TSTP Solution File: MGT029+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT029+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:21:58 EDT 2022
% Result : Theorem 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : MGT029+1 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:39:28 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 tff(greater_or_equal_type, type, (
% 0.22/0.43 greater_or_equal: ( $i * $i ) > $o)).
% 0.22/0.43 tff(tptp_fun_To_0_type, type, (
% 0.22/0.43 tptp_fun_To_0: $i > $i)).
% 0.22/0.43 tff(tptp_fun_E_2_type, type, (
% 0.22/0.43 tptp_fun_E_2: $i)).
% 0.22/0.43 tff(tptp_fun_T_3_type, type, (
% 0.22/0.43 tptp_fun_T_3: $i > $i)).
% 0.22/0.43 tff(tptp_fun_T_1_type, type, (
% 0.22/0.43 tptp_fun_T_1: $i > $i)).
% 0.22/0.43 tff(greater_type, type, (
% 0.22/0.43 greater: ( $i * $i ) > $o)).
% 0.22/0.43 tff(equilibrium_type, type, (
% 0.22/0.43 equilibrium: $i > $i)).
% 0.22/0.43 tff(growth_rate_type, type, (
% 0.22/0.43 growth_rate: ( $i * $i ) > $i)).
% 0.22/0.43 tff(first_movers_type, type, (
% 0.22/0.43 first_movers: $i)).
% 0.22/0.43 tff(efficient_producers_type, type, (
% 0.22/0.43 efficient_producers: $i)).
% 0.22/0.43 tff(zero_type, type, (
% 0.22/0.43 zero: $i)).
% 0.22/0.43 tff(subpopulations_type, type, (
% 0.22/0.43 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.22/0.43 tff(in_environment_type, type, (
% 0.22/0.43 in_environment: ( $i * $i ) > $o)).
% 0.22/0.43 tff(stable_type, type, (
% 0.22/0.43 stable: $i > $o)).
% 0.22/0.43 tff(environment_type, type, (
% 0.22/0.43 environment: $i > $o)).
% 0.22/0.43 tff(1,plain,
% 0.22/0.43 (^[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))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(2,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.43 tff(3,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(4,plain,
% 0.22/0.43 (^[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))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(5,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.22/0.43 tff(6,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal')).
% 0.22/0.43 tff(7,plain,
% 0.22/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.43 tff(8,plain,
% 0.22/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.43 tff(9,plain,(
% 0.22/0.43 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[8])).
% 0.22/0.43 tff(10,plain,
% 0.22/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.22/0.43 tff(11,plain,
% 0.22/0.43 ((~![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))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(12,plain,
% 0.22/0.43 (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)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.22/0.43 tff(13,plain,
% 0.22/0.43 (((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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(14,plain,
% 0.22/0.43 ((~(~(environment(E!2) & stable(E!2)))) <=> (environment(E!2) & stable(E!2))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(15,plain,
% 0.22/0.44 (((~(~(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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[14])).
% 0.22/0.44 tff(16,plain,
% 0.22/0.44 (((~(~(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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[15, 13])).
% 0.22/0.44 tff(17,plain,
% 0.22/0.44 ((~![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), zero) & greater(zero, 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), zero) & greater(zero, growth_rate(first_movers, T)))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(18,plain,
% 0.22/0.44 ((~![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), zero) & greater(zero, 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), zero) & greater(zero, growth_rate(first_movers, T)))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(19,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), zero) & greater(zero, growth_rate(first_movers, T))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l11')).
% 0.22/0.44 tff(20,plain,
% 0.22/0.44 (~![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), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.22/0.44 tff(21,plain,
% 0.22/0.44 (~![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), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.22/0.44 tff(22,plain,
% 0.22/0.44 (~![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), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.22/0.44 tff(23,plain,
% 0.22/0.44 (~![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), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.22/0.44 tff(24,plain,
% 0.22/0.44 (~![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), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.22/0.44 tff(25,plain,
% 0.22/0.44 (~![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), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.22/0.44 tff(26,plain,
% 0.22/0.44 (~![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), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.22/0.44 tff(27,plain,
% 0.22/0.44 (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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.22/0.44 tff(28,plain,
% 0.22/0.44 (stable(E!2)),
% 0.22/0.44 inference(and_elim,[status(thm)],[27])).
% 0.22/0.44 tff(29,plain,
% 0.22/0.44 (environment(E!2)),
% 0.22/0.44 inference(and_elim,[status(thm)],[27])).
% 0.22/0.44 tff(30,plain,
% 0.22/0.44 (^[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)))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(31,plain,
% 0.22/0.44 (![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))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[30])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (^[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)))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(33,plain,
% 0.22/0.44 (![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))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 (![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))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[33, 31])).
% 0.22/0.44 tff(35,plain,
% 0.22/0.44 (^[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))))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(36,plain,
% 0.22/0.44 (![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))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[35])).
% 0.22/0.44 tff(37,plain,
% 0.22/0.44 (![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)))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(38,plain,
% 0.22/0.45 (^[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)))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(39,plain,
% 0.22/0.45 (![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)))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.45 tff(40,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')).
% 0.22/0.45 tff(41,plain,
% 0.22/0.45 (![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)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.22/0.45 tff(42,plain,
% 0.22/0.45 (![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)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.22/0.45 tff(43,plain,(
% 0.22/0.45 ![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)))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[42])).
% 0.22/0.45 tff(44,plain,
% 0.22/0.45 (![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))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.22/0.45 tff(45,plain,
% 0.22/0.45 (![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))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.22/0.45 tff(46,plain,
% 0.22/0.45 (((~![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))))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(47,plain,
% 0.22/0.45 ((~![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))))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(48,plain,
% 0.22/0.45 ((~![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)))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.45 tff(49,plain,
% 0.22/0.45 (~((~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))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[48, 45, 29, 28])).
% 0.22/0.45 tff(50,plain,
% 0.22/0.45 (((~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)))))) | in_environment(E!2, tptp_fun_To_0(E!2))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(51,plain,
% 0.22/0.45 (in_environment(E!2, tptp_fun_To_0(E!2))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.22/0.45 tff(52,plain,
% 0.22/0.45 (^[To: $i] : refl(((~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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))) <=> ((~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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(53,plain,
% 0.22/0.45 (![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))) <=> ![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[52])).
% 0.22/0.45 tff(54,plain,
% 0.22/0.45 (^[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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))) <=> ((~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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(55,plain,
% 0.22/0.45 (![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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To))))))) <=> ![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.22/0.45 tff(56,plain,
% 0.22/0.45 (![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))) | (greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero) & greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))),
% 0.22/0.45 inference(and_elim,[status(thm)],[27])).
% 0.22/0.45 tff(57,plain,
% 0.22/0.45 (![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.22/0.45 tff(58,plain,
% 0.22/0.45 (![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.22/0.45 tff(59,plain,
% 0.22/0.45 (((~![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | ((~in_environment(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))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | (~in_environment(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))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(60,plain,
% 0.22/0.45 ((~![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | ((~in_environment(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))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(61,plain,
% 0.22/0.45 ((~![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | (~in_environment(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))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.45 tff(62,plain,
% 0.22/0.45 (~((~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))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[61, 58, 51])).
% 0.22/0.45 tff(63,plain,
% 0.22/0.45 (((~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))), zero)) | (~greater(zero, growth_rate(first_movers, 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))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(64,plain,
% 0.22/0.46 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.22/0.46 tff(65,plain,
% 0.22/0.46 (((~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))), zero)) | (~greater(zero, 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)))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(66,plain,
% 0.22/0.46 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_To_0(E!2)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.22/0.46 tff(67,plain,
% 0.22/0.46 (((~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)))))) | ![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))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(68,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[67, 49])).
% 0.22/0.46 tff(69,plain,
% 0.22/0.46 (((~![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_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)))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(70,plain,
% 0.22/0.46 ((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)))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(71,plain,
% 0.22/0.46 (((~![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_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))))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[70])).
% 0.22/0.46 tff(72,plain,
% 0.22/0.46 (((~![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_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)))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[71, 69])).
% 0.22/0.46 tff(73,plain,
% 0.22/0.46 ((~![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_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))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(74,plain,
% 0.22/0.46 ((~![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_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))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.46 tff(75,plain,
% 0.22/0.46 (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))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[74, 68, 66, 64])).
% 0.22/0.46 tff(76,assumption,(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.22/0.46 tff(77,assumption,(~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)), introduced(assumption)).
% 0.22/0.46 tff(78,assumption,(greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)), introduced(assumption)).
% 0.22/0.46 tff(79,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(80,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(81,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.22/0.46 tff(82,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(83,plain,
% 0.22/0.46 (^[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)))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(84,plain,
% 0.22/0.46 (![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))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[83])).
% 0.22/0.46 tff(85,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')).
% 0.22/0.46 tff(86,plain,
% 0.22/0.46 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.22/0.46 tff(87,plain,
% 0.22/0.46 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.22/0.46 tff(88,plain,(
% 0.22/0.46 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.22/0.46 inference(skolemize,[status(sab)],[87])).
% 0.22/0.46 tff(89,plain,
% 0.22/0.46 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.22/0.46 tff(90,plain,
% 0.22/0.46 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.22/0.46 tff(91,plain,
% 0.22/0.46 (((~![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))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(92,plain,
% 0.22/0.46 ((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))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(93,plain,
% 0.22/0.46 (((~![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)))))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.22/0.46 tff(94,plain,
% 0.22/0.46 (((~![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))))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[93, 91])).
% 0.22/0.46 tff(95,plain,
% 0.22/0.46 ((~![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)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(96,plain,
% 0.22/0.46 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.22/0.46 tff(97,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[96, 90, 77, 78, 75])).
% 0.22/0.46 tff(98,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,[]))).
% 0.22/0.46 tff(99,plain,
% 0.22/0.46 (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[98, 77])).
% 0.22/0.46 tff(100,plain,
% 0.22/0.46 (((~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)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(101,plain,
% 0.22/0.46 ((~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)))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.22/0.46 tff(102,plain,
% 0.22/0.46 (((~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))), zero)) | (~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))))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(103,plain,
% 0.22/0.46 ((~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)))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[102, 62])).
% 0.22/0.46 tff(104,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(105,plain,
% 0.22/0.46 (![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))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[104])).
% 0.22/0.46 tff(106,plain,
% 0.22/0.46 (^[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))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(107,plain,
% 0.22/0.47 (![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))))) <=> ![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))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[106])).
% 0.22/0.47 tff(108,plain,
% 0.22/0.47 (![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))))) <=> ![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)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(109,plain,
% 0.22/0.47 (^[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)))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(110,plain,
% 0.22/0.47 (![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)))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[109])).
% 0.22/0.47 tff(111,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')).
% 0.22/0.47 tff(112,plain,
% 0.22/0.47 (![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)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.47 tff(113,plain,
% 0.22/0.47 (![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)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.22/0.47 tff(114,plain,(
% 0.22/0.47 ![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)))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[113])).
% 0.22/0.47 tff(115,plain,
% 0.22/0.47 (![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))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.22/0.47 tff(116,plain,
% 0.22/0.47 (![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))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.22/0.47 tff(117,plain,
% 0.22/0.47 (((~![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)) | (~subpopulations(first_movers, efficient_producers, E!2, 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))))))) | (~((~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))))) <=> ((~![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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(118,plain,
% 0.22/0.47 (((~((~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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(119,plain,
% 0.22/0.47 ((~((~(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))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(120,plain,
% 0.22/0.47 ((~((~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)))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(121,plain,
% 0.22/0.47 ((~((~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(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)))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(122,plain,
% 0.22/0.47 (((~((~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(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))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[121, 120, 119])).
% 0.22/0.47 tff(123,plain,
% 0.22/0.47 (((~((~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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[122, 118])).
% 0.22/0.47 tff(124,plain,
% 0.22/0.47 (((~![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_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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[123])).
% 0.22/0.48 tff(125,plain,
% 0.22/0.48 (((~![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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[124, 117])).
% 0.22/0.48 tff(126,plain,
% 0.22/0.48 ((~![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))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(127,plain,
% 0.22/0.48 ((~![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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.22/0.48 tff(128,plain,
% 0.22/0.48 ((~((~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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[127, 116, 29, 66, 103])).
% 0.22/0.48 tff(129,plain,
% 0.22/0.48 (~((~(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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[128, 101, 76])).
% 0.22/0.48 tff(130,plain,
% 0.22/0.48 (((~(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)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(131,plain,
% 0.22/0.48 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.22/0.48 tff(132,plain,
% 0.22/0.48 (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)))) <=> greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[131])).
% 0.22/0.48 tff(133,plain,
% 0.22/0.48 (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))))),
% 0.22/0.48 inference(symmetry,[status(thm)],[132])).
% 0.22/0.48 tff(134,plain,
% 0.22/0.48 ((~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)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[133])).
% 0.22/0.48 tff(135,plain,
% 0.22/0.48 (~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))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[77, 134])).
% 0.22/0.48 tff(136,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[75, 135])).
% 0.22/0.48 tff(137,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,[]))).
% 0.22/0.48 tff(138,plain,
% 0.22/0.48 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), zero)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[137, 76])).
% 0.22/0.48 tff(139,plain,
% 0.22/0.48 ((~((~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(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)))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(140,plain,
% 0.22/0.48 ((~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)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[139, 103])).
% 0.22/0.48 tff(141,plain,
% 0.22/0.48 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[140, 138])).
% 0.22/0.48 tff(142,assumption,(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero), introduced(assumption)).
% 0.22/0.48 tff(143,plain,
% 0.22/0.48 (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)))) <=> greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[142])).
% 0.22/0.48 tff(144,plain,
% 0.22/0.48 (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))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.22/0.48 inference(symmetry,[status(thm)],[143])).
% 0.22/0.48 tff(145,plain,
% 0.22/0.48 ((~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))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[144])).
% 0.22/0.48 tff(146,assumption,(~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2))))), introduced(assumption)).
% 0.22/0.48 tff(147,plain,
% 0.22/0.48 (~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))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.22/0.48 tff(148,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[75, 147])).
% 0.22/0.48 tff(149,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,[]))).
% 0.22/0.48 tff(150,plain,
% 0.22/0.48 (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))) = zero)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[149, 141])).
% 0.22/0.48 tff(151,plain,
% 0.22/0.48 (((~(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)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(152,plain,
% 0.22/0.48 ((~(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))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.22/0.48 tff(153,plain,
% 0.22/0.48 (~((~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))))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[128, 152, 76])).
% 0.22/0.48 tff(154,plain,
% 0.22/0.48 (((~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))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(155,plain,
% 0.22/0.48 (greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.22/0.48 tff(156,plain,
% 0.22/0.48 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_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))))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(157,plain,
% 0.22/0.48 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_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))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(158,plain,
% 0.22/0.48 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_To_0(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_To_0(E!2)))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.22/0.48 tff(159,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[158, 90, 141, 155, 75])).
% 0.22/0.48 tff(160,plain,(~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(161,plain,
% 0.22/0.48 ((~(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))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(162,plain,
% 0.22/0.48 ((~(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))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.22/0.48 tff(163,plain,
% 0.22/0.48 (~((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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[162, 12])).
% 0.22/0.48 tff(164,plain,
% 0.22/0.48 (((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)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(165,plain,
% 0.22/0.48 (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.22/0.48 tff(166,assumption,(~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.22/0.48 tff(167,assumption,(greater(tptp_fun_To_0(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.22/0.48 tff(168,assumption,(greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.22/0.48 tff(169,plain,
% 0.22/0.48 (((~![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))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(170,plain,
% 0.22/0.48 ((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))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(171,plain,
% 0.22/0.48 (((~![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)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[170])).
% 0.22/0.48 tff(172,plain,
% 0.22/0.48 (((~![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))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[171, 169])).
% 0.22/0.48 tff(173,plain,
% 0.22/0.48 ((~![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))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(174,plain,
% 0.22/0.48 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.22/0.48 tff(175,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[174, 90, 168, 166, 167])).
% 0.22/0.48 tff(176,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(177,plain,
% 0.22/0.48 (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[176, 167, 166])).
% 0.22/0.48 tff(178,plain,
% 0.22/0.48 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_3(tptp_fun_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))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(179,plain,
% 0.22/0.48 (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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[178, 10])).
% 0.22/0.48 tff(180,plain,
% 0.22/0.48 ((~(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)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(181,plain,
% 0.22/0.48 ((~(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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[180, 64])).
% 0.22/0.48 tff(182,plain,
% 0.22/0.48 ((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))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[181, 179])).
% 0.22/0.48 tff(183,plain,
% 0.22/0.48 ((~((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))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(184,plain,
% 0.22/0.48 ((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))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.22/0.48 tff(185,plain,
% 0.22/0.48 (tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[184, 177])).
% 0.22/0.48 tff(186,plain,
% 0.22/0.48 (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) <=> greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[185])).
% 0.22/0.48 tff(187,plain,
% 0.22/0.48 (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.22/0.48 inference(symmetry,[status(thm)],[186])).
% 0.22/0.48 tff(188,plain,
% 0.22/0.48 (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[167, 187])).
% 0.22/0.48 tff(189,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[166, 188])).
% 0.22/0.48 tff(190,plain,((~greater(tptp_fun_To_0(E!2), equilibrium(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.48 tff(191,plain,
% 0.22/0.48 (~greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[190, 165])).
% 0.22/0.48 tff(192,assumption,(tptp_fun_T_1(E!2) = equilibrium(E!2)), introduced(assumption)).
% 0.22/0.48 tff(193,assumption,(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)), introduced(assumption)).
% 0.22/0.48 tff(194,plain,
% 0.22/0.48 (tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)),
% 0.22/0.48 inference(symmetry,[status(thm)],[193])).
% 0.22/0.48 tff(195,plain,
% 0.22/0.48 (tptp_fun_To_0(E!2) = equilibrium(E!2)),
% 0.22/0.48 inference(transitivity,[status(thm)],[194, 192])).
% 0.22/0.48 tff(196,plain,
% 0.22/0.48 (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)), equilibrium(E!2))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[195])).
% 0.22/0.48 tff(197,plain,
% 0.22/0.48 (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_To_0(E!2))),
% 0.22/0.48 inference(symmetry,[status(thm)],[196])).
% 0.22/0.48 tff(198,plain,
% 0.22/0.48 ((~![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)), 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))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(199,plain,
% 0.22/0.48 (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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[198, 10])).
% 0.22/0.48 tff(200,assumption,(~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.22/0.48 tff(201,plain,
% 0.22/0.48 ((~(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))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(202,plain,
% 0.22/0.48 ((~(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))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.22/0.48 tff(203,plain,
% 0.22/0.48 (~((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)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[202, 199])).
% 0.22/0.48 tff(204,plain,
% 0.22/0.48 (((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)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(205,plain,
% 0.22/0.48 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.22/0.48 tff(206,plain,
% 0.22/0.48 (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)), equilibrium(E!2))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[192])).
% 0.22/0.48 tff(207,plain,
% 0.22/0.48 (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))),
% 0.22/0.48 inference(symmetry,[status(thm)],[206])).
% 0.22/0.48 tff(208,plain,
% 0.22/0.48 ((~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)))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[207])).
% 0.22/0.48 tff(209,plain,
% 0.22/0.48 (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[200, 208])).
% 0.22/0.48 tff(210,plain,
% 0.22/0.48 (^[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)))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(211,plain,
% 0.22/0.48 (![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))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[210])).
% 0.22/0.48 tff(212,plain,
% 0.22/0.48 (^[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))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(213,plain,
% 0.22/0.49 (![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))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[212])).
% 0.22/0.49 tff(214,plain,
% 0.22/0.49 (![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))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(215,plain,
% 0.22/0.49 (^[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)))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(216,plain,
% 0.22/0.49 (![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))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[215])).
% 0.22/0.49 tff(217,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')).
% 0.22/0.49 tff(218,plain,
% 0.22/0.49 (![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.22/0.49 tff(219,plain,
% 0.22/0.49 (![E: $i] : ((~(environment(E) & stable(E))) | ?[T: $i] : (in_environment(E, T) & greater_or_equal(T, equilibrium(E))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.22/0.49 tff(220,plain,(
% 0.22/0.49 ![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_T_1(E)) & greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))),
% 0.22/0.49 inference(skolemize,[status(sab)],[219])).
% 0.22/0.49 tff(221,plain,
% 0.22/0.49 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.22/0.49 tff(222,plain,
% 0.22/0.49 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_T_1(E))) | (~greater_or_equal(tptp_fun_T_1(E), equilibrium(E))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[221, 211])).
% 0.22/0.49 tff(223,plain,
% 0.22/0.49 (((~![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))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(224,plain,
% 0.22/0.49 ((~![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))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(225,plain,
% 0.22/0.49 ((~![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)))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.22/0.49 tff(226,plain,
% 0.22/0.49 (~((~in_environment(E!2, tptp_fun_T_1(E!2))) | (~greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[225, 222, 29, 28])).
% 0.22/0.49 tff(227,plain,
% 0.22/0.49 (((~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))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(228,plain,
% 0.22/0.49 (in_environment(E!2, tptp_fun_T_1(E!2))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.22/0.49 tff(229,plain,
% 0.22/0.49 (((~![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), 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))))))))))) <=> ((~![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), 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))))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(230,plain,
% 0.22/0.49 ((~![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)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), 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))))))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(231,plain,
% 0.22/0.49 ((~![To: $i] : ((~in_environment(E!2, To)) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(To))) | (~greater_or_equal(tptp_fun_T_3(To), To)) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(To)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(To)))))))))) | (~in_environment(E!2, tptp_fun_T_1(E!2))) | (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.22/0.49 tff(232,plain,
% 0.22/0.49 (~((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[231, 58, 228])).
% 0.22/0.49 tff(233,plain,
% 0.22/0.49 (((~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(234,plain,
% 0.22/0.49 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.22/0.49 tff(235,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[234, 209])).
% 0.22/0.49 tff(236,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,[]))).
% 0.22/0.49 tff(237,plain,
% 0.22/0.49 (~(tptp_fun_T_1(E!2) = equilibrium(E!2))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[236, 200])).
% 0.22/0.49 tff(238,plain,
% 0.22/0.49 ((~![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))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(239,plain,
% 0.22/0.49 (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)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[238, 10])).
% 0.22/0.49 tff(240,plain,
% 0.22/0.49 (((~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))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(241,plain,
% 0.22/0.49 (greater_or_equal(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[240, 226])).
% 0.22/0.49 tff(242,plain,
% 0.22/0.49 ((~(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)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(243,plain,
% 0.22/0.49 ((~(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)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.22/0.49 tff(244,plain,
% 0.22/0.49 ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[243, 239])).
% 0.22/0.49 tff(245,plain,
% 0.22/0.49 ((~((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))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(246,plain,
% 0.22/0.49 ((tptp_fun_T_1(E!2) = equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.22/0.49 tff(247,plain,
% 0.22/0.49 (greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[246, 237])).
% 0.22/0.49 tff(248,assumption,(~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.22/0.49 tff(249,assumption,(greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.22/0.49 tff(250,assumption,(greater(tptp_fun_T_1(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.22/0.49 tff(251,plain,
% 0.22/0.49 (((~![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)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(252,plain,
% 0.22/0.49 ((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)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(253,plain,
% 0.22/0.49 (((~![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))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[252])).
% 0.22/0.49 tff(254,plain,
% 0.22/0.49 (((~![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)))),
% 0.22/0.49 inference(transitivity,[status(thm)],[253, 251])).
% 0.22/0.49 tff(255,plain,
% 0.22/0.49 ((~![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))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(256,plain,
% 0.22/0.49 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.22/0.49 tff(257,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[256, 90, 250, 249, 248])).
% 0.22/0.49 tff(258,plain,((~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_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.49 tff(259,plain,
% 0.22/0.49 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[258, 247, 205])).
% 0.22/0.49 tff(260,plain,
% 0.22/0.49 ((~![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))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(261,plain,
% 0.22/0.49 (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)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[260, 10])).
% 0.22/0.49 tff(262,plain,
% 0.22/0.49 ((~(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)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(263,plain,
% 0.22/0.49 ((~(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)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[262, 234])).
% 0.22/0.49 tff(264,plain,
% 0.22/0.49 ((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))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[263, 261])).
% 0.22/0.49 tff(265,plain,
% 0.22/0.49 ((~((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))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(266,plain,
% 0.22/0.49 ((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))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.22/0.49 tff(267,plain,
% 0.22/0.49 (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[266, 259])).
% 0.22/0.49 tff(268,plain,
% 0.22/0.49 (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))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[267])).
% 0.22/0.49 tff(269,plain,
% 0.22/0.49 (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))),
% 0.22/0.49 inference(symmetry,[status(thm)],[268])).
% 0.22/0.49 tff(270,plain,
% 0.22/0.49 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[241, 269])).
% 0.22/0.49 tff(271,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[200, 270])).
% 0.22/0.49 tff(272,plain,(greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.49 tff(273,plain,
% 0.22/0.49 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[272, 197])).
% 0.22/0.49 tff(274,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)).
% 0.22/0.49 tff(275,assumption,(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero), introduced(assumption)).
% 0.22/0.49 tff(276,plain,
% 0.22/0.49 (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))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[275])).
% 0.22/0.49 tff(277,plain,
% 0.22/0.49 (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))))),
% 0.22/0.49 inference(symmetry,[status(thm)],[276])).
% 0.22/0.49 tff(278,plain,
% 0.22/0.49 ((~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)))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[277])).
% 0.22/0.49 tff(279,assumption,(~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)), introduced(assumption)).
% 0.22/0.49 tff(280,assumption,(greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)), introduced(assumption)).
% 0.22/0.49 tff(281,plain,
% 0.22/0.49 (((~![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_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))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(282,plain,
% 0.22/0.49 ((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))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(283,plain,
% 0.22/0.49 (((~![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_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)))))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[282])).
% 0.22/0.49 tff(284,plain,
% 0.22/0.49 (((~![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_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))))))),
% 0.22/0.49 inference(transitivity,[status(thm)],[283, 281])).
% 0.22/0.49 tff(285,plain,
% 0.22/0.49 ((~![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_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)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(286,plain,
% 0.22/0.49 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero) | (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.22/0.49 tff(287,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[286, 90, 279, 280, 274])).
% 0.22/0.49 tff(288,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,[]))).
% 0.22/0.49 tff(289,plain,
% 0.22/0.49 (~greater(growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[288, 274, 279])).
% 0.22/0.49 tff(290,plain,
% 0.22/0.49 (((~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)),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(291,plain,
% 0.22/0.49 ((~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)))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[290, 289])).
% 0.22/0.49 tff(292,plain,
% 0.22/0.49 (((~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))) | (~((~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(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))))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(293,plain,
% 0.22/0.49 ((~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)))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[292, 232])).
% 0.22/0.49 tff(294,plain,
% 0.22/0.49 (((~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))) | (~((~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)))))))) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(295,plain,
% 0.22/0.49 (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[294, 232])).
% 0.22/0.49 tff(296,plain,
% 0.22/0.49 (((~![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_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))))))) | (~((~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))))) <=> ((~![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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(297,plain,
% 0.22/0.50 (((~((~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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(298,plain,
% 0.22/0.50 ((~((~(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))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(299,plain,
% 0.22/0.50 ((~((~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)))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(300,plain,
% 0.22/0.50 ((~((~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(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)))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(301,plain,
% 0.22/0.50 (((~((~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(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))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[300, 299, 298])).
% 0.22/0.50 tff(302,plain,
% 0.22/0.50 (((~((~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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[301, 297])).
% 0.22/0.50 tff(303,plain,
% 0.22/0.50 (((~![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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[302])).
% 0.22/0.50 tff(304,plain,
% 0.22/0.50 (((~![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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[303, 296])).
% 0.22/0.50 tff(305,plain,
% 0.22/0.50 ((~![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))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(306,plain,
% 0.22/0.50 ((~![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(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)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), equilibrium(E!2)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.22/0.50 tff(307,plain,
% 0.22/0.50 ((~((~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)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[306, 116, 29, 295, 293])).
% 0.22/0.50 tff(308,plain,
% 0.22/0.50 ((~((~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))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[307, 272])).
% 0.22/0.50 tff(309,plain,
% 0.22/0.50 (~((~(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)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[308, 291])).
% 0.22/0.50 tff(310,plain,
% 0.22/0.50 (((~(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)),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(311,plain,
% 0.22/0.50 (growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.22/0.50 tff(312,plain,
% 0.22/0.50 (((~(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)),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(313,plain,
% 0.22/0.50 (growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[312, 309])).
% 0.22/0.50 tff(314,plain,
% 0.22/0.50 (zero = growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2)))),
% 0.22/0.50 inference(symmetry,[status(thm)],[313])).
% 0.22/0.50 tff(315,plain,
% 0.22/0.50 (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)),
% 0.22/0.50 inference(monotonicity,[status(thm)],[314, 311])).
% 0.22/0.50 tff(316,plain,
% 0.22/0.50 (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))))),
% 0.22/0.50 inference(symmetry,[status(thm)],[315])).
% 0.22/0.50 tff(317,plain,
% 0.22/0.50 ((~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)))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[316])).
% 0.22/0.50 tff(318,plain,
% 0.22/0.50 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[279, 317])).
% 0.22/0.50 tff(319,plain,
% 0.22/0.50 (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))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[313])).
% 0.22/0.50 tff(320,plain,
% 0.22/0.50 (greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[274, 319])).
% 0.22/0.50 tff(321,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[320, 318])).
% 0.22/0.50 tff(322,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))))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(323,plain,
% 0.22/0.50 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), zero)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[322, 274])).
% 0.22/0.50 tff(324,plain,
% 0.22/0.50 ((~((~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(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)))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(325,plain,
% 0.22/0.50 ((~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)))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[324, 293])).
% 0.22/0.50 tff(326,plain,
% 0.22/0.50 (~greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[325, 323])).
% 0.22/0.50 tff(327,plain,
% 0.22/0.50 (~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))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[326, 278])).
% 0.22/0.50 tff(328,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[274, 327])).
% 0.22/0.50 tff(329,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,[]))).
% 0.22/0.50 tff(330,plain,
% 0.22/0.50 (~(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))) = zero)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[329, 274])).
% 0.22/0.50 tff(331,plain,
% 0.22/0.50 ((~(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))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[312, 330])).
% 0.22/0.50 tff(332,plain,
% 0.22/0.50 (~((~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))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[308, 331])).
% 0.22/0.50 tff(333,plain,
% 0.22/0.50 (((~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))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(334,plain,
% 0.22/0.50 (greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[333, 332])).
% 0.22/0.50 tff(335,plain,
% 0.22/0.50 (((~![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_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))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(336,plain,
% 0.22/0.50 ((~![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_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))))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(337,plain,
% 0.22/0.50 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | greater(zero, growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))))) | (~greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.22/0.50 tff(338,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[337, 90, 326, 334, 274])).
% 0.22/0.50 tff(339,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,[]))).
% 0.22/0.50 tff(340,plain,
% 0.22/0.50 (((~![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))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(341,plain,
% 0.22/0.50 ((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))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(342,plain,
% 0.22/0.50 (((~![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)))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[341])).
% 0.22/0.50 tff(343,plain,
% 0.22/0.50 (((~![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))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[342, 340])).
% 0.22/0.51 tff(344,plain,
% 0.22/0.51 ((~![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))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(345,plain,
% 0.22/0.51 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_0(E!2))))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.22/0.51 tff(346,plain,
% 0.22/0.51 (greater(growth_rate(efficient_producers, tptp_fun_T_3(tptp_fun_T_1(E!2))), growth_rate(first_movers, tptp_fun_T_3(tptp_fun_T_1(E!2)))) | (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[345, 68, 295])).
% 0.22/0.51 tff(347,plain,
% 0.22/0.51 (~greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[346, 339])).
% 0.22/0.51 tff(348,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[347, 273])).
% 0.22/0.51 tff(349,plain,((~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2))) | (~(tptp_fun_T_1(E!2) = equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(350,plain,
% 0.22/0.51 (~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[349, 192])).
% 0.22/0.51 tff(351,assumption,(greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.22/0.51 tff(352,plain,
% 0.22/0.51 ((~![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_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(353,plain,
% 0.22/0.51 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[352, 10])).
% 0.22/0.51 tff(354,plain,
% 0.22/0.51 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[192])).
% 0.22/0.51 tff(355,plain,
% 0.22/0.51 (greater_or_equal(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)), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(symmetry,[status(thm)],[354])).
% 0.22/0.51 tff(356,plain,
% 0.22/0.51 ((~greater_or_equal(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)), tptp_fun_T_1(E!2)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[355])).
% 0.22/0.51 tff(357,assumption,(~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))), introduced(assumption)).
% 0.22/0.51 tff(358,plain,
% 0.22/0.51 (~greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.22/0.51 tff(359,plain,
% 0.22/0.51 ((~(greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) <=> ((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(360,plain,
% 0.22/0.51 (~((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[359, 358, 353])).
% 0.22/0.51 tff(361,plain,
% 0.22/0.51 (((tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_T_1(E!2)) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(362,plain,
% 0.22/0.51 (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[361, 360])).
% 0.22/0.51 tff(363,plain,
% 0.22/0.51 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(364,plain,
% 0.22/0.51 (greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[363, 10])).
% 0.22/0.51 tff(365,plain,
% 0.22/0.51 (((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(366,plain,
% 0.22/0.51 ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[365, 351])).
% 0.22/0.51 tff(367,plain,
% 0.22/0.51 ((~(greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))) | greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) | (~((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(368,plain,
% 0.22/0.51 ((~(greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> ((tptp_fun_To_0(E!2) = tptp_fun_T_1(E!2)) | greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))) | greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[367, 366])).
% 0.22/0.51 tff(369,plain,
% 0.22/0.51 (greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[368, 364])).
% 0.22/0.51 tff(370,plain,
% 0.22/0.51 (equilibrium(E!2) = tptp_fun_T_1(E!2)),
% 0.22/0.51 inference(symmetry,[status(thm)],[192])).
% 0.22/0.51 tff(371,assumption,(tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2)), introduced(assumption)).
% 0.22/0.51 tff(372,plain,
% 0.22/0.51 (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), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[371, 370])).
% 0.22/0.51 tff(373,plain,
% 0.22/0.51 (greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)) <=> greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.22/0.51 inference(symmetry,[status(thm)],[372])).
% 0.22/0.51 tff(374,assumption,(greater_or_equal(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.22/0.51 tff(375,plain,
% 0.22/0.51 (greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.22/0.51 tff(376,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[357, 375])).
% 0.22/0.51 tff(377,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), tptp_fun_T_1(E!2))) | (~(tptp_fun_T_1(E!2) = equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(378,plain,
% 0.22/0.51 (~(tptp_fun_T_3(tptp_fun_To_0(E!2)) = tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[377, 369, 357, 192])).
% 0.22/0.51 tff(379,plain,
% 0.22/0.51 (greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[184, 378])).
% 0.22/0.51 tff(380,plain,
% 0.22/0.51 (((~![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)), tptp_fun_T_1(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_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_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(381,plain,
% 0.22/0.51 ((greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(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), tptp_fun_T_1(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)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(382,plain,
% 0.22/0.51 (((~![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_T_1(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), 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_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_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[381])).
% 0.22/0.51 tff(383,plain,
% 0.22/0.51 (((~![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_T_1(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), 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_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_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[382, 380])).
% 0.22/0.51 tff(384,plain,
% 0.22/0.51 ((~![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_T_1(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), tptp_fun_T_1(E!2))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(385,plain,
% 0.22/0.51 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_To_0(E!2))) | greater(tptp_fun_T_3(tptp_fun_To_0(E!2)), tptp_fun_T_1(E!2)) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.22/0.51 tff(386,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[385, 90, 379, 362, 351])).
% 0.22/0.51 tff(387,plain,((~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater_or_equal(tptp_fun_T_3(tptp_fun_To_0(E!2)), equilibrium(E!2)) | (~(tptp_fun_T_1(E!2) = equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(388,plain,
% 0.22/0.51 (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[387, 192, 160])).
% 0.22/0.51 tff(389,plain,
% 0.22/0.51 (^[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))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(390,plain,
% 0.22/0.51 (![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)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[389])).
% 0.22/0.51 tff(391,plain,
% 0.22/0.51 (^[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)))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(392,plain,
% 0.22/0.51 (![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)))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[391])).
% 0.22/0.51 tff(393,plain,
% 0.22/0.51 (![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))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(394,plain,
% 0.22/0.51 (^[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))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(395,plain,
% 0.22/0.51 (![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))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[394])).
% 0.22/0.51 tff(396,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')).
% 0.22/0.51 tff(397,plain,
% 0.22/0.51 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.22/0.51 tff(398,plain,
% 0.22/0.51 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[397, 393])).
% 0.22/0.51 tff(399,plain,(
% 0.22/0.51 ![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~(in_environment(E, T1) & in_environment(E, T2))))),
% 0.22/0.51 inference(skolemize,[status(sab)],[398])).
% 0.22/0.51 tff(400,plain,
% 0.22/0.51 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[399, 392])).
% 0.22/0.51 tff(401,plain,
% 0.22/0.51 (![E: $i, T1: $i, T2: $i] : (greater(T1, T2) | (T2 = T1) | greater(T2, T1) | (~in_environment(E, T1)) | (~in_environment(E, T2)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[400, 390])).
% 0.22/0.51 tff(402,plain,
% 0.22/0.51 (((~![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)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(403,plain,
% 0.22/0.51 ((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)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(404,plain,
% 0.22/0.51 (((~![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))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[403])).
% 0.22/0.51 tff(405,plain,
% 0.22/0.51 (((~![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)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[404, 402])).
% 0.22/0.51 tff(406,plain,
% 0.22/0.51 ((~![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))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(407,plain,
% 0.22/0.51 ((~![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))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.22/0.51 tff(408,plain,
% 0.22/0.51 ((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))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[407, 401, 51, 228])).
% 0.22/0.51 tff(409,plain,
% 0.22/0.51 (greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[408, 388, 350])).
% 0.22/0.51 tff(410,plain,
% 0.22/0.51 ((~![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))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(411,plain,
% 0.22/0.51 (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)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[410, 10])).
% 0.22/0.51 tff(412,plain,
% 0.22/0.51 ((~(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))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(413,plain,
% 0.22/0.51 ((~(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))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[412, 347])).
% 0.22/0.51 tff(414,plain,
% 0.22/0.51 (~((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)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[413, 411])).
% 0.22/0.51 tff(415,plain,
% 0.22/0.51 (((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)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(416,plain,
% 0.22/0.51 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[415, 414])).
% 0.22/0.51 tff(417,assumption,(~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.22/0.51 tff(418,assumption,(greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.22/0.51 tff(419,plain,
% 0.22/0.51 (((~![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))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(420,plain,
% 0.22/0.51 ((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))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(421,plain,
% 0.22/0.51 (((~![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)))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[420])).
% 0.22/0.51 tff(422,plain,
% 0.22/0.51 (((~![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))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[421, 419])).
% 0.22/0.51 tff(423,plain,
% 0.22/0.51 ((~![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))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(424,plain,
% 0.22/0.51 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))) | greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.22/0.51 tff(425,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[424, 90, 249, 418, 417])).
% 0.22/0.51 tff(426,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,[]))).
% 0.22/0.51 tff(427,plain,
% 0.22/0.51 ((~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)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[426, 416])).
% 0.22/0.51 tff(428,plain,
% 0.22/0.51 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[427, 409])).
% 0.22/0.51 tff(429,plain,
% 0.22/0.51 (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[266, 428])).
% 0.22/0.51 tff(430,plain,
% 0.22/0.51 (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_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[429])).
% 0.22/0.51 tff(431,plain,
% 0.22/0.51 (greater_or_equal(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))),
% 0.22/0.51 inference(symmetry,[status(thm)],[430])).
% 0.22/0.51 tff(432,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)).
% 0.22/0.51 tff(433,plain,
% 0.22/0.51 (((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)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(434,plain,
% 0.22/0.51 (~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[433, 432])).
% 0.22/0.51 tff(435,plain,
% 0.22/0.51 (((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)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(436,plain,
% 0.22/0.51 (~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[435, 432])).
% 0.22/0.51 tff(437,assumption,(~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))), introduced(assumption)).
% 0.22/0.51 tff(438,plain,
% 0.22/0.51 ((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))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[407, 401, 51, 228, 437])).
% 0.22/0.51 tff(439,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[438, 436, 434])).
% 0.22/0.51 tff(440,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,[]))).
% 0.22/0.51 tff(441,plain,
% 0.22/0.51 ((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))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[440, 388])).
% 0.22/0.51 tff(442,assumption,(~(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))))), introduced(assumption)).
% 0.22/0.51 tff(443,plain,
% 0.22/0.51 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) <=> ((tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(444,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[443, 10, 442])).
% 0.22/0.51 tff(445,plain,(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)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(446,plain,
% 0.22/0.51 ((~(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))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(447,plain,
% 0.22/0.51 (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))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[446, 445])).
% 0.22/0.51 tff(448,plain,
% 0.22/0.51 (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[447, 441])).
% 0.22/0.51 tff(449,plain,
% 0.22/0.51 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[448, 431])).
% 0.22/0.51 tff(450,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[347, 449])).
% 0.22/0.51 tff(451,plain,(~(tptp_fun_T_1(E!2) = equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(452,plain,
% 0.22/0.51 (greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[246, 451])).
% 0.22/0.51 tff(453,assumption,(~greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))), introduced(assumption)).
% 0.22/0.51 tff(454,assumption,(~greater(tptp_fun_To_0(E!2), equilibrium(E!2))), introduced(assumption)).
% 0.22/0.51 tff(455,plain,
% 0.22/0.51 (((~![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), tptp_fun_T_1(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_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(456,plain,
% 0.22/0.51 ((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), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(457,plain,
% 0.22/0.52 (((~![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), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[456])).
% 0.22/0.52 tff(458,plain,
% 0.22/0.52 (((~![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), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2)))),
% 0.22/0.52 inference(transitivity,[status(thm)],[457, 455])).
% 0.22/0.52 tff(459,plain,
% 0.22/0.52 ((~![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))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(460,plain,
% 0.22/0.52 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.22/0.52 tff(461,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[460, 90, 250, 351, 454])).
% 0.22/0.52 tff(462,plain,((~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_To_0(E!2), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.52 tff(463,plain,
% 0.22/0.52 (~greater(tptp_fun_To_0(E!2), tptp_fun_T_1(E!2))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[462, 454, 250])).
% 0.22/0.52 tff(464,plain,
% 0.22/0.52 (greater(tptp_fun_T_1(E!2), equilibrium(E!2)) <=> greater(tptp_fun_To_0(E!2), equilibrium(E!2))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[193])).
% 0.22/0.52 tff(465,plain,
% 0.22/0.52 (greater(tptp_fun_To_0(E!2), equilibrium(E!2)) <=> greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.52 inference(symmetry,[status(thm)],[464])).
% 0.22/0.52 tff(466,plain,
% 0.22/0.52 ((~greater(tptp_fun_To_0(E!2), equilibrium(E!2))) <=> (~greater(tptp_fun_T_1(E!2), equilibrium(E!2)))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[465])).
% 0.22/0.52 tff(467,plain,
% 0.22/0.52 (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[454, 466])).
% 0.22/0.52 tff(468,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[250, 467])).
% 0.22/0.52 tff(469,plain,((~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2))) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2))) | greater(tptp_fun_To_0(E!2), equilibrium(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.52 tff(470,plain,
% 0.22/0.52 (~(tptp_fun_T_1(E!2) = tptp_fun_To_0(E!2))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[469, 454, 250])).
% 0.22/0.52 tff(471,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[408, 470, 463, 453])).
% 0.22/0.52 tff(472,plain,(greater(tptp_fun_To_0(E!2), equilibrium(E!2)) | greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2)) | (~greater(tptp_fun_T_1(E!2), equilibrium(E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.52 tff(473,plain,
% 0.22/0.52 (greater(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[472, 452, 191])).
% 0.22/0.52 tff(474,plain,
% 0.22/0.52 (~greater(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_T_1(E!2))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[427, 473])).
% 0.22/0.52 tff(475,plain,
% 0.22/0.52 (tptp_fun_T_3(tptp_fun_T_1(E!2)) = tptp_fun_T_1(E!2)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[266, 474])).
% 0.22/0.52 tff(476,plain,
% 0.22/0.52 (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_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[475])).
% 0.22/0.52 tff(477,plain,
% 0.22/0.52 (greater_or_equal(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))),
% 0.22/0.52 inference(symmetry,[status(thm)],[476])).
% 0.22/0.52 tff(478,plain,
% 0.22/0.52 ((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))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[435, 473])).
% 0.22/0.52 tff(479,plain,
% 0.22/0.52 (greater_or_equal(tptp_fun_T_1(E!2), tptp_fun_To_0(E!2))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[447, 478])).
% 0.22/0.52 tff(480,plain,
% 0.22/0.52 (greater_or_equal(tptp_fun_T_3(tptp_fun_T_1(E!2)), tptp_fun_To_0(E!2))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[479, 477])).
% 0.22/0.52 tff(481,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[347, 480])).
% 0.22/0.52 % SZS output end Proof
%------------------------------------------------------------------------------