%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT036+2 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:03 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 12:43:54 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(greater_type, type, (
% 0.13/0.40 greater: ( $i * $i ) > $o)).
% 0.13/0.40 tff(growth_rate_type, type, (
% 0.13/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_T_0_type, type, (
% 0.13/0.40 tptp_fun_T_0: $i)).
% 0.13/0.40 tff(efficient_producers_type, type, (
% 0.13/0.40 efficient_producers: $i)).
% 0.13/0.40 tff(zero_type, type, (
% 0.13/0.40 zero: $i)).
% 0.13/0.40 tff(greater_or_equal_type, type, (
% 0.13/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.40 tff(first_movers_type, type, (
% 0.13/0.40 first_movers: $i)).
% 0.13/0.40 tff(outcompetes_type, type, (
% 0.13/0.40 outcompetes: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(subpopulations_type, type, (
% 0.13/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_E_1_type, type, (
% 0.13/0.40 tptp_fun_E_1: $i)).
% 0.13/0.40 tff(environment_type, type, (
% 0.13/0.40 environment: $i > $o)).
% 0.13/0.40 tff(in_environment_type, type, (
% 0.13/0.40 in_environment: ( $i * $i ) > $o)).
% 0.13/0.40 tff(resilience_type, type, (
% 0.13/0.40 resilience: $i > $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))) <=> (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~outcompetes(first_movers, efficient_producers, T)))) <=> (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,axiom,(~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~outcompetes(first_movers, efficient_producers, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t5')).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.40 tff(8,plain,(
% 0.13/0.40 ~((~outcompetes(first_movers, efficient_producers, T!0)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.40 inference(or_elim,[status(thm)],[8])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.40 inference(and_elim,[status(thm)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (environment(E!1)),
% 0.13/0.40 inference(and_elim,[status(thm)],[9])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T)) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.40 tff(19,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_symmetry_of_subpopulations')).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.13/0.40 tff(22,plain,(
% 0.13/0.40 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.13/0.40 inference(skolemize,[status(sab)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 ((subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[26])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.13/0.40 inference(transitivity,[status(thm)],[27, 25])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 24, 11, 10])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T)))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T)) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T))))), trans(trans(monotonicity(rewrite((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> (~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))))), (((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))), rewrite(((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)) <=> (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T)))), (((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))), rewrite((~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))) <=> (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T)))), (((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T))) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T)))))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T))) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T)))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.13/0.40 tff(39,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2')).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.13/0.41 tff(42,plain,(
% 0.13/0.41 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[41])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))) | ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) <=> outcompetes(first_movers, efficient_producers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) <=> outcompetes(first_movers, efficient_producers, T!0))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))) | ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) <=> outcompetes(first_movers, efficient_producers, T!0))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~(((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero))) <=> outcompetes(S2, S1, T))))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | (~(((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (~(((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) <=> outcompetes(first_movers, efficient_producers, T!0))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[47, 44, 11, 31])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (outcompetes(first_movers, efficient_producers, T!0)),
% 0.13/0.41 inference(or_elim,[status(thm)],[8])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 ((((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) <=> outcompetes(first_movers, efficient_producers, T!0)) | (~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) | (~outcompetes(first_movers, efficient_producers, T!0))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 ((((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) <=> outcompetes(first_movers, efficient_producers, T!0)) | (~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (greater(zero, growth_rate(efficient_producers, T!0))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (^[E: $i, T: $i] : refl((in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.13/0.41 tff(62,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_time_point_occur')).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.13/0.41 tff(65,plain,(
% 0.13/0.41 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.13/0.41 inference(skolemize,[status(sab)],[64])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 ((in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[69])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.13/0.41 inference(transitivity,[status(thm)],[70, 68])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (in_environment(E!1, T!0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[73, 67, 11, 10])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(rewrite((greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))) <=> (greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)))) <=> (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))), ((~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)))) <=> (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(78,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[77])).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(80,plain,
% 0.13/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(trans(monotonicity(rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))), ((((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))))), rewrite((((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))))), ((((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)))))), rewrite((~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)))) <=> (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))))), ((((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(81,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.13/0.42 tff(82,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_growth_rate_relationships')).
% 0.13/0.42 tff(83,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.13/0.42 tff(84,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.13/0.42 tff(85,plain,(
% 0.13/0.42 ![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[84])).
% 0.13/0.42 tff(86,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.13/0.42 tff(87,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.13/0.42 tff(88,plain,
% 0.13/0.42 (((~![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))) | (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))) | (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(89,plain,
% 0.13/0.42 ((~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)))) <=> (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(90,plain,
% 0.13/0.42 ((greater(zero, growth_rate(first_movers, T!0)) <=> (greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> (greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(91,plain,
% 0.13/0.42 ((~(greater(zero, growth_rate(first_movers, T!0)) <=> (greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))))) <=> (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.13/0.42 tff(92,plain,
% 0.13/0.42 ((~(greater(zero, growth_rate(first_movers, T!0)) <=> (greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))))) <=> (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[91, 89])).
% 0.13/0.42 tff(93,plain,
% 0.13/0.42 (((~![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))) | (~(greater(zero, growth_rate(first_movers, T!0)) <=> (greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))) | (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.13/0.42 tff(94,plain,
% 0.13/0.42 (((~![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))) | (~(greater(zero, growth_rate(first_movers, T!0)) <=> (greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))) | (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[93, 88])).
% 0.13/0.42 tff(95,plain,
% 0.13/0.42 ((~![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))) | (~(greater(zero, growth_rate(first_movers, T!0)) <=> (greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(96,plain,
% 0.13/0.42 ((~![E: $i, S1: $i, S2: $i, T: $i] : (~(greater(zero, growth_rate(S1, T)) <=> (greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))) | (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.13/0.42 tff(97,plain,
% 0.13/0.42 (~(greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[96, 87])).
% 0.13/0.42 tff(98,plain,
% 0.13/0.42 (((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) | greater_or_equal(growth_rate(first_movers, T!0), zero)),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(99,plain,
% 0.13/0.42 (greater_or_equal(growth_rate(first_movers, T!0), zero)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[98, 52])).
% 0.13/0.42 tff(100,plain,
% 0.13/0.42 (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(101,plain,
% 0.13/0.42 ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.13/0.42 tff(102,plain,
% 0.13/0.42 ((greater(zero, growth_rate(first_movers, T!0)) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero))) | (~greater(zero, growth_rate(first_movers, T!0))) | (~((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(103,plain,
% 0.13/0.42 (~greater(zero, growth_rate(first_movers, T!0))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[102, 101, 97])).
% 0.13/0.42 tff(104,plain,
% 0.13/0.42 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))) <=> (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(105,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.13/0.42 tff(106,plain,
% 0.13/0.42 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) <=> (~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))), ((~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))) <=> (~(~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))))), rewrite((~(~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))) <=> (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))), ((~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))) <=> (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))), (((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ((~greater(zero, growth_rate(S2, T))) | (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))))), rewrite(((~greater(zero, growth_rate(S2, T))) | (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) <=> (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))), (((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(107,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[106])).
% 0.13/0.42 tff(108,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(109,plain,
% 0.13/0.42 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))))), ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> ((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))))), rewrite(((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))), ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))), (((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))))), rewrite(((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))), (((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(110,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[109])).
% 0.13/0.42 tff(111,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a13')).
% 0.13/0.42 tff(112,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.13/0.42 tff(113,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.13/0.42 tff(114,plain,(
% 0.13/0.42 ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[113])).
% 0.13/0.42 tff(115,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.13/0.42 tff(116,plain,
% 0.13/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.13/0.42 tff(117,plain,
% 0.13/0.42 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(118,axiom,(greater(resilience(efficient_producers), resilience(first_movers))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a2')).
% 0.13/0.42 tff(119,plain,
% 0.13/0.42 (greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.13/0.42 tff(120,plain,
% 0.13/0.42 (((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(121,plain,
% 0.13/0.42 ((greater(zero, growth_rate(first_movers, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers)))) <=> ((~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(122,plain,
% 0.13/0.42 (((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (greater(zero, growth_rate(first_movers, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[121])).
% 0.13/0.43 tff(123,plain,
% 0.13/0.43 (((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (greater(zero, growth_rate(first_movers, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[122, 120])).
% 0.13/0.43 tff(124,plain,
% 0.13/0.43 ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (greater(zero, growth_rate(first_movers, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(125,plain,
% 0.13/0.43 ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.13/0.43 tff(126,plain,
% 0.13/0.43 ($false),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[125, 119, 116, 11, 103, 74, 54])).
% 0.13/0.43 % SZS output end Proof
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------