TSTP Solution File: MGT035+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT035+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 05:22:03 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT035+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 03:06:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(greater_type, type, (
% 0.12/0.39 greater: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_T_1_type, type, (
% 0.12/0.39 tptp_fun_T_1: $i > $i)).
% 0.12/0.39 tff(tptp_fun_E_2_type, type, (
% 0.12/0.39 tptp_fun_E_2: $i)).
% 0.12/0.39 tff(tptp_fun_To_0_type, type, (
% 0.12/0.39 tptp_fun_To_0: $i > $i)).
% 0.12/0.39 tff(equilibrium_type, type, (
% 0.12/0.39 equilibrium: $i > $i)).
% 0.12/0.39 tff(greater_or_equal_type, type, (
% 0.12/0.39 greater_or_equal: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_T_3_type, type, (
% 0.12/0.39 tptp_fun_T_3: $i > $i)).
% 0.12/0.39 tff(growth_rate_type, type, (
% 0.12/0.39 growth_rate: ( $i * $i ) > $i)).
% 0.12/0.39 tff(first_movers_type, type, (
% 0.12/0.39 first_movers: $i)).
% 0.12/0.39 tff(efficient_producers_type, type, (
% 0.12/0.39 efficient_producers: $i)).
% 0.12/0.39 tff(zero_type, type, (
% 0.12/0.39 zero: $i)).
% 0.12/0.39 tff(outcompetes_type, type, (
% 0.12/0.39 outcompetes: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(subpopulations_type, type, (
% 0.12/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.39 tff(in_environment_type, type, (
% 0.12/0.39 in_environment: ( $i * $i ) > $o)).
% 0.12/0.39 tff(stable_type, type, (
% 0.12/0.39 stable: $i > $o)).
% 0.12/0.39 tff(environment_type, type, (
% 0.12/0.39 environment: $i > $o)).
% 0.12/0.39 tff(1,assumption,(greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.39 tff(7,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')).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.39 tff(10,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[9])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.12/0.39 tff(14,assumption,(~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)), introduced(assumption)).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.18/0.39 tff(17,assumption,(greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)), introduced(assumption)).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(X, Y) & greater(Y, Z)) <=> (~((~greater(X, Y)) | (~greater(Y, Z))))), ((~(greater(X, Y) & greater(Y, Z))) <=> (~(~((~greater(X, Y)) | (~greater(Y, Z))))))), rewrite((~(~((~greater(X, Y)) | (~greater(Y, Z))))) <=> ((~greater(X, Y)) | (~greater(Y, Z)))), ((~(greater(X, Y) & greater(Y, Z))) <=> ((~greater(X, Y)) | (~greater(Y, Z))))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)))), rewrite((((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (^[X: $i, Y: $i, Z: $i] : rewrite(((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.39 tff(24,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_transitivity')).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.18/0.39 tff(27,plain,(
% 0.18/0.39 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.39 inference(skolemize,[status(sab)],[26])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 ((greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))) <=> (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[32, 30])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[35, 29, 17, 14, 1])).
% 0.18/0.40 tff(37,plain,((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[37, 14, 1])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 (((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))) | greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 ((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[41, 11])).
% 0.18/0.40 tff(43,assumption,(~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) | (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[45, 42])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (((tptp_fun_T_3(tptp_fun_T_1(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.18/0.40 tff(49,assumption,(tptp_fun_T_1(E!2) = equilibrium(E!2)), introduced(assumption)).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.40 inference(symmetry,[status(thm)],[50])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 ((~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) <=> (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[43, 52])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (((environment(E!2) & stable(E!2)) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)))))) <=> (environment(E!2) & stable(E!2) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 ((~(~(environment(E!2) & stable(E!2)))) <=> (environment(E!2) & stable(E!2))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (((~(~(environment(E!2) & stable(E!2)))) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)))))) <=> ((environment(E!2) & stable(E!2)) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[55])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (((~(~(environment(E!2) & stable(E!2)))) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)))))) <=> (environment(E!2) & stable(E!2) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To))))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[56, 54])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 ((~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 ((~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => outcompetes(efficient_producers, first_movers, T))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(60,axiom,(~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => outcompetes(efficient_producers, first_movers, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t4')).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | outcompetes(efficient_producers, first_movers, T))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (environment(E!2) & stable(E!2) & ![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (stable(E!2)),
% 0.18/0.40 inference(and_elim,[status(thm)],[68])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (environment(E!2)),
% 0.18/0.40 inference(and_elim,[status(thm)],[68])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & stable(E)) <=> (~((~environment(E)) | (~stable(E))))), ((~(environment(E) & stable(E))) <=> (~(~((~environment(E)) | (~stable(E))))))), rewrite((~(~((~environment(E)) | (~stable(E))))) <=> ((~environment(E)) | (~stable(E)))), ((~(environment(E) & stable(E))) <=> ((~environment(E)) | (~stable(E))))), rewrite((in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E))) <=> (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))) <=> (((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E)))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E)))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (^[E: $i] : rewrite(((environment(E) & stable(E)) => ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E)))) <=> ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (![E: $i] : ((environment(E) & stable(E)) => ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E)))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.40 tff(78,axiom,(![E: $i] : ((environment(E) & stable(E)) => ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a4')).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.18/0.40 tff(81,plain,(
% 0.18/0.40 ![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[80])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[86, 83, 70, 69])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 (((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))) | in_environment(E!2, tptp_fun_T_1(E!2))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (in_environment(E!2, tptp_fun_T_1(E!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (^[To: $i] : refl(((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To))))) <=> ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To))))) <=> ![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (^[To: $i] : rewrite(((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To))))) <=> ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 (![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To))))) <=> ![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 (![To: $i] : ((~in_environment(E!2, To)) | (~((~(subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To)) & greater_or_equal(tptp_fun_T_3(To), To))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)))))),
% 0.18/0.41 inference(and_elim,[status(thm)],[68])).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 (![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 (((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | ((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))))) <=> ((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 (((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))))) <=> ((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | ((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))))) <=> ((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | ((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[98])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 (((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | ((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))))) <=> ((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[99, 97])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 ((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | ((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 ((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[102, 96, 89])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[105, 53])).
% 0.18/0.41 tff(107,plain,((~(tptp_fun_T_1(E!2) = equilibrium(E!2))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (~(tptp_fun_T_1(E!2) = equilibrium(E!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[107, 43])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[109, 11])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 (((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))) | greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[111, 87])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 ((~(greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 ((~(greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) | ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 ((~((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2)))) | (tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[117, 108])).
% 0.18/0.41 tff(119,assumption,(~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.18/0.41 tff(120,assumption,(greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.18/0.41 tff(121,assumption,(greater(tptp_fun_T_1(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 ((greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2)))) <=> ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[123])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[124, 122])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[127, 29, 121, 120, 119])).
% 0.18/0.41 tff(129,plain,((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[129, 118, 48])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[131, 11])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))))) | ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[133, 105])).
% 0.18/0.42 tff(135,plain,
% 0.18/0.42 ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[134, 132])).
% 0.18/0.42 tff(136,plain,
% 0.18/0.42 ((~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))) | (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(137,plain,
% 0.18/0.42 ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.18/0.42 tff(138,plain,
% 0.18/0.42 (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[137, 130])).
% 0.18/0.42 tff(139,plain,
% 0.18/0.42 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[138])).
% 0.18/0.42 tff(140,plain,
% 0.18/0.42 (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.18/0.42 inference(symmetry,[status(thm)],[139])).
% 0.18/0.42 tff(141,plain,
% 0.18/0.42 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[112, 140])).
% 0.18/0.42 tff(142,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[43, 141])).
% 0.18/0.42 tff(143,plain,(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(144,plain,
% 0.18/0.42 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(145,plain,
% 0.18/0.42 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[144, 103])).
% 0.18/0.42 tff(146,plain,
% 0.18/0.42 (^[E: $i, T: $i] : refl(((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(147,plain,
% 0.18/0.42 (![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))) <=> ![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[146])).
% 0.18/0.42 tff(148,plain,
% 0.18/0.42 (^[E: $i, T: $i] : trans(monotonicity(rewrite((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) <=> (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))), rewrite((greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) <=> (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T)))))), rewrite(((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) <=> (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero))))), trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E)))))), (((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))))), rewrite(((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))), (((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(149,plain,
% 0.18/0.42 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))) <=> ![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[148])).
% 0.18/0.42 tff(150,plain,
% 0.18/0.42 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))) <=> ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(151,plain,
% 0.18/0.42 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))), rewrite(((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))) => ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))) => ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(152,plain,
% 0.18/0.42 (![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[151])).
% 0.18/0.42 tff(153,axiom,(![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l6')).
% 0.18/0.42 tff(154,plain,
% 0.18/0.42 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.18/0.42 tff(155,plain,
% 0.18/0.42 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.18/0.43 tff(156,plain,(
% 0.18/0.43 ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[155])).
% 0.18/0.43 tff(157,plain,
% 0.18/0.43 (![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.18/0.43 tff(158,plain,
% 0.18/0.43 (![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.18/0.43 tff(159,plain,
% 0.18/0.43 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(160,plain,
% 0.18/0.43 (((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(161,plain,
% 0.18/0.43 ((~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) <=> (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(162,plain,
% 0.18/0.43 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(163,plain,
% 0.18/0.43 ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(164,plain,
% 0.18/0.43 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))) <=> ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[163, 162, 161])).
% 0.18/0.43 tff(165,plain,
% 0.18/0.43 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[164, 160])).
% 0.18/0.43 tff(166,plain,
% 0.18/0.43 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[165])).
% 0.18/0.43 tff(167,plain,
% 0.18/0.43 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[166, 159])).
% 0.18/0.44 tff(168,plain,
% 0.18/0.44 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(169,plain,
% 0.18/0.44 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.18/0.44 tff(170,plain,
% 0.18/0.44 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[169, 158, 70, 145])).
% 0.18/0.44 tff(171,plain,
% 0.18/0.44 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[170, 143])).
% 0.18/0.44 tff(172,plain,
% 0.18/0.44 (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[171, 40, 16])).
% 0.18/0.44 tff(173,plain,
% 0.18/0.44 (((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))) | (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(174,plain,
% 0.18/0.44 (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.18/0.44 tff(175,plain,
% 0.18/0.44 (zero = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.44 inference(symmetry,[status(thm)],[174])).
% 0.18/0.44 tff(176,plain,
% 0.18/0.44 (((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))) | (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(177,plain,
% 0.18/0.44 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[176, 172])).
% 0.18/0.44 tff(178,plain,
% 0.18/0.44 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[177, 175])).
% 0.18/0.44 tff(179,plain,
% 0.18/0.44 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[178])).
% 0.18/0.44 tff(180,plain,
% 0.18/0.44 (greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.44 inference(symmetry,[status(thm)],[179])).
% 0.18/0.44 tff(181,plain,
% 0.18/0.44 ((~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) <=> (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[180])).
% 0.18/0.44 tff(182,plain,
% 0.18/0.44 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) <=> greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[174, 175])).
% 0.18/0.44 tff(183,plain,
% 0.18/0.44 ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) <=> (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[182])).
% 0.18/0.44 tff(184,plain,
% 0.18/0.44 (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[14, 183])).
% 0.18/0.44 tff(185,plain,
% 0.18/0.44 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[184, 181])).
% 0.18/0.44 tff(186,plain,
% 0.18/0.44 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[174])).
% 0.18/0.44 tff(187,plain,
% 0.18/0.44 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[1, 186])).
% 0.18/0.44 tff(188,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[187, 185])).
% 0.18/0.44 tff(189,plain,(greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(190,plain,
% 0.18/0.44 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[189, 1])).
% 0.18/0.44 tff(191,plain,
% 0.18/0.44 (((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(192,plain,
% 0.18/0.44 ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.18/0.44 tff(193,plain,
% 0.18/0.44 ((~(greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))) | greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(194,plain,
% 0.18/0.44 ((~(greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)))) | greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.18/0.44 tff(195,plain,
% 0.18/0.44 (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[194, 13])).
% 0.18/0.44 tff(196,plain,
% 0.18/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(197,plain,
% 0.18/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[196])).
% 0.18/0.44 tff(198,plain,
% 0.18/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T)) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T))))), rewrite(((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T))) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T))) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(199,plain,
% 0.18/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[198])).
% 0.18/0.44 tff(200,plain,
% 0.18/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(201,plain,
% 0.18/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(202,plain,
% 0.18/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[201])).
% 0.18/0.44 tff(203,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2')).
% 0.18/0.44 tff(204,plain,
% 0.18/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.18/0.44 tff(205,plain,
% 0.18/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.18/0.44 tff(206,plain,(
% 0.18/0.44 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[205])).
% 0.18/0.44 tff(207,plain,
% 0.18/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.18/0.44 tff(208,plain,
% 0.18/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[207, 197])).
% 0.18/0.44 tff(209,plain,
% 0.18/0.44 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(210,plain,
% 0.18/0.44 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(211,plain,
% 0.18/0.44 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.18/0.44 tff(212,plain,
% 0.18/0.44 ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[211, 208, 70, 145])).
% 0.18/0.45 tff(213,plain,
% 0.18/0.45 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))) | (~outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(214,plain,
% 0.18/0.45 (~outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[213, 103])).
% 0.18/0.45 tff(215,plain,
% 0.18/0.45 ((~((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | ((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(216,plain,
% 0.18/0.45 ((~((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | ((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.18/0.45 tff(217,plain,
% 0.18/0.45 ((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[216, 212])).
% 0.18/0.45 tff(218,plain,
% 0.18/0.45 ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(219,plain,
% 0.18/0.45 ((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.18/0.45 tff(220,plain,
% 0.18/0.45 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[219, 195])).
% 0.18/0.45 tff(221,plain,
% 0.18/0.45 (((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(222,plain,
% 0.18/0.45 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.18/0.45 tff(223,assumption,(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero), introduced(assumption)).
% 0.18/0.45 tff(224,plain,
% 0.18/0.45 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[223])).
% 0.18/0.45 tff(225,plain,
% 0.18/0.45 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.45 inference(symmetry,[status(thm)],[224])).
% 0.18/0.45 tff(226,plain,
% 0.18/0.45 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) <=> (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[225])).
% 0.18/0.45 tff(227,plain,
% 0.18/0.45 (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[220, 226])).
% 0.18/0.45 tff(228,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[1, 227])).
% 0.18/0.45 tff(229,plain,((~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(230,plain,
% 0.18/0.45 (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[229, 1])).
% 0.18/0.45 tff(231,plain,
% 0.18/0.45 ((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[173, 230])).
% 0.18/0.45 tff(232,plain,
% 0.18/0.45 (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[171, 231, 222])).
% 0.18/0.45 tff(233,plain,
% 0.18/0.45 (((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))) | greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(234,plain,
% 0.18/0.45 (greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.18/0.45 tff(235,plain,
% 0.18/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(236,plain,
% 0.18/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(237,plain,
% 0.18/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.18/0.45 tff(238,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[237, 29, 220, 234, 1])).
% 0.18/0.45 tff(239,plain,(~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(240,plain,
% 0.18/0.45 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(241,plain,
% 0.18/0.45 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[240])).
% 0.18/0.45 tff(242,plain,
% 0.18/0.45 (^[E: $i] : rewrite(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(243,plain,
% 0.18/0.45 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[242])).
% 0.18/0.45 tff(244,plain,
% 0.18/0.45 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[243, 241])).
% 0.18/0.45 tff(245,plain,
% 0.18/0.45 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & stable(E)) <=> (~((~environment(E)) | (~stable(E))))), ((~(environment(E) & stable(E))) <=> (~(~((~environment(E)) | (~stable(E))))))), rewrite((~(~((~environment(E)) | (~stable(E))))) <=> ((~environment(E)) | (~stable(E)))), ((~(environment(E) & stable(E))) <=> ((~environment(E)) | (~stable(E))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), rewrite((((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))), ((in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))), rewrite((in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))) <=> (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))), ((in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(246,plain,
% 0.18/0.45 (![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[245])).
% 0.18/0.45 tff(247,plain,
% 0.18/0.45 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(248,plain,
% 0.18/0.45 (^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[To: $i] : rewrite((in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))), rewrite(((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(249,plain,
% 0.18/0.45 (![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[248])).
% 0.18/0.45 tff(250,axiom,(![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1')).
% 0.18/0.45 tff(251,plain,
% 0.18/0.45 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.18/0.45 tff(252,plain,
% 0.18/0.45 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (in_environment(E, To) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.18/0.45 tff(253,plain,(
% 0.18/0.45 ![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_0(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_0(E)))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[252])).
% 0.18/0.45 tff(254,plain,
% 0.18/0.45 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.18/0.45 tff(255,plain,
% 0.18/0.45 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[254, 244])).
% 0.18/0.45 tff(256,plain,
% 0.18/0.45 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(257,plain,
% 0.18/0.45 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(258,plain,
% 0.18/0.45 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_0(E))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_0(E))))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2)))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.18/0.45 tff(259,plain,
% 0.18/0.45 (~((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[258, 255, 70, 69])).
% 0.18/0.45 tff(260,plain,
% 0.18/0.45 (((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2)))))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(261,plain,
% 0.18/0.45 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.18/0.45 tff(262,plain,
% 0.18/0.45 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(263,plain,
% 0.18/0.46 ((greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))) <=> ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(264,plain,
% 0.18/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[263])).
% 0.18/0.46 tff(265,plain,
% 0.18/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[264, 262])).
% 0.18/0.46 tff(266,plain,
% 0.18/0.46 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(267,plain,
% 0.18/0.46 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.18/0.46 tff(268,plain,
% 0.18/0.46 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[267, 261, 145])).
% 0.18/0.46 tff(269,plain,
% 0.18/0.46 (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[268, 239])).
% 0.18/0.46 tff(270,assumption,(~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.18/0.46 tff(271,assumption,(~((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))), introduced(assumption)).
% 0.18/0.46 tff(272,plain,
% 0.18/0.46 (((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | (~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(273,plain,
% 0.18/0.46 (~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.18/0.46 tff(274,plain,
% 0.18/0.46 (((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(275,plain,
% 0.18/0.46 (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[274, 271])).
% 0.18/0.46 tff(276,plain,
% 0.18/0.46 (((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2)))))) | in_environment(E!2, tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(277,plain,
% 0.18/0.46 (in_environment(E!2, tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[276, 259])).
% 0.18/0.46 tff(278,plain,
% 0.18/0.46 (^[E: $i, T1: $i, T2: $i] : refl((greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(279,plain,
% 0.18/0.46 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2))) <=> ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[278])).
% 0.18/0.46 tff(280,plain,
% 0.18/0.46 (^[E: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite((in_environment(E, T1) & in_environment(E, T2)) <=> (~((~in_environment(E, T1)) | (~in_environment(E, T2))))), ((~(in_environment(E, T1) & in_environment(E, T2))) <=> (~(~((~in_environment(E, T1)) | (~in_environment(E, T2))))))), rewrite((~(~((~in_environment(E, T1)) | (~in_environment(E, T2))))) <=> ((~in_environment(E, T1)) | (~in_environment(E, T2)))), ((~(in_environment(E, T1) & in_environment(E, T2))) <=> ((~in_environment(E, T1)) | (~in_environment(E, T2))))), ((greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2)))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | ((~in_environment(E, T1)) | (~in_environment(E, T2)))))), rewrite((greater(T1, T2) | (T2 = T1) | greater(T2, T1) | ((~in_environment(E, T1)) | (~in_environment(E, T2)))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))), ((greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2)))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(281,plain,
% 0.18/0.46 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2)))) <=> ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[280])).
% 0.18/0.46 tff(282,plain,
% 0.18/0.46 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2)))) <=> ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(283,plain,
% 0.18/0.46 (^[E: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(T2, T1) | (T2 = T1)) <=> ((T2 = T1) | greater(T2, T1))), (((greater(T2, T1) | (T2 = T1)) | greater(T1, T2)) <=> (((T2 = T1) | greater(T2, T1)) | greater(T1, T2)))), rewrite((((T2 = T1) | greater(T2, T1)) | greater(T1, T2)) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1))), (((greater(T2, T1) | (T2 = T1)) | greater(T1, T2)) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1)))), (((in_environment(E, T1) & in_environment(E, T2)) => ((greater(T2, T1) | (T2 = T1)) | greater(T1, T2))) <=> ((in_environment(E, T1) & in_environment(E, T2)) => (greater(T1, T2) | (T2 = T1) | greater(T2, T1))))), rewrite(((in_environment(E, T1) & in_environment(E, T2)) => (greater(T1, T2) | (T2 = T1) | greater(T2, T1))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))), (((in_environment(E, T1) & in_environment(E, T2)) => ((greater(T2, T1) | (T2 = T1)) | greater(T1, T2))) <=> (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(284,plain,
% 0.18/0.46 (![E: $i, T1: $i, T2: $i] : ((in_environment(E, T1) & in_environment(E, T2)) => ((greater(T2, T1) | (T2 = T1)) | greater(T1, T2))) <=> ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[283])).
% 0.18/0.46 tff(285,axiom,(![E: $i, T1: $i, T2: $i] : ((in_environment(E, T1) & in_environment(E, T2)) => ((greater(T2, T1) | (T2 = T1)) | greater(T1, T2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_times_in_environment')).
% 0.18/0.46 tff(286,plain,
% 0.18/0.46 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.18/0.46 tff(287,plain,
% 0.18/0.46 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.18/0.46 tff(288,plain,(
% 0.18/0.46 ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[287])).
% 0.18/0.46 tff(289,plain,
% 0.18/0.46 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[288, 281])).
% 0.18/0.46 tff(290,plain,
% 0.18/0.46 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[289, 279])).
% 0.18/0.46 tff(291,plain,
% 0.18/0.46 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(292,plain,
% 0.18/0.46 ((greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2)))) <=> ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(293,plain,
% 0.18/0.46 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[292])).
% 0.18/0.46 tff(294,plain,
% 0.18/0.46 (((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[293, 291])).
% 0.18/0.46 tff(295,plain,
% 0.18/0.46 ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(296,plain,
% 0.18/0.46 ((~![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.18/0.46 tff(297,plain,
% 0.18/0.46 ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[296, 290, 277, 89, 270])).
% 0.18/0.46 tff(298,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[297, 275, 273])).
% 0.18/0.46 tff(299,plain,(((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(300,plain,
% 0.18/0.46 ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[299, 270])).
% 0.18/0.46 tff(301,plain,
% 0.18/0.46 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(302,plain,
% 0.18/0.46 (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[301, 11])).
% 0.18/0.46 tff(303,assumption,((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.18/0.46 tff(304,plain,
% 0.18/0.46 ((~(greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) | greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(305,plain,
% 0.18/0.46 ((~(greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) | greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.18/0.46 tff(306,plain,
% 0.18/0.46 (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[305, 302])).
% 0.18/0.46 tff(307,assumption,(tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)), introduced(assumption)).
% 0.18/0.46 tff(308,plain,
% 0.18/0.46 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2))) <=> subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[307])).
% 0.18/0.46 tff(309,plain,
% 0.18/0.46 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2)) <=> subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.46 inference(symmetry,[status(thm)],[308])).
% 0.18/0.46 tff(310,plain,
% 0.18/0.46 ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) <=> (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[309])).
% 0.18/0.46 tff(311,assumption,(~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.18/0.46 tff(312,plain,
% 0.18/0.46 (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.18/0.46 tff(313,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[145, 312])).
% 0.18/0.46 tff(314,plain,((~(tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2))) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(315,plain,
% 0.18/0.46 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[314, 307])).
% 0.18/0.46 tff(316,plain,
% 0.18/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(317,plain,
% 0.18/0.46 ((greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))) <=> ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(318,plain,
% 0.18/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[317])).
% 0.18/0.46 tff(319,plain,
% 0.18/0.46 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[318, 316])).
% 0.18/0.46 tff(320,plain,
% 0.18/0.46 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(321,plain,
% 0.18/0.46 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.18/0.46 tff(322,plain,
% 0.18/0.46 (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[321, 261, 315])).
% 0.18/0.46 tff(323,plain,
% 0.18/0.46 (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[322, 306])).
% 0.18/0.46 tff(324,plain,
% 0.18/0.46 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(325,plain,
% 0.18/0.46 (((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(326,plain,
% 0.18/0.46 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2)))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[325])).
% 0.18/0.46 tff(327,plain,
% 0.18/0.46 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[326, 324])).
% 0.18/0.46 tff(328,plain,
% 0.18/0.46 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(329,plain,
% 0.18/0.46 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.18/0.47 tff(330,plain,
% 0.18/0.47 ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[329, 208, 70, 315])).
% 0.18/0.47 tff(331,plain,
% 0.18/0.47 (tptp_fun_T_1(E!2) = tptp_fun_T_3(tptp_fun_T_1(E!2))),
% 0.18/0.47 inference(symmetry,[status(thm)],[307])).
% 0.18/0.47 tff(332,plain,
% 0.18/0.47 (outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2)) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[331])).
% 0.18/0.47 tff(333,plain,
% 0.18/0.47 (outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))),
% 0.18/0.47 inference(symmetry,[status(thm)],[332])).
% 0.18/0.47 tff(334,plain,
% 0.18/0.47 ((~outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> (~outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[333])).
% 0.18/0.47 tff(335,plain,
% 0.18/0.47 (~outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[214, 334])).
% 0.18/0.47 tff(336,plain,
% 0.18/0.47 ((~((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2)))) | ((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_1(E!2))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(337,plain,
% 0.18/0.47 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[336, 335, 330])).
% 0.18/0.47 tff(338,plain,
% 0.18/0.47 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(339,plain,
% 0.18/0.47 (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[338, 11])).
% 0.18/0.47 tff(340,plain,
% 0.18/0.47 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = growth_rate(first_movers, tptp_fun_T_1(E!2))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[307])).
% 0.18/0.47 tff(341,plain,
% 0.18/0.47 (growth_rate(first_movers, tptp_fun_T_1(E!2)) = growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(symmetry,[status(thm)],[340])).
% 0.18/0.47 tff(342,plain,
% 0.18/0.47 (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = growth_rate(efficient_producers, tptp_fun_T_1(E!2))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[307])).
% 0.18/0.47 tff(343,plain,
% 0.18/0.47 (growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(symmetry,[status(thm)],[342])).
% 0.18/0.47 tff(344,assumption,(~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)), introduced(assumption)).
% 0.18/0.47 tff(345,plain,
% 0.18/0.47 (((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(346,plain,
% 0.18/0.47 ((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[345, 344])).
% 0.18/0.47 tff(347,assumption,(greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))), introduced(assumption)).
% 0.18/0.47 tff(348,assumption,(greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)), introduced(assumption)).
% 0.18/0.47 tff(349,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(350,plain,
% 0.18/0.47 ((greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero))) <=> (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(351,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[350])).
% 0.18/0.47 tff(352,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[351, 349])).
% 0.18/0.47 tff(353,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(354,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.18/0.47 tff(355,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[354, 29, 344, 348, 347])).
% 0.18/0.47 tff(356,plain,((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(357,plain,
% 0.18/0.47 (~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[356, 344, 347])).
% 0.18/0.47 tff(358,plain,
% 0.18/0.47 (((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2))))) | greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(359,plain,
% 0.18/0.47 ((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[358, 357])).
% 0.18/0.47 tff(360,plain,
% 0.18/0.47 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(361,plain,
% 0.18/0.47 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(362,plain,
% 0.18/0.47 ((~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) <=> (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(363,plain,
% 0.18/0.47 ((~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) <=> (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(364,plain,
% 0.18/0.47 ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) <=> (~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(365,plain,
% 0.18/0.47 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))) <=> ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[364, 363, 362])).
% 0.18/0.47 tff(366,plain,
% 0.18/0.47 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[365, 361])).
% 0.18/0.47 tff(367,plain,
% 0.18/0.47 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[366])).
% 0.18/0.47 tff(368,plain,
% 0.18/0.47 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[367, 360])).
% 0.18/0.47 tff(369,plain,
% 0.18/0.47 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(370,plain,
% 0.18/0.47 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.18/0.47 tff(371,plain,
% 0.18/0.47 ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))) | (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[370, 158, 70, 112])).
% 0.18/0.47 tff(372,plain,
% 0.18/0.47 (~((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[371, 359, 346, 315])).
% 0.18/0.47 tff(373,plain,
% 0.18/0.47 (((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero))) | (growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(374,plain,
% 0.18/0.47 (growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[373, 372])).
% 0.18/0.47 tff(375,plain,
% 0.18/0.47 (zero = growth_rate(efficient_producers, tptp_fun_T_1(E!2))),
% 0.18/0.47 inference(symmetry,[status(thm)],[374])).
% 0.18/0.47 tff(376,plain,
% 0.18/0.47 (zero = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[375, 343])).
% 0.18/0.47 tff(377,plain,
% 0.18/0.47 (greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[376, 341])).
% 0.18/0.47 tff(378,plain,
% 0.18/0.47 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.47 inference(symmetry,[status(thm)],[377])).
% 0.18/0.47 tff(379,plain,
% 0.18/0.47 (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[343, 341])).
% 0.18/0.48 tff(380,plain,
% 0.18/0.48 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[347, 379])).
% 0.18/0.48 tff(381,plain,
% 0.18/0.48 (greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[380, 378])).
% 0.18/0.48 tff(382,plain,
% 0.18/0.48 (((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(383,plain,
% 0.18/0.48 ((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[382, 374])).
% 0.18/0.48 tff(384,plain,
% 0.18/0.48 ((~(greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) | greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(385,plain,
% 0.18/0.48 (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[384, 383, 339])).
% 0.18/0.48 tff(386,plain,
% 0.18/0.48 ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(387,plain,
% 0.18/0.48 (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[386, 385, 337])).
% 0.18/0.48 tff(388,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[387, 381])).
% 0.18/0.48 tff(389,plain,(greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) | (~(tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(390,plain,
% 0.18/0.48 (greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[389, 307, 323])).
% 0.18/0.48 tff(391,plain,
% 0.18/0.48 (((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(392,plain,
% 0.18/0.48 ((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.18/0.48 tff(393,plain,
% 0.18/0.48 ((~(greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)))) | greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[384, 392])).
% 0.18/0.48 tff(394,plain,
% 0.18/0.48 (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[393, 339])).
% 0.18/0.48 tff(395,plain,
% 0.18/0.48 (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[386, 394, 337])).
% 0.18/0.48 tff(396,plain,
% 0.18/0.48 (((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(397,plain,
% 0.18/0.48 ((~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[396, 395])).
% 0.18/0.48 tff(398,plain,
% 0.18/0.48 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[323, 379])).
% 0.18/0.48 tff(399,assumption,(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero), introduced(assumption)).
% 0.18/0.48 tff(400,plain,
% 0.18/0.48 (zero = growth_rate(efficient_producers, tptp_fun_T_1(E!2))),
% 0.18/0.48 inference(symmetry,[status(thm)],[399])).
% 0.18/0.48 tff(401,plain,
% 0.18/0.48 (zero = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[400, 343])).
% 0.18/0.48 tff(402,plain,
% 0.18/0.48 (greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[401, 341])).
% 0.18/0.48 tff(403,plain,
% 0.18/0.48 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(symmetry,[status(thm)],[402])).
% 0.18/0.48 tff(404,plain,
% 0.18/0.48 (greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[1, 403])).
% 0.18/0.48 tff(405,assumption,(~greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2)))), introduced(assumption)).
% 0.18/0.48 tff(406,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[405, 404])).
% 0.18/0.48 tff(407,plain,((~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)) | greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~(tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(408,plain,
% 0.18/0.48 (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[407, 395, 398, 307])).
% 0.18/0.48 tff(409,plain,
% 0.18/0.48 ((~(growth_rate(first_movers, tptp_fun_T_1(E!2)) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_1(E!2)) = zero))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[373, 408])).
% 0.18/0.48 tff(410,plain,
% 0.18/0.48 (~((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[371, 409, 397, 315])).
% 0.18/0.48 tff(411,plain,
% 0.18/0.48 (((~greater(growth_rate(first_movers, tptp_fun_T_1(E!2)), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2))))) | greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(412,plain,
% 0.18/0.48 (greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[411, 410])).
% 0.18/0.48 tff(413,plain,
% 0.18/0.48 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(414,plain,
% 0.18/0.48 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(415,plain,
% 0.18/0.48 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_1(E!2))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_1(E!2)))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_1(E!2)), growth_rate(first_movers, tptp_fun_T_1(E!2))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.18/0.48 tff(416,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[415, 29, 395, 412, 323])).
% 0.18/0.48 tff(417,plain,((~(tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2))) | (~((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(418,plain,
% 0.18/0.48 (~(tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[417, 300])).
% 0.18/0.48 tff(419,plain,
% 0.18/0.48 (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[137, 418])).
% 0.18/0.48 tff(420,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(421,plain,
% 0.18/0.48 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[420, 11])).
% 0.18/0.48 tff(422,assumption,(~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.18/0.48 tff(423,plain,
% 0.18/0.48 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(424,plain,
% 0.18/0.48 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))) | (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[423, 422])).
% 0.18/0.48 tff(425,plain,
% 0.18/0.48 (~((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[424, 421])).
% 0.18/0.48 tff(426,plain,
% 0.18/0.48 (((tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(427,plain,
% 0.18/0.48 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[426, 425])).
% 0.18/0.48 tff(428,assumption,(~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.18/0.48 tff(429,assumption,(greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.18/0.48 tff(430,plain,
% 0.18/0.48 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(431,plain,
% 0.18/0.48 ((greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))) <=> ((~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(432,plain,
% 0.18/0.48 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[431])).
% 0.18/0.48 tff(433,plain,
% 0.18/0.48 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[432, 430])).
% 0.18/0.48 tff(434,plain,
% 0.18/0.48 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(435,plain,
% 0.18/0.48 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.18/0.48 tff(436,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[435, 29, 120, 429, 428])).
% 0.18/0.48 tff(437,plain,((~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(438,plain,
% 0.18/0.48 (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[437, 427, 419])).
% 0.18/0.48 tff(439,plain,
% 0.18/0.48 (tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[297, 438])).
% 0.18/0.48 tff(440,plain,
% 0.18/0.48 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[439])).
% 0.18/0.48 tff(441,plain,
% 0.18/0.48 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.48 inference(symmetry,[status(thm)],[440])).
% 0.18/0.48 tff(442,plain,
% 0.18/0.48 ((~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))) <=> (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2)))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[441])).
% 0.18/0.48 tff(443,plain,
% 0.18/0.48 (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[422, 442])).
% 0.18/0.48 tff(444,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[105, 443])).
% 0.18/0.48 tff(445,plain,(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(446,plain,
% 0.18/0.48 (greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[445, 269])).
% 0.18/0.48 tff(447,assumption,(greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.18/0.48 tff(448,plain,
% 0.18/0.48 (((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))))) <=> ((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(449,plain,
% 0.18/0.48 ((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | ((~in_environment(E!2, tptp_fun_To_0(E!2))) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(450,plain,
% 0.18/0.48 ((~![To: $i] : ((~in_environment(E!2, To)) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(To)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)))))) | (~in_environment(E!2, tptp_fun_To_0(E!2))) | (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.18/0.48 tff(451,plain,
% 0.18/0.48 (~(outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[450, 96, 277])).
% 0.18/0.48 tff(452,plain,
% 0.18/0.48 ((outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(453,plain,
% 0.18/0.48 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[452, 451])).
% 0.18/0.48 tff(454,plain,
% 0.18/0.48 ((outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(455,plain,
% 0.18/0.48 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[454, 451])).
% 0.18/0.48 tff(456,plain,
% 0.18/0.48 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(457,plain,
% 0.18/0.48 ((greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))) <=> ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(458,plain,
% 0.18/0.48 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | ((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[457])).
% 0.18/0.48 tff(459,plain,
% 0.18/0.48 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[458, 456])).
% 0.18/0.48 tff(460,plain,
% 0.18/0.48 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(461,plain,
% 0.18/0.48 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.18/0.48 tff(462,plain,
% 0.18/0.48 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[461, 261, 455, 453])).
% 0.18/0.48 tff(463,plain,
% 0.18/0.48 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(464,plain,
% 0.18/0.48 (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[463, 11])).
% 0.18/0.48 tff(465,assumption,(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.18/0.48 tff(466,assumption,(~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)), introduced(assumption)).
% 0.18/0.48 tff(467,plain,
% 0.18/0.48 (((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(468,plain,
% 0.18/0.48 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[467, 466])).
% 0.18/0.48 tff(469,assumption,(greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)), introduced(assumption)).
% 0.18/0.48 tff(470,plain,
% 0.18/0.48 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(471,plain,
% 0.18/0.48 ((greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))) <=> (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(472,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[471])).
% 0.18/0.49 tff(473,plain,
% 0.18/0.49 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[472, 470])).
% 0.18/0.49 tff(474,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(475,plain,
% 0.18/0.49 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.18/0.49 tff(476,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[475, 29, 469, 466, 462])).
% 0.18/0.49 tff(477,plain,((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(478,plain,
% 0.18/0.49 (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[477, 466])).
% 0.18/0.49 tff(479,plain,
% 0.18/0.49 (((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))) | greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(480,plain,
% 0.18/0.49 ((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[479, 478])).
% 0.18/0.49 tff(481,plain,
% 0.18/0.49 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(482,plain,
% 0.18/0.49 (((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(483,plain,
% 0.18/0.49 ((~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) <=> (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(484,plain,
% 0.18/0.49 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(485,plain,
% 0.18/0.49 ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(486,plain,
% 0.18/0.49 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))) <=> ((~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[485, 484, 483])).
% 0.18/0.49 tff(487,plain,
% 0.18/0.49 (((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))) <=> ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[486, 482])).
% 0.18/0.49 tff(488,plain,
% 0.18/0.49 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[487])).
% 0.18/0.49 tff(489,plain,
% 0.18/0.49 (((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) <=> ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[488, 481])).
% 0.18/0.49 tff(490,plain,
% 0.18/0.49 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | ((~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(491,plain,
% 0.18/0.49 ((~![E: $i, T: $i] : ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.18/0.49 tff(492,plain,
% 0.18/0.49 ((~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[491, 158, 70, 455])).
% 0.18/0.49 tff(493,plain,
% 0.18/0.49 (~((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[492, 480, 465, 468])).
% 0.18/0.49 tff(494,plain,
% 0.18/0.49 (((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))) | (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(495,plain,
% 0.18/0.49 (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[494, 493])).
% 0.18/0.49 tff(496,plain,
% 0.18/0.49 (zero = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.18/0.49 inference(symmetry,[status(thm)],[495])).
% 0.18/0.49 tff(497,plain,
% 0.18/0.49 (((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))) | (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(498,plain,
% 0.18/0.49 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[497, 493])).
% 0.18/0.49 tff(499,plain,
% 0.18/0.49 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[498, 496])).
% 0.18/0.49 tff(500,plain,
% 0.18/0.49 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) <=> greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[499])).
% 0.18/0.49 tff(501,plain,
% 0.18/0.49 (greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.49 inference(symmetry,[status(thm)],[500])).
% 0.18/0.49 tff(502,plain,
% 0.18/0.49 ((~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) <=> (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[501])).
% 0.18/0.49 tff(503,plain,
% 0.18/0.49 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) <=> greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[495, 496])).
% 0.18/0.49 tff(504,plain,
% 0.18/0.49 ((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) <=> (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[503])).
% 0.18/0.49 tff(505,plain,
% 0.18/0.49 (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[466, 504])).
% 0.18/0.49 tff(506,plain,
% 0.18/0.49 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[505, 502])).
% 0.18/0.49 tff(507,plain,
% 0.18/0.49 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[495])).
% 0.18/0.49 tff(508,plain,
% 0.18/0.49 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[462, 507])).
% 0.18/0.49 tff(509,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[508, 506])).
% 0.18/0.49 tff(510,plain,(greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(511,plain,
% 0.18/0.49 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[510, 465])).
% 0.18/0.49 tff(512,plain,
% 0.18/0.49 (((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(513,plain,
% 0.18/0.49 ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[512, 511])).
% 0.18/0.49 tff(514,plain,
% 0.18/0.49 ((~(greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))) | greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(515,plain,
% 0.18/0.49 ((~(greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) <=> ((growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)))) | greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[514, 513])).
% 0.18/0.49 tff(516,plain,
% 0.18/0.49 (greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[515, 464])).
% 0.18/0.49 tff(517,plain,
% 0.18/0.49 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(518,plain,
% 0.18/0.49 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(519,plain,
% 0.18/0.49 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!2)) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.18/0.49 tff(520,plain,
% 0.18/0.49 ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[519, 208, 70, 455])).
% 0.18/0.49 tff(521,plain,
% 0.18/0.49 ((outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))) | (~outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(522,plain,
% 0.18/0.50 (~outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[521, 451])).
% 0.18/0.50 tff(523,plain,
% 0.18/0.50 ((~((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | ((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))) | outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(524,plain,
% 0.18/0.50 ((~((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> outcompetes(efficient_producers, first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | ((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[523, 522])).
% 0.18/0.50 tff(525,plain,
% 0.18/0.50 ((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[524, 520])).
% 0.18/0.50 tff(526,plain,
% 0.18/0.50 ((~((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) | (~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(527,plain,
% 0.18/0.50 ((~greater_or_equal(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[526, 525])).
% 0.18/0.50 tff(528,plain,
% 0.18/0.50 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[527, 516])).
% 0.18/0.50 tff(529,plain,
% 0.18/0.50 (((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(530,plain,
% 0.18/0.50 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[529, 528])).
% 0.18/0.50 tff(531,assumption,(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero), introduced(assumption)).
% 0.18/0.50 tff(532,plain,
% 0.18/0.50 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[531])).
% 0.18/0.50 tff(533,plain,
% 0.18/0.50 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(symmetry,[status(thm)],[532])).
% 0.18/0.50 tff(534,plain,
% 0.18/0.50 ((~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) <=> (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[533])).
% 0.18/0.50 tff(535,assumption,(~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))), introduced(assumption)).
% 0.18/0.50 tff(536,plain,
% 0.18/0.50 (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.18/0.50 tff(537,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[462, 536])).
% 0.18/0.50 tff(538,plain,((~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(539,plain,
% 0.18/0.50 (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[538, 528])).
% 0.18/0.50 tff(540,plain,
% 0.18/0.50 ((~(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)) | (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[494, 539])).
% 0.18/0.50 tff(541,plain,
% 0.18/0.50 (~((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[492, 540, 465, 530])).
% 0.18/0.50 tff(542,plain,
% 0.18/0.50 (((~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))) | greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(543,plain,
% 0.18/0.50 (greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[542, 541])).
% 0.18/0.50 tff(544,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(545,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(546,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.18/0.50 tff(547,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[546, 29, 528, 543, 462])).
% 0.18/0.50 tff(548,plain,(~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(549,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(550,plain,
% 0.18/0.50 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[549, 11])).
% 0.18/0.50 tff(551,assumption,(~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.18/0.50 tff(552,plain,
% 0.18/0.50 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(553,plain,
% 0.18/0.50 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))) | (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[552, 551])).
% 0.18/0.50 tff(554,plain,
% 0.18/0.50 (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[553, 550])).
% 0.18/0.50 tff(555,plain,
% 0.18/0.50 (((tptp_fun_T_3(tptp_fun_To_0(E!2)) = equilibrium(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(556,plain,
% 0.18/0.50 (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[555, 554])).
% 0.18/0.50 tff(557,assumption,(greater(tptp_fun_To_0(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.18/0.50 tff(558,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> ((tptp_fun_To_0(E!2) = equilibrium(E!2)) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(559,plain,
% 0.18/0.50 (greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> ((tptp_fun_To_0(E!2) = equilibrium(E!2)) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[558, 11])).
% 0.18/0.50 tff(560,plain,
% 0.18/0.50 (((tptp_fun_To_0(E!2) = equilibrium(E!2)) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(561,plain,
% 0.18/0.50 ((tptp_fun_To_0(E!2) = equilibrium(E!2)) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[560, 557])).
% 0.18/0.50 tff(562,plain,
% 0.18/0.50 ((~(greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> ((tptp_fun_To_0(E!2) = equilibrium(E!2)) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))))) | greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~((tptp_fun_To_0(E!2) = equilibrium(E!2)) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(563,plain,
% 0.18/0.50 ((~(greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> ((tptp_fun_To_0(E!2) = equilibrium(E!2)) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))))) | greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[562, 561])).
% 0.18/0.50 tff(564,plain,
% 0.18/0.50 (greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[563, 559])).
% 0.18/0.50 tff(565,assumption,(tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)), introduced(assumption)).
% 0.18/0.50 tff(566,plain,
% 0.18/0.50 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[565])).
% 0.18/0.50 tff(567,plain,
% 0.18/0.50 (greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.18/0.50 inference(symmetry,[status(thm)],[566])).
% 0.18/0.50 tff(568,assumption,(greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.18/0.50 tff(569,plain,
% 0.18/0.50 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.18/0.50 tff(570,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[551, 569])).
% 0.18/0.50 tff(571,plain,((~(tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater_or_equal(tptp_fun_To_0(E!2), equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(572,plain,
% 0.18/0.50 (~(tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[571, 551, 564])).
% 0.18/0.50 tff(573,plain,
% 0.18/0.50 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(574,plain,
% 0.18/0.50 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[573, 11])).
% 0.18/0.50 tff(575,plain,
% 0.18/0.50 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(576,plain,
% 0.18/0.50 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))))) | ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[575, 453])).
% 0.18/0.50 tff(577,plain,
% 0.18/0.50 ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[576, 574])).
% 0.18/0.50 tff(578,plain,
% 0.18/0.50 ((~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2)))) | (tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(579,plain,
% 0.18/0.50 ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[578, 577])).
% 0.18/0.50 tff(580,plain,
% 0.18/0.50 (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[579, 572])).
% 0.18/0.50 tff(581,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(582,plain,
% 0.18/0.50 ((greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))) <=> ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(583,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[582])).
% 0.18/0.50 tff(584,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[583, 581])).
% 0.18/0.50 tff(585,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(586,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.18/0.50 tff(587,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[586, 29, 580, 557, 556])).
% 0.18/0.50 tff(588,plain,(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(589,plain,
% 0.18/0.50 (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[588, 548])).
% 0.18/0.50 tff(590,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(591,plain,
% 0.18/0.50 ((greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2)))) <=> ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(592,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[591])).
% 0.18/0.50 tff(593,plain,
% 0.18/0.50 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[592, 590])).
% 0.18/0.50 tff(594,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(595,plain,
% 0.18/0.50 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.18/0.50 tff(596,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[595, 29, 121, 589, 447])).
% 0.18/0.50 tff(597,plain,((~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(598,plain,
% 0.18/0.50 (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[597, 446])).
% 0.18/0.50 tff(599,plain,
% 0.18/0.50 (tptp_fun_T_1(E!2) = equilibrium(E!2)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[117, 598])).
% 0.18/0.50 tff(600,plain,
% 0.18/0.50 (greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[599])).
% 0.18/0.50 tff(601,plain,
% 0.18/0.50 (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.18/0.50 inference(symmetry,[status(thm)],[600])).
% 0.18/0.50 tff(602,plain,
% 0.18/0.50 ((~greater(tptp_fun_To_0(E!2), equilibrium(E!2))) <=> (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[601])).
% 0.18/0.50 tff(603,plain,
% 0.18/0.50 (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[589, 602])).
% 0.18/0.50 tff(604,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[446, 603])).
% 0.18/0.50 % SZS output end Proof
%------------------------------------------------------------------------------