%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT024+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n006.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 06:24:00 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
% 0.00/0.02 % Problem : MGT024+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 12:09:18 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(zero_type, type, (
% 0.13/0.40 zero: $i)).
% 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(first_movers_type, type, (
% 0.13/0.40 first_movers: $i)).
% 0.13/0.40 tff(efficient_producers_type, type, (
% 0.13/0.40 efficient_producers: $i)).
% 0.13/0.40 tff(greater_type, type, (
% 0.13/0.40 greater: ( $i * $i ) > $o)).
% 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(equilibrium_type, type, (
% 0.13/0.40 equilibrium: $i > $i)).
% 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(subpopulations_type, type, (
% 0.13/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.40 tff(environment_type, type, (
% 0.13/0.40 environment: $i > $o)).
% 0.13/0.40 tff(constant_type, type, (
% 0.13/0.40 constant: $i > $o)).
% 0.13/0.40 tff(number_of_organizations_type, type, (
% 0.13/0.40 number_of_organizations: ( $i * $i ) > $i)).
% 0.13/0.40 tff(resources_type, type, (
% 0.13/0.40 resources: ( $i * $i ) > $i)).
% 0.13/0.40 tff(decreases_type, type, (
% 0.13/0.40 decreases: $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(1,assumption,(~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))) | greater(growth_rate(efficient_producers, T!0), zero)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (greater(growth_rate(efficient_producers, T!0), zero)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))) | greater(zero, growth_rate(first_movers, T!0))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (greater(zero, growth_rate(first_movers, T!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 ((~(~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))))) <=> ((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 ((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) <=> (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~(greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0)))) <=> (~(~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ((~(greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0)))) <=> ((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[8, 6])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((~((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) | (greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) | ((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & greater_or_equal(T!0, equilibrium(E!1)))))) <=> (~((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) | (greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) | ((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & greater_or_equal(T!0, equilibrium(E!1))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))) <=> (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 ((~![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(13,axiom,(~![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(T, equilibrium(E))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l6')).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.13/0.41 tff(18,plain,(
% 0.13/0.41 ~((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) | (greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) | ((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & greater_or_equal(T!0, equilibrium(E!1)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[17])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (~((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) | (greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) | ((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & greater_or_equal(T!0, equilibrium(E!1)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (~(greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0)))),
% 0.13/0.41 inference(or_elim,[status(thm)],[19])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 ((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 9])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[21, 5, 3])).
% 0.13/0.41 tff(23,plain,((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(24,assumption,(~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))), introduced(assumption)).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) | greater(growth_rate(first_movers, T!0), zero)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (greater(growth_rate(first_movers, T!0), zero)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (greater(zero, growth_rate(efficient_producers, T!0))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 ((~(~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))))) <=> ((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 ((greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) <=> (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 ((~(greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0)))) <=> (~(~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[30])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 ((~(greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0)))) <=> ((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[31, 29])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (~(greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.13/0.41 inference(or_elim,[status(thm)],[19])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 ((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[34, 28, 26])).
% 0.13/0.41 tff(36,plain,((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & greater_or_equal(T!0, equilibrium(E!1))),
% 0.13/0.41 inference(or_elim,[status(thm)],[19])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.41 inference(and_elim,[status(thm)],[37])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (environment(E!1)),
% 0.13/0.41 inference(and_elim,[status(thm)],[37])).
% 0.13/0.41 tff(40,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(41,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)],[40])).
% 0.13/0.41 tff(42,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(43,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)],[42])).
% 0.13/0.41 tff(44,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(45,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(46,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)],[45])).
% 0.13/0.41 tff(47,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_time_point_occur')).
% 0.13/0.41 tff(48,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)],[47, 46])).
% 0.13/0.41 tff(49,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)],[48, 44])).
% 0.13/0.41 tff(50,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)],[49])).
% 0.13/0.41 tff(51,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)],[50, 43])).
% 0.13/0.41 tff(52,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)],[51, 41])).
% 0.13/0.41 tff(53,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(54,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(55,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)],[54])).
% 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)))) | (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)],[55, 53])).
% 0.13/0.41 tff(57,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(58,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)],[57, 56])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (in_environment(E!1, T!0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[58, 52, 39, 38])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(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)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), rewrite((((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))) <=> (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))), (((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> (((~environment(E)) | (~in_environment(E, T))) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))))), rewrite((((~environment(E)) | (~in_environment(E, T))) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))), (((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T)))) <=> (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))), (((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ((environment(E) & in_environment(E, T)) => (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))), rewrite(((environment(E) & in_environment(E, T)) => (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))), (((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.13/0.41 tff(67,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a6')).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.13/0.41 tff(70,plain,(
% 0.13/0.41 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[69])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~((~decreases(number_of_organizations(E!1, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0))))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~((~decreases(number_of_organizations(E!1, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0))))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(74,plain,
% 0.13/0.42 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~((~decreases(number_of_organizations(E!1, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0))))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(75,plain,
% 0.13/0.42 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~((~decreases(number_of_organizations(E!1, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0)))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.13/0.42 tff(76,plain,
% 0.13/0.42 (~((~((~decreases(number_of_organizations(E!1, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0))))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[75, 72, 39, 59])).
% 0.13/0.42 tff(77,plain,
% 0.13/0.42 (((~((~decreases(number_of_organizations(E!1, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0)))))) | (constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0))))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 (constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 (^[E: $i, T: $i] : refl((greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(80,plain,
% 0.13/0.42 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[79])).
% 0.13/0.42 tff(81,plain,
% 0.13/0.42 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(82,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.13/0.42 tff(83,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(84,plain,
% 0.13/0.42 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater(number_of_organizations(E, T), zero)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(85,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.13/0.42 tff(86,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater(number_of_organizations(E, T), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_positive_number_of_organizations')).
% 0.13/0.42 tff(87,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.13/0.42 tff(88,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.13/0.42 tff(89,plain,(
% 0.13/0.42 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.13/0.42 inference(skolemize,[status(sab)],[88])).
% 0.13/0.42 tff(90,plain,
% 0.13/0.42 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.13/0.42 tff(91,plain,
% 0.13/0.42 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.13/0.42 tff(92,plain,
% 0.13/0.42 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(93,plain,
% 0.13/0.42 ((greater(number_of_organizations(E!1, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(94,plain,
% 0.13/0.42 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(number_of_organizations(E!1, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[93])).
% 0.13/0.42 tff(95,plain,
% 0.13/0.42 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(number_of_organizations(E!1, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero))),
% 0.13/0.42 inference(transitivity,[status(thm)],[94, 92])).
% 0.13/0.42 tff(96,plain,
% 0.13/0.42 ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(number_of_organizations(E!1, 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(97,plain,
% 0.13/0.42 ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.13/0.42 tff(98,plain,
% 0.13/0.42 (greater(number_of_organizations(E!1, T!0), zero)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[97, 91, 39, 38])).
% 0.13/0.42 tff(99,plain,
% 0.13/0.42 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(100,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.13/0.42 tff(101,plain,
% 0.13/0.42 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))), ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)))), ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))), trans(monotonicity(rewrite(((~greater(equilibrium(E), T)) | decreases(resources(E, T))) <=> ((~greater(equilibrium(E), T)) | decreases(resources(E, T)))), rewrite((greater(equilibrium(E), T) | constant(resources(E, T))) <=> (greater(equilibrium(E), T) | constant(resources(E, T)))), ((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))) <=> (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))))), rewrite((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))) <=> (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T))))))), ((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))) <=> (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))), (((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T))))) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T))))))))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))), (((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(102,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[101])).
% 0.13/0.42 tff(103,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(104,plain,
% 0.13/0.42 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))), rewrite(((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T)))) <=> (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T))))), ((((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) => (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T))))))), rewrite(((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) => (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T))))) <=> ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))))), ((((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(105,plain,
% 0.13/0.42 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.13/0.42 tff(106,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a3')).
% 0.13/0.42 tff(107,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.13/0.42 tff(108,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.13/0.42 tff(109,plain,(
% 0.13/0.42 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (greater(equilibrium(E), T) | constant(resources(E, T)))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[108])).
% 0.13/0.42 tff(110,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.13/0.42 tff(111,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.13/0.42 tff(112,plain,
% 0.13/0.42 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0)))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(113,plain,
% 0.13/0.42 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0)))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(114,plain,
% 0.13/0.42 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(greater(equilibrium(E), T) | constant(resources(E, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.13/0.42 tff(115,plain,
% 0.13/0.42 (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0)))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[114, 111, 39, 59, 98])).
% 0.13/0.42 tff(116,plain,
% 0.13/0.42 (((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0))))) | (greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0)))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(117,plain,
% 0.13/0.42 (greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.13/0.42 tff(118,plain,
% 0.13/0.42 (greater_or_equal(T!0, equilibrium(E!1))),
% 0.13/0.42 inference(and_elim,[status(thm)],[37])).
% 0.13/0.42 tff(119,plain,
% 0.13/0.42 (^[E: $i, T: $i] : refl(((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E)))) <=> ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(120,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E)))) <=> ![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[119])).
% 0.13/0.42 tff(121,plain,
% 0.13/0.42 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & greater_or_equal(T, equilibrium(E))) <=> (~((~environment(E)) | (~greater_or_equal(T, equilibrium(E)))))), ((~(environment(E) & greater_or_equal(T, equilibrium(E)))) <=> (~(~((~environment(E)) | (~greater_or_equal(T, equilibrium(E)))))))), rewrite((~(~((~environment(E)) | (~greater_or_equal(T, equilibrium(E)))))) <=> ((~environment(E)) | (~greater_or_equal(T, equilibrium(E))))), ((~(environment(E) & greater_or_equal(T, equilibrium(E)))) <=> ((~environment(E)) | (~greater_or_equal(T, equilibrium(E)))))), (((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E))))) <=> ((~greater(equilibrium(E), T)) | ((~environment(E)) | (~greater_or_equal(T, equilibrium(E))))))), rewrite(((~greater(equilibrium(E), T)) | ((~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) <=> ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))), (((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E))))) <=> ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(122,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E))))) <=> ![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[121])).
% 0.13/0.43 tff(123,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E))))) <=> ![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(124,plain,
% 0.13/0.43 (^[E: $i, T: $i] : rewrite(((environment(E) & greater_or_equal(T, equilibrium(E))) => (~greater(equilibrium(E), T))) <=> ((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(125,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((environment(E) & greater_or_equal(T, equilibrium(E))) => (~greater(equilibrium(E), T))) <=> ![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[124])).
% 0.13/0.43 tff(126,axiom,(![E: $i, T: $i] : ((environment(E) & greater_or_equal(T, equilibrium(E))) => (~greater(equilibrium(E), T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_equilibrium')).
% 0.13/0.43 tff(127,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.13/0.43 tff(128,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.13/0.43 tff(129,plain,(
% 0.13/0.43 ![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~(environment(E) & greater_or_equal(T, equilibrium(E)))))),
% 0.13/0.43 inference(skolemize,[status(sab)],[128])).
% 0.13/0.43 tff(130,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.13/0.43 tff(131,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.13/0.43 tff(132,plain,
% 0.13/0.43 (((~![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!1)) | (~greater(equilibrium(E!1), T!0)) | (~greater_or_equal(T!0, equilibrium(E!1))))) <=> ((~![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!1)) | (~greater(equilibrium(E!1), T!0)) | (~greater_or_equal(T!0, equilibrium(E!1))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(133,plain,
% 0.13/0.43 (((~greater(equilibrium(E!1), T!0)) | (~environment(E!1)) | (~greater_or_equal(T!0, equilibrium(E!1)))) <=> ((~environment(E!1)) | (~greater(equilibrium(E!1), T!0)) | (~greater_or_equal(T!0, equilibrium(E!1))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(134,plain,
% 0.13/0.43 (((~![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) | ((~greater(equilibrium(E!1), T!0)) | (~environment(E!1)) | (~greater_or_equal(T!0, equilibrium(E!1))))) <=> ((~![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) | ((~environment(E!1)) | (~greater(equilibrium(E!1), T!0)) | (~greater_or_equal(T!0, equilibrium(E!1)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[133])).
% 0.13/0.43 tff(135,plain,
% 0.13/0.43 (((~![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) | ((~greater(equilibrium(E!1), T!0)) | (~environment(E!1)) | (~greater_or_equal(T!0, equilibrium(E!1))))) <=> ((~![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!1)) | (~greater(equilibrium(E!1), T!0)) | (~greater_or_equal(T!0, equilibrium(E!1))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[134, 132])).
% 0.13/0.43 tff(136,plain,
% 0.13/0.43 ((~![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) | ((~greater(equilibrium(E!1), T!0)) | (~environment(E!1)) | (~greater_or_equal(T!0, equilibrium(E!1))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(137,plain,
% 0.13/0.43 ((~![E: $i, T: $i] : ((~greater(equilibrium(E), T)) | (~environment(E)) | (~greater_or_equal(T, equilibrium(E))))) | (~environment(E!1)) | (~greater(equilibrium(E!1), T!0)) | (~greater_or_equal(T!0, equilibrium(E!1)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.13/0.43 tff(138,plain,
% 0.13/0.43 (~greater(equilibrium(E!1), T!0)),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[137, 131, 39, 118])).
% 0.13/0.43 tff(139,plain,
% 0.13/0.43 ((~(greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0)))) | greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(140,plain,
% 0.13/0.43 ((~(greater(equilibrium(E!1), T!0) | constant(resources(E!1, T!0)))) | constant(resources(E!1, T!0))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.13/0.43 tff(141,plain,
% 0.13/0.43 (constant(resources(E!1, T!0))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[140, 117])).
% 0.13/0.43 tff(142,plain,
% 0.13/0.43 ((~(constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0))))) | constant(number_of_organizations(E!1, T!0)) | (~constant(resources(E!1, T!0)))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(143,plain,
% 0.13/0.43 (constant(number_of_organizations(E!1, T!0))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[142, 141, 78])).
% 0.13/0.43 tff(144,plain,
% 0.13/0.43 (^[E: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T)))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T)))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(145,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T)))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[144])).
% 0.13/0.43 tff(146,plain,
% 0.13/0.43 (^[E: $i, T: $i] : trans(monotonicity(rewrite((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) <=> (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T)))))), rewrite((greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) <=> (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T)))))), rewrite(((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) <=> (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero))))), trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~constant(number_of_organizations(E, T)))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~constant(number_of_organizations(E, T)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~constant(number_of_organizations(E, T)))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~constant(number_of_organizations(E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~constant(number_of_organizations(E, T)))))), (((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))))) <=> ((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~constant(number_of_organizations(E, T))))))), rewrite(((~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~constant(number_of_organizations(E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))), (((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(147,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[146])).
% 0.13/0.43 tff(148,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))))) <=> ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(149,plain,
% 0.13/0.43 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & constant(number_of_organizations(E, T))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))), rewrite(((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & constant(number_of_organizations(E, T))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))) => ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))) => ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & constant(number_of_organizations(E, T))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(150,plain,
% 0.13/0.43 (![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & constant(number_of_organizations(E, T))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[149])).
% 0.13/0.43 tff(151,axiom,(![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & constant(number_of_organizations(E, T))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l7')).
% 0.13/0.43 tff(152,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.13/0.43 tff(153,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.13/0.44 tff(154,plain,(
% 0.13/0.44 ![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.13/0.44 inference(skolemize,[status(sab)],[153])).
% 0.13/0.44 tff(155,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.13/0.44 tff(156,plain,
% 0.13/0.44 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[155, 145])).
% 0.13/0.44 tff(157,plain,
% 0.13/0.44 (((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))) | ((~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~constant(number_of_organizations(E!1, T!0))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~constant(number_of_organizations(E!1, T!0))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(158,plain,
% 0.13/0.44 (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~constant(number_of_organizations(E!1, T!0)))) <=> ((~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~constant(number_of_organizations(E!1, T!0))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(159,plain,
% 0.13/0.44 ((~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) <=> (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(160,plain,
% 0.13/0.44 ((~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) <=> (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(161,plain,
% 0.13/0.44 ((~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) <=> (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(162,plain,
% 0.13/0.44 (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~constant(number_of_organizations(E!1, T!0)))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~constant(number_of_organizations(E!1, T!0))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[161, 160, 159])).
% 0.13/0.44 tff(163,plain,
% 0.13/0.44 (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~constant(number_of_organizations(E!1, T!0)))) <=> ((~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~constant(number_of_organizations(E!1, T!0))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[162, 158])).
% 0.13/0.44 tff(164,plain,
% 0.13/0.44 (((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~constant(number_of_organizations(E!1, T!0))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))) | ((~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~constant(number_of_organizations(E!1, T!0)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[163])).
% 0.13/0.44 tff(165,plain,
% 0.13/0.44 (((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~constant(number_of_organizations(E!1, T!0))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~constant(number_of_organizations(E!1, T!0))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[164, 157])).
% 0.13/0.44 tff(166,plain,
% 0.13/0.44 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~constant(number_of_organizations(E!1, T!0))))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(167,plain,
% 0.13/0.45 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(growth_rate(efficient_producers, T), zero)) | (~greater(zero, growth_rate(first_movers, T))))) | (~((~greater(growth_rate(first_movers, T), zero)) | (~greater(zero, growth_rate(efficient_producers, T))))) | (~((~(growth_rate(first_movers, T) = zero)) | (~(growth_rate(efficient_producers, T) = zero)))) | (~constant(number_of_organizations(E, T))))) | (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~constant(number_of_organizations(E!1, T!0)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.13/0.45 tff(168,plain,
% 0.13/0.45 ((~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))) | (~constant(number_of_organizations(E!1, T!0)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[167, 156, 39, 38])).
% 0.13/0.45 tff(169,plain,
% 0.13/0.45 ((~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[168, 143])).
% 0.13/0.45 tff(170,plain,
% 0.13/0.45 (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[169, 36, 23])).
% 0.13/0.45 tff(171,plain,
% 0.13/0.45 (((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))) | (growth_rate(first_movers, T!0) = zero)),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(172,plain,
% 0.13/0.45 (growth_rate(first_movers, T!0) = zero),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.13/0.45 tff(173,plain,
% 0.13/0.45 (((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))) | (growth_rate(efficient_producers, T!0) = zero)),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(174,plain,
% 0.13/0.45 (growth_rate(efficient_producers, T!0) = zero),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[173, 170])).
% 0.13/0.45 tff(175,plain,
% 0.13/0.45 ((~(~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))))) <=> ((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(176,plain,
% 0.13/0.45 (((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) <=> (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(177,plain,
% 0.13/0.45 ((~((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero))) <=> (~(~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[176])).
% 0.13/0.45 tff(178,plain,
% 0.13/0.45 ((~((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero))) <=> ((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))),
% 0.13/0.45 inference(transitivity,[status(thm)],[177, 175])).
% 0.13/0.45 tff(179,plain,
% 0.13/0.45 (~((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero))),
% 0.13/0.45 inference(or_elim,[status(thm)],[19])).
% 0.13/0.45 tff(180,plain,
% 0.13/0.45 ((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.13/0.45 tff(181,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[180, 174, 172])).
% 0.13/0.45 % SZS output end Proof
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------