((decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)) <=> ((~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))), ((((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) => (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))) <=> ((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)) => ((~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))))), rewrite(((environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T)) => ((~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))), ((((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) => (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(332,plain,
% 0.21/0.50 (![E: $i, T: $i, To: $i] : (((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) => (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero))) <=> ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[331])).
% 0.21/0.50 tff(333,axiom,(![E: $i, T: $i, To: $i] : (((((environment(E) & in_environment(E, To)) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) & greater_or_equal(T, appear(efficient_producers, E))) & greater(To, T)) => (decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) => greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_decreasing_function')).
% 0.21/0.50 tff(334,plain,
% 0.21/0.50 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.21/0.50 tff(335,plain,
% 0.21/0.50 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[334, 330])).
% 0.21/0.50 tff(336,plain,(
% 0.21/0.50 ![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~(environment(E) & in_environment(E, To) & greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero) & greater_or_equal(T, appear(efficient_producers, E)) & greater(To, T))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[335])).
% 0.21/0.50 tff(337,plain,
% 0.21/0.50 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[336, 329])).
% 0.21/0.50 tff(338,plain,
% 0.21/0.50 (![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[337, 327])).
% 0.21/0.50 tff(339,plain,
% 0.21/0.50 (((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))) <=> ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(340,plain,
% 0.21/0.50 ((greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0))) <=> ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(341,plain,
% 0.21/0.50 (((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))) <=> ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | ((~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[340])).
% 0.21/0.50 tff(342,plain,
% 0.21/0.50 (((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))) <=> ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[341, 339])).
% 0.21/0.50 tff(343,plain,
% 0.21/0.50 ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(344,plain,
% 0.21/0.50 ((~![E: $i, T: $i, To: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) | (~decreases(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (~environment(E)) | (~in_environment(E, To)) | (~greater_or_equal(difference(growth_rate(first_movers, To), growth_rate(efficient_producers, To)), zero)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~greater(To, T)))) | (~environment(E!1)) | (~in_environment(E!1, critical_point(E!1))) | greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))) | (~greater(critical_point(E!1), T!0))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.21/0.50 tff(345,plain,
% 0.21/0.50 (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(E!1)), growth_rate(efficient_producers, critical_point(E!1))), zero))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[344, 338, 40, 39, 144, 137])).
% 0.21/0.50 tff(346,plain,
% 0.21/0.50 (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) | (~decreases(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[345, 325])).
% 0.21/0.50 tff(347,plain,
% 0.21/0.50 (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[346, 261])).
% 0.21/0.50 tff(348,assumption,(~(greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) <=> greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))), introduced(assumption)).
% 0.21/0.50 tff(349,plain,
% 0.21/0.50 (^[T: $i] : refl((greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(350,plain,
% 0.21/0.50 (![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> ![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[349])).
% 0.21/0.50 tff(351,plain,
% 0.21/0.50 (![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T))) <=> ![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(352,axiom,(![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_positive_growth_rate_difference')).
% 0.21/0.50 tff(353,plain,
% 0.21/0.50 (![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.21/0.50 tff(354,plain,(
% 0.21/0.50 ![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[353])).
% 0.21/0.50 tff(355,plain,
% 0.21/0.50 (![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[354, 350])).
% 0.21/0.50 tff(356,plain,
% 0.21/0.50 ((~![T: $i] : (greater(difference(growth_rate(first_movers, T), growth_rate(efficient_producers, T)), zero) <=> greater(growth_rate(first_movers, T), growth_rate(efficient_producers, T)))) | (greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) <=> greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(357,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[356, 355, 348])).
% 0.21/0.50 tff(358,plain,(greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) <=> greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(359,plain,
% 0.21/0.50 ((~(greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero) <=> greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)))) | (~greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero)) | greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(360,plain,
% 0.21/0.50 ((~greater(difference(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0)), zero)) | greater(growth_rate(first_movers, T!0), growth_rate(efficient_producers, T!0))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[359, 358])).
% 0.21/0.50 tff(361,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[360, 347, 204])).
% 0.21/0.50 % SZS output end Proof
%------------------------------------------------------------------------------