TSTP Solution File: MGT028+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 0.14s 0.33s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% 0.02/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n020.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri Sep 2 02:44:44 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.29 Usage: tptp [options] [-file:]file
% 0.09/0.29 -h, -? prints this message.
% 0.09/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.29 -m, -model generate model.
% 0.09/0.29 -p, -proof generate proof.
% 0.09/0.29 -c, -core generate unsat core of named formulas.
% 0.09/0.29 -st, -statistics display statistics.
% 0.09/0.29 -t:timeout set timeout (in second).
% 0.09/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.29 -<param>:<value> configuration parameter and value.
% 0.09/0.29 -o:<output-file> file to place output in.
% 0.14/0.33 % SZS status Theorem
% 0.14/0.33 % SZS output start Proof
% 0.14/0.33 tff(greater_type, type, (
% 0.14/0.33 greater: ( $i * $i ) > $o)).
% 0.14/0.33 tff(growth_rate_type, type, (
% 0.14/0.33 growth_rate: ( $i * $i ) > $i)).
% 0.14/0.33 tff(tptp_fun_T_0_type, type, (
% 0.14/0.33 tptp_fun_T_0: ( $i * $i ) > $i)).
% 0.14/0.33 tff(tptp_fun_E_3_type, type, (
% 0.14/0.33 tptp_fun_E_3: $i)).
% 0.14/0.33 tff(tptp_fun_To_2_type, type, (
% 0.14/0.33 tptp_fun_To_2: $i > $i)).
% 0.14/0.33 tff(first_movers_type, type, (
% 0.14/0.33 first_movers: $i)).
% 0.14/0.33 tff(zero_type, type, (
% 0.14/0.33 zero: $i)).
% 0.14/0.33 tff(efficient_producers_type, type, (
% 0.14/0.33 efficient_producers: $i)).
% 0.14/0.33 tff(greater_or_equal_type, type, (
% 0.14/0.33 greater_or_equal: ( $i * $i ) > $o)).
% 0.14/0.33 tff(subpopulations_type, type, (
% 0.14/0.33 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.14/0.33 tff(in_environment_type, type, (
% 0.14/0.33 in_environment: ( $i * $i ) > $o)).
% 0.14/0.33 tff(stable_type, type, (
% 0.14/0.33 stable: $i > $o)).
% 0.14/0.33 tff(tptp_fun_T_4_type, type, (
% 0.14/0.33 tptp_fun_T_4: $i > $i)).
% 0.14/0.33 tff(appear_type, type, (
% 0.14/0.33 appear: ( $i * $i ) > $i)).
% 0.14/0.33 tff(environment_type, type, (
% 0.14/0.33 environment: $i > $o)).
% 0.14/0.33 tff(tptp_fun_T2_1_type, type, (
% 0.14/0.33 tptp_fun_T2_1: $i > $i)).
% 0.14/0.33 tff(1,plain,
% 0.14/0.33 (((environment(E!3) & stable(E!3)) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))))))) <=> (environment(E!3) & stable(E!3) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To)))))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(2,plain,
% 0.14/0.33 ((~(~(environment(E!3) & stable(E!3)))) <=> (environment(E!3) & stable(E!3))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(3,plain,
% 0.14/0.33 (((~(~(environment(E!3) & stable(E!3)))) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))))))) <=> ((environment(E!3) & stable(E!3)) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To)))))))),
% 0.14/0.33 inference(monotonicity,[status(thm)],[2])).
% 0.14/0.33 tff(4,plain,
% 0.14/0.33 (((~(~(environment(E!3) & stable(E!3)))) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))))))) <=> (environment(E!3) & stable(E!3) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To)))))))),
% 0.14/0.33 inference(transitivity,[status(thm)],[3, 1])).
% 0.14/0.33 tff(5,plain,
% 0.14/0.33 ((~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(6,plain,
% 0.14/0.33 ((~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(7,axiom,(~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l10')).
% 0.14/0.33 tff(8,plain,
% 0.14/0.33 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.14/0.33 tff(9,plain,
% 0.14/0.33 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.14/0.33 tff(10,plain,
% 0.14/0.33 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.33 tff(11,plain,
% 0.14/0.33 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.14/0.33 tff(12,plain,
% 0.14/0.33 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.14/0.33 tff(13,plain,
% 0.14/0.33 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.33 tff(14,plain,
% 0.14/0.33 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.14/0.33 tff(15,plain,
% 0.14/0.33 (environment(E!3) & stable(E!3) & ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))))))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.14/0.33 tff(16,plain,
% 0.14/0.33 (stable(E!3)),
% 0.14/0.33 inference(and_elim,[status(thm)],[15])).
% 0.14/0.33 tff(17,plain,
% 0.14/0.33 (environment(E!3)),
% 0.14/0.33 inference(and_elim,[status(thm)],[15])).
% 0.14/0.33 tff(18,plain,
% 0.14/0.33 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(19,plain,
% 0.14/0.33 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.33 tff(20,plain,
% 0.14/0.33 (^[E: $i] : rewrite(((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(21,plain,
% 0.14/0.33 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.33 tff(22,plain,
% 0.14/0.33 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.14/0.33 inference(transitivity,[status(thm)],[21, 19])).
% 0.14/0.33 tff(23,plain,
% 0.14/0.33 (^[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_2(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))))), 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)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))), rewrite((((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E)))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> ![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))), ((in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))), rewrite((in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) <=> (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))), ((in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> (((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))), (((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(24,plain,
% 0.14/0.34 (![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[23])).
% 0.14/0.34 tff(25,plain,
% 0.14/0.34 (![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))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(26,plain,
% 0.14/0.34 (^[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), zero) & greater(zero, 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), zero) & greater(zero, 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), zero) & greater(zero, 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), zero) & greater(zero, 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), zero) & greater(zero, 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), zero) & greater(zero, 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), zero) & greater(zero, 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), zero) & greater(zero, 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), zero) & greater(zero, 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), zero) & greater(zero, growth_rate(first_movers, T))))))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(27,plain,
% 0.14/0.34 (![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))))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[26])).
% 0.14/0.34 tff(28,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/sandbox2/benchmark/theBenchmark.p','l11')).
% 0.14/0.34 tff(29,plain,
% 0.14/0.34 (![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))))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.14/0.34 tff(30,plain,
% 0.14/0.34 (![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))))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.14/0.34 tff(31,plain,(
% 0.14/0.34 ![E: $i] : ((~(environment(E) & stable(E))) | (in_environment(E, tptp_fun_To_2(E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_2(E)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))))),
% 0.14/0.34 inference(skolemize,[status(sab)],[30])).
% 0.14/0.34 tff(32,plain,
% 0.14/0.34 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.14/0.34 tff(33,plain,
% 0.14/0.34 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.14/0.34 tff(34,plain,
% 0.14/0.34 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) | ((~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) | (~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(35,plain,
% 0.14/0.34 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) | ((~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(36,plain,
% 0.14/0.34 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~in_environment(E, tptp_fun_To_2(E))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_2(E))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))))) | (~environment(E!3)) | (~stable(E!3)) | (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.14/0.34 tff(37,plain,
% 0.14/0.34 (~((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[36, 33, 17, 16])).
% 0.14/0.34 tff(38,plain,
% 0.14/0.34 (((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))) | in_environment(E!3, tptp_fun_To_2(E!3))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(39,plain,
% 0.14/0.34 (in_environment(E!3, tptp_fun_To_2(E!3))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.14/0.34 tff(40,assumption,(~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))), introduced(assumption)).
% 0.14/0.35 tff(41,plain,
% 0.14/0.35 (((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))) | greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(42,plain,
% 0.14/0.35 (greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.14/0.35 tff(43,plain,
% 0.14/0.35 (^[To: $i] : refl(((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To))))) <=> ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(44,plain,
% 0.14/0.35 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To))))) <=> ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[43])).
% 0.14/0.35 tff(45,plain,
% 0.14/0.35 (^[To: $i] : rewrite(((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(46,plain,
% 0.14/0.35 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To)))))) <=> ![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[45])).
% 0.14/0.35 tff(47,plain,
% 0.14/0.35 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~((~(subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To)) & greater_or_equal(tptp_fun_T_4(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))))))),
% 0.14/0.35 inference(and_elim,[status(thm)],[15])).
% 0.14/0.35 tff(48,plain,
% 0.14/0.35 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.14/0.35 tff(49,plain,
% 0.14/0.35 (![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.14/0.35 tff(50,plain,
% 0.14/0.35 (((~![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))) | ((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))))) <=> ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))) | (~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(51,plain,
% 0.14/0.35 ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))) | ((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(52,plain,
% 0.14/0.35 ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(To))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(To))) | (~greater_or_equal(tptp_fun_T_4(To), To)))))) | (~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.14/0.35 tff(53,plain,
% 0.14/0.35 (~(greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[52, 49, 42])).
% 0.14/0.35 tff(54,plain,
% 0.14/0.35 ((greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))) | greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(55,plain,
% 0.14/0.35 (greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.14/0.35 tff(56,plain,
% 0.14/0.35 ((greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))) | subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(57,plain,
% 0.14/0.35 (subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.14/0.35 tff(58,plain,
% 0.14/0.35 ((greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(59,plain,
% 0.14/0.35 (~greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[58, 53])).
% 0.14/0.35 tff(60,plain,
% 0.14/0.35 (((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))) | ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(61,plain,
% 0.14/0.35 (![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[60, 40])).
% 0.14/0.35 tff(62,plain,
% 0.14/0.35 (((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))) <=> ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(63,plain,
% 0.14/0.35 ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(64,plain,
% 0.14/0.35 ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_4(tptp_fun_T2_1(E!3)))) | (~greater_or_equal(tptp_fun_T_4(tptp_fun_T2_1(E!3)), tptp_fun_T2_1(E!3)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.14/0.35 tff(65,plain,
% 0.14/0.35 ($false),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[64, 61, 59, 57, 55])).
% 0.14/0.35 tff(66,plain,((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.35 tff(67,plain,
% 0.14/0.35 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(68,plain,
% 0.14/0.35 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[67])).
% 0.14/0.35 tff(69,plain,
% 0.14/0.35 (^[E: $i] : rewrite(((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(70,plain,
% 0.14/0.35 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[69])).
% 0.14/0.35 tff(71,plain,
% 0.14/0.35 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.14/0.36 inference(transitivity,[status(thm)],[70, 68])).
% 0.14/0.36 tff(72,plain,
% 0.14/0.36 (^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[T1: $i] : rewrite(((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) <=> ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))))), (![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) <=> ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))))), 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_T2_1(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))), rewrite((((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))), ((greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))) <=> (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))), rewrite((greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))) <=> (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))), ((greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))) <=> (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))), (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))))), rewrite(((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))), (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(73,plain,
% 0.14/0.36 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[72])).
% 0.14/0.36 tff(74,plain,
% 0.14/0.36 (^[E: $i] : trans(monotonicity(rewrite(((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))))), rewrite((greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))) <=> (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))), ((((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))))), rewrite((((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))), ((((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(75,plain,
% 0.14/0.36 (![E: $i] : (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[74])).
% 0.14/0.36 tff(76,plain,
% 0.14/0.36 (![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(77,plain,
% 0.14/0.36 (^[E: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[T1: $i] : rewrite((in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T)))) <=> (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))), (?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T)))) <=> ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) <=> ((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))))), rewrite(((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))) <=> (environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) <=> (environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))))), quant_intro(proof_bind(^[T2: $i] : rewrite((greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T)))) <=> (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))), (?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T)))) <=> ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))), ((((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T))))) <=> ((environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T))))))), rewrite(((environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))), ((((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(78,plain,
% 0.14/0.37 (![E: $i] : (((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[77])).
% 0.14/0.37 tff(79,axiom,(![E: $i] : (((environment(E) & stable(E)) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1)) => greater(zero, growth_rate(first_movers, T))))) => ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2)) => greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_first_movers_negative_growth')).
% 0.14/0.37 tff(80,plain,
% 0.14/0.37 (![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.14/0.37 tff(81,plain,
% 0.14/0.37 (![E: $i] : ((~(environment(E) & stable(E) & ?[T1: $i] : (in_environment(E, T1) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T1))) | greater(zero, growth_rate(first_movers, T)))))) | ?[T2: $i] : (greater(T2, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, T2))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.14/0.37 tff(82,plain,(
% 0.14/0.37 ![E: $i] : (((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.37 inference(skolemize,[status(sab)],[81])).
% 0.14/0.37 tff(83,plain,
% 0.14/0.37 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~((~(subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E)) & greater_or_equal(tptp_fun_T_0(T1, E), T1))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E)))))) | (greater(tptp_fun_T2_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_T2_1(E)))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.14/0.37 tff(84,plain,
% 0.14/0.37 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.14/0.37 tff(85,plain,
% 0.14/0.37 (![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[84, 71])).
% 0.14/0.37 tff(86,plain,
% 0.14/0.37 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | ((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | (~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(87,plain,
% 0.14/0.37 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | ((~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3))))))))),
% 0.14/0.37 inference(quant_inst,[status(thm)],[])).
% 0.14/0.37 tff(88,plain,
% 0.14/0.37 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | ![T1: $i] : ((~in_environment(E, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E))) | (~subpopulations(first_movers, efficient_producers, E, tptp_fun_T_0(T1, E))) | (~greater_or_equal(tptp_fun_T_0(T1, E), T1))))) | (~((~greater(tptp_fun_T2_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E))))))))) | (~environment(E!3)) | (~stable(E!3)) | ![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.14/0.37 tff(89,plain,
% 0.14/0.37 (![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1))))) | (~((~greater(tptp_fun_T2_1(E!3), appear(efficient_producers, E!3))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_T2_1(E!3)))))))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[88, 85, 17, 16])).
% 0.14/0.37 tff(90,plain,
% 0.14/0.37 (![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[89, 66])).
% 0.14/0.37 tff(91,plain,
% 0.14/0.37 (((~![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))) | ((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))))))) <=> ((~![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))) | (~in_environment(E!3, tptp_fun_To_2(E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(92,plain,
% 0.14/0.37 ((~![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))) | ((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))))))),
% 0.14/0.37 inference(quant_inst,[status(thm)],[])).
% 0.14/0.37 tff(93,plain,
% 0.14/0.37 ((~![T1: $i] : ((~in_environment(E!3, T1)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(T1, E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(T1, E!3))) | (~greater_or_equal(tptp_fun_T_0(T1, E!3), T1)))))) | (~in_environment(E!3, tptp_fun_To_2(E!3))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.14/0.37 tff(94,plain,
% 0.14/0.37 (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[93, 90, 39])).
% 0.14/0.37 tff(95,plain,
% 0.14/0.37 ((greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))),
% 0.14/0.37 inference(tautology,[status(thm)],[])).
% 0.14/0.37 tff(96,plain,
% 0.14/0.37 (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.14/0.37 tff(97,plain,
% 0.14/0.37 (((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))),
% 0.14/0.37 inference(tautology,[status(thm)],[])).
% 0.14/0.37 tff(98,plain,
% 0.14/0.37 ((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.14/0.37 tff(99,plain,
% 0.14/0.37 ((greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))) | greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))),
% 0.14/0.37 inference(tautology,[status(thm)],[])).
% 0.14/0.37 tff(100,plain,
% 0.14/0.37 (greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[99, 94])).
% 0.14/0.37 tff(101,plain,
% 0.14/0.37 ((greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3)))) | subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))),
% 0.14/0.37 inference(tautology,[status(thm)],[])).
% 0.14/0.37 tff(102,plain,
% 0.14/0.37 (subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[101, 94])).
% 0.14/0.37 tff(103,plain,
% 0.14/0.37 (((~in_environment(E!3, tptp_fun_To_2(E!3))) | (~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))))) | ![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))),
% 0.14/0.37 inference(tautology,[status(thm)],[])).
% 0.14/0.37 tff(104,plain,
% 0.14/0.37 (![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[103, 37])).
% 0.14/0.38 tff(105,plain,
% 0.14/0.38 (((~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) | ((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))))))) <=> ((~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(106,plain,
% 0.14/0.38 ((~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) | ((~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)))))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(107,plain,
% 0.14/0.38 ((~![T: $i] : ((~subpopulations(first_movers, efficient_producers, E!3, T)) | (~greater_or_equal(T, tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))))) | (~subpopulations(first_movers, efficient_producers, E!3, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_2(E!3), E!3), tptp_fun_To_2(E!3))) | (~((~greater(growth_rate(efficient_producers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3)), zero)) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_2(E!3), E!3))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.14/0.38 tff(108,plain,
% 0.14/0.38 ($false),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[107, 104, 102, 100, 98])).
% 0.14/0.38 % SZS output end Proof
%------------------------------------------------------------------------------