%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT025+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n007.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 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT025+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 7 12:08:12 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(greater_type, type, (
% 0.12/0.40 greater: ( $i * $i ) > $o)).
% 0.12/0.40 tff(growth_rate_type, type, (
% 0.12/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_T_0_type, type, (
% 0.12/0.40 tptp_fun_T_0: $i)).
% 0.12/0.40 tff(efficient_producers_type, type, (
% 0.12/0.40 efficient_producers: $i)).
% 0.12/0.40 tff(zero_type, type, (
% 0.12/0.40 zero: $i)).
% 0.12/0.40 tff(decreases_type, type, (
% 0.12/0.40 decreases: $i > $o)).
% 0.12/0.40 tff(cardinality_at_time_type, type, (
% 0.12/0.40 cardinality_at_time: ( $i * $i ) > $i)).
% 0.12/0.40 tff(increases_type, type, (
% 0.12/0.40 increases: $i > $o)).
% 0.12/0.40 tff(first_movers_type, type, (
% 0.12/0.40 first_movers: $i)).
% 0.12/0.40 tff(constant_type, type, (
% 0.12/0.40 constant: $i > $o)).
% 0.12/0.40 tff(subpopulation_type, type, (
% 0.12/0.40 subpopulation: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_E_1_type, type, (
% 0.12/0.40 tptp_fun_E_1: $i)).
% 0.12/0.40 tff(in_environment_type, type, (
% 0.12/0.40 in_environment: ( $i * $i ) > $o)).
% 0.12/0.40 tff(subpopulations_type, type, (
% 0.12/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.40 tff(number_of_organizations_type, type, (
% 0.12/0.40 number_of_organizations: ( $i * $i ) > $i)).
% 0.12/0.40 tff(environment_type, type, (
% 0.12/0.40 environment: $i > $o)).
% 0.12/0.40 tff(sum_type, type, (
% 0.12/0.40 sum: ( $i * $i ) > $i)).
% 0.12/0.40 tff(1,assumption,(~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0)))) | decreases(cardinality_at_time(first_movers, T!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (decreases(cardinality_at_time(first_movers, T!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 ((~((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) & 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))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 ((~![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) & 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))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 ((~![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))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(7,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','prove_l7')).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (~![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) & constant(number_of_organizations(E, T)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (~![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) & constant(number_of_organizations(E, T)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (~![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) & constant(number_of_organizations(E, T)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (~![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) & constant(number_of_organizations(E, T)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.40 tff(12,plain,(
% 0.12/0.40 ~((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) & constant(number_of_organizations(E!1, T!0)))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[11])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (~((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) & constant(number_of_organizations(E!1, T!0)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & constant(number_of_organizations(E!1, T!0))),
% 0.12/0.40 inference(or_elim,[status(thm)],[13])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.12/0.41 inference(and_elim,[status(thm)],[14])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (environment(E!1)),
% 0.12/0.41 inference(and_elim,[status(thm)],[14])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 (^[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))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(18,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.41 tff(19,plain,
% 0.12/0.41 (^[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)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(20,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.41 tff(21,plain,
% 0.12/0.41 (![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))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 (^[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)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(23,plain,
% 0.12/0.41 (![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))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.41 tff(24,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')).
% 0.12/0.41 tff(25,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.41 tff(26,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.41 tff(27,plain,(
% 0.12/0.41 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.12/0.41 inference(skolemize,[status(sab)],[26])).
% 0.12/0.41 tff(28,plain,
% 0.12/0.41 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.41 tff(29,plain,
% 0.12/0.41 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 (((~![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))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(31,plain,
% 0.12/0.41 ((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))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(32,plain,
% 0.12/0.41 (((~![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)))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[31])).
% 0.12/0.41 tff(33,plain,
% 0.12/0.41 (((~![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))),
% 0.12/0.41 inference(transitivity,[status(thm)],[32, 30])).
% 0.12/0.41 tff(34,plain,
% 0.12/0.41 ((~![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)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(35,plain,
% 0.12/0.41 ((~![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)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 (in_environment(E!1, T!0)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[35, 29, 16, 15])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 (^[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((subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)) <=> (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))), (((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> (((~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))))), rewrite((((~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))), (((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(40,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (^[E: $i, T: $i] : rewrite(((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(43,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.41 tff(44,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_subpopulations')).
% 0.12/0.41 tff(45,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.41 tff(46,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.41 tff(47,plain,(
% 0.12/0.41 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[46])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.12/0.41 tff(50,plain,
% 0.12/0.41 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(51,plain,
% 0.12/0.41 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(52,plain,
% 0.12/0.41 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[52, 49, 16, 36])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))) | subpopulation(first_movers, E!1, T!0)),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 (subpopulation(first_movers, E!1, T!0)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 (^[E: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.12/0.41 tff(58,plain,
% 0.12/0.41 (^[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))))), rewrite((greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(59,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.41 tff(60,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(61,plain,
% 0.12/0.41 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(62,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.12/0.41 tff(63,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_non_zero_producers')).
% 0.12/0.41 tff(64,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.12/0.41 tff(65,plain,
% 0.12/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.12/0.42 tff(66,plain,(
% 0.12/0.42 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.12/0.42 inference(skolemize,[status(sab)],[65])).
% 0.12/0.42 tff(67,plain,
% 0.12/0.42 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.12/0.42 tff(68,plain,
% 0.12/0.42 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.12/0.42 tff(69,plain,
% 0.12/0.42 (((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(70,plain,
% 0.12/0.42 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(71,plain,
% 0.12/0.42 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.42 tff(72,plain,
% 0.12/0.42 (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[71, 68, 16, 15])).
% 0.12/0.42 tff(73,plain,
% 0.12/0.42 (((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) | greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.12/0.42 inference(tautology,[status(thm)],[])).
% 0.12/0.42 tff(74,plain,
% 0.12/0.42 (greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.12/0.42 tff(75,plain,
% 0.12/0.42 (^[X: $i, E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(76,plain,
% 0.12/0.42 (![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))) <=> ![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[75])).
% 0.12/0.42 tff(77,plain,
% 0.12/0.42 (^[X: $i, E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))), ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))), ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))), rewrite((((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))) <=> (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))), (((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> (((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))), (((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(78,plain,
% 0.12/0.42 (![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> ![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.12/0.42 tff(79,plain,
% 0.12/0.42 (![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> ![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(80,plain,
% 0.12/0.42 (^[X: $i, E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) <=> (environment(E) & in_environment(E, T) & subpopulation(X, E, T))), ((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) <=> ((environment(E) & in_environment(E, T) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) <=> (environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))), ((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) <=> (environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))), trans(monotonicity(rewrite(((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) <=> (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)))), rewrite((decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T))) <=> ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))), ((((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T)))) <=> ((((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))), rewrite(((((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))) <=> (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))), ((((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T)))) <=> (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))), (((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => (((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T))))) <=> ((environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) => (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))), rewrite(((environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) => (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))), (((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => (((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T))))) <=> ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(81,plain,
% 0.12/0.42 (![X: $i, E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => (((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T))))) <=> ![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.12/0.42 tff(82,axiom,(![X: $i, E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => (((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_growth_rate')).
% 0.12/0.42 tff(83,plain,
% 0.12/0.42 (![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.12/0.42 tff(84,plain,
% 0.12/0.42 (![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.12/0.42 tff(85,plain,(
% 0.12/0.42 ![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.12/0.42 inference(skolemize,[status(sab)],[84])).
% 0.12/0.42 tff(86,plain,
% 0.12/0.42 (![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.12/0.42 tff(87,plain,
% 0.12/0.42 (![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.12/0.42 tff(88,plain,
% 0.12/0.42 (((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))))))) <=> ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(89,plain,
% 0.12/0.42 ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))))))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(90,plain,
% 0.12/0.42 ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.12/0.42 tff(91,plain,
% 0.12/0.42 (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[90, 87, 16, 74, 36, 55])).
% 0.12/0.42 tff(92,plain,
% 0.12/0.42 (((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))))) | ((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))),
% 0.12/0.42 inference(tautology,[status(thm)],[])).
% 0.12/0.42 tff(93,plain,
% 0.12/0.42 ((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.12/0.42 tff(94,plain,
% 0.12/0.42 ((~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))) | (~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))),
% 0.12/0.42 inference(tautology,[status(thm)],[])).
% 0.12/0.42 tff(95,plain,
% 0.12/0.42 ((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.12/0.42 tff(96,plain,
% 0.12/0.42 (greater(zero, growth_rate(first_movers, T!0))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[95, 3])).
% 0.12/0.42 tff(97,plain,
% 0.12/0.42 (((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0)))) | increases(cardinality_at_time(efficient_producers, T!0))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(98,plain,
% 0.12/0.43 (increases(cardinality_at_time(efficient_producers, T!0))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[97, 1])).
% 0.12/0.43 tff(99,plain,
% 0.12/0.43 (((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))) | subpopulation(efficient_producers, E!1, T!0)),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(100,plain,
% 0.12/0.43 (subpopulation(efficient_producers, E!1, T!0)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[99, 53])).
% 0.12/0.43 tff(101,plain,
% 0.12/0.43 (((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) | greater(cardinality_at_time(efficient_producers, T!0), zero)),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(102,plain,
% 0.12/0.43 (greater(cardinality_at_time(efficient_producers, T!0), zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[101, 72])).
% 0.12/0.43 tff(103,plain,
% 0.12/0.43 (((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))))))) <=> ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(104,plain,
% 0.12/0.43 ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))))))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(105,plain,
% 0.12/0.43 ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.12/0.43 tff(106,plain,
% 0.12/0.43 (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[105, 87, 16, 102, 36, 100])).
% 0.12/0.43 tff(107,plain,
% 0.12/0.43 (((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))))) | ((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(108,plain,
% 0.12/0.43 ((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.12/0.43 tff(109,plain,
% 0.12/0.43 ((~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero)),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(110,plain,
% 0.12/0.43 ((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.12/0.43 tff(111,plain,
% 0.12/0.43 (greater(growth_rate(efficient_producers, T!0), zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[110, 98])).
% 0.12/0.43 tff(112,plain,
% 0.12/0.43 ((~(~((~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))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(113,plain,
% 0.12/0.43 ((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)))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(114,plain,
% 0.12/0.43 ((~(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))))))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[113])).
% 0.12/0.43 tff(115,plain,
% 0.12/0.43 ((~(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))))),
% 0.12/0.43 inference(transitivity,[status(thm)],[114, 112])).
% 0.12/0.43 tff(116,plain,
% 0.12/0.43 (~(greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0)))),
% 0.12/0.43 inference(or_elim,[status(thm)],[13])).
% 0.12/0.43 tff(117,plain,
% 0.12/0.43 ((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.12/0.43 tff(118,plain,
% 0.12/0.43 ($false),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[117, 111, 96])).
% 0.12/0.43 tff(119,plain,((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.43 tff(120,assumption,(~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))), introduced(assumption)).
% 0.12/0.43 tff(121,plain,
% 0.12/0.43 (((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))) | constant(cardinality_at_time(efficient_producers, T!0))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(122,plain,
% 0.12/0.43 (constant(cardinality_at_time(efficient_producers, T!0))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.12/0.43 tff(123,plain,
% 0.12/0.43 (((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))))) | ((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(124,plain,
% 0.12/0.43 ((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[123, 106])).
% 0.12/0.43 tff(125,plain,
% 0.12/0.43 ((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero)),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(126,plain,
% 0.12/0.43 ((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.12/0.43 tff(127,plain,
% 0.12/0.43 (growth_rate(efficient_producers, T!0) = zero),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.12/0.43 tff(128,plain,
% 0.12/0.43 (((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))) | constant(cardinality_at_time(first_movers, T!0))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(129,plain,
% 0.12/0.43 (constant(cardinality_at_time(first_movers, T!0))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[128, 120])).
% 0.12/0.43 tff(130,plain,
% 0.12/0.43 (((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))))) | ((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(131,plain,
% 0.12/0.43 ((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[130, 91])).
% 0.12/0.43 tff(132,plain,
% 0.12/0.43 ((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero)),
% 0.12/0.43 inference(tautology,[status(thm)],[])).
% 0.12/0.43 tff(133,plain,
% 0.12/0.43 ((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.12/0.43 tff(134,plain,
% 0.12/0.43 (growth_rate(first_movers, T!0) = zero),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[133, 129])).
% 0.12/0.43 tff(135,plain,
% 0.12/0.43 ((~(~((~(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)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(136,plain,
% 0.12/0.43 (((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))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(137,plain,
% 0.12/0.43 ((~((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)))))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.12/0.43 tff(138,plain,
% 0.12/0.43 ((~((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)))),
% 0.12/0.43 inference(transitivity,[status(thm)],[137, 135])).
% 0.12/0.43 tff(139,plain,
% 0.12/0.43 (~((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero))),
% 0.12/0.43 inference(or_elim,[status(thm)],[13])).
% 0.12/0.43 tff(140,plain,
% 0.12/0.43 ((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.12/0.43 tff(141,plain,
% 0.12/0.43 ($false),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[140, 134, 127])).
% 0.12/0.43 tff(142,plain,((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.43 tff(143,plain,
% 0.12/0.43 (^[E: $i, X: $i, T: $i] : refl(((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) <=> ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(144,plain,
% 0.12/0.43 (![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) <=> ![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[143])).
% 0.12/0.43 tff(145,plain,
% 0.12/0.43 (^[E: $i, X: $i, T: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))) <=> ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))), ((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) <=> (environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), rewrite((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) <=> (~((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))), ((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) <=> (~((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))))), ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) <=> (~(~((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))))), rewrite((~(~((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))) <=> ((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) <=> ((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))), (((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> (((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))))), rewrite((((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), (((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(146,plain,
% 0.12/0.43 (![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[145])).
% 0.12/0.43 tff(147,plain,
% 0.12/0.43 (![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(148,plain,
% 0.12/0.43 (^[E: $i, X: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers))) <=> ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))), (((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) <=> ((environment(E) & subpopulation(X, E, T)) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), rewrite(((environment(E) & subpopulation(X, E, T)) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) <=> (environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))), (((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) <=> (environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), ((((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))))), rewrite(((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))), ((((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(149,plain,
% 0.12/0.44 (![E: $i, X: $i, T: $i] : (((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[148])).
% 0.12/0.44 tff(150,axiom,(![E: $i, X: $i, T: $i] : (((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_only_members')).
% 0.12/0.44 tff(151,plain,
% 0.12/0.44 (![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.12/0.44 tff(152,plain,
% 0.12/0.44 (![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.12/0.44 tff(153,plain,(
% 0.12/0.44 ![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.12/0.44 inference(skolemize,[status(sab)],[152])).
% 0.12/0.44 tff(154,plain,
% 0.12/0.44 (![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.12/0.44 tff(155,plain,
% 0.12/0.44 (![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.12/0.44 tff(156,plain,
% 0.12/0.44 (((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))) <=> ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(157,plain,
% 0.12/0.44 (((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | $false) <=> ((~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(158,plain,
% 0.12/0.44 ((~$true) <=> $false),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(159,plain,
% 0.12/0.44 (((efficient_producers = first_movers) | $true | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) <=> $true),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(160,plain,
% 0.12/0.44 ((efficient_producers = efficient_producers) <=> $true),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(161,plain,
% 0.12/0.44 (((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) <=> ((efficient_producers = first_movers) | $true | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.12/0.44 inference(monotonicity,[status(thm)],[160])).
% 0.12/0.44 tff(162,plain,
% 0.12/0.44 (((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) <=> $true),
% 0.12/0.44 inference(transitivity,[status(thm)],[161, 159])).
% 0.12/0.44 tff(163,plain,
% 0.12/0.44 ((~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> (~$true)),
% 0.12/0.44 inference(monotonicity,[status(thm)],[162])).
% 0.12/0.44 tff(164,plain,
% 0.12/0.44 ((~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> $false),
% 0.12/0.44 inference(transitivity,[status(thm)],[163, 158])).
% 0.12/0.44 tff(165,plain,
% 0.12/0.44 (((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))))) <=> ((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | $false)),
% 0.12/0.44 inference(monotonicity,[status(thm)],[164])).
% 0.12/0.44 tff(166,plain,
% 0.12/0.44 (((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))))) <=> ((~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))),
% 0.12/0.44 inference(transitivity,[status(thm)],[165, 157])).
% 0.12/0.44 tff(167,plain,
% 0.12/0.44 (((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))) <=> ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))))),
% 0.12/0.44 inference(monotonicity,[status(thm)],[166])).
% 0.12/0.44 tff(168,plain,
% 0.12/0.44 (((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))) <=> ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))),
% 0.12/0.44 inference(transitivity,[status(thm)],[167, 156])).
% 0.12/0.44 tff(169,plain,
% 0.12/0.44 ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(170,plain,
% 0.12/0.44 ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.12/0.44 tff(171,plain,
% 0.12/0.44 (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[170, 155, 16, 100])).
% 0.12/0.44 tff(172,plain,
% 0.12/0.44 (sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = number_of_organizations(E!1, T!0)),
% 0.12/0.44 inference(symmetry,[status(thm)],[171])).
% 0.12/0.44 tff(173,plain,
% 0.12/0.44 (constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) <=> constant(number_of_organizations(E!1, T!0))),
% 0.12/0.44 inference(monotonicity,[status(thm)],[172])).
% 0.12/0.44 tff(174,plain,
% 0.12/0.44 (constant(number_of_organizations(E!1, T!0)) <=> constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))),
% 0.12/0.44 inference(symmetry,[status(thm)],[173])).
% 0.12/0.44 tff(175,plain,
% 0.12/0.44 (constant(number_of_organizations(E!1, T!0))),
% 0.12/0.44 inference(and_elim,[status(thm)],[14])).
% 0.12/0.44 tff(176,plain,
% 0.12/0.44 (constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.12/0.44 tff(177,plain,
% 0.12/0.44 (^[B: $i, C: $i] : refl(((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C))))) <=> ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C))))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(178,plain,
% 0.12/0.44 (![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C))))) <=> ![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[177])).
% 0.12/0.44 tff(179,plain,
% 0.12/0.44 (^[B: $i, C: $i] : trans(monotonicity(rewrite((decreases(B) & increases(C)) <=> (~((~decreases(B)) | (~increases(C))))), rewrite((increases(B) & decreases(C)) <=> (~((~increases(B)) | (~decreases(C))))), rewrite((constant(B) & constant(C)) <=> (~((~constant(B)) | (~constant(C))))), (((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C)))) <=> ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~constant(sum(B, C)))))), rewrite(((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~constant(sum(B, C)))) <=> ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))), (((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C)))) <=> ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(180,plain,
% 0.12/0.44 (![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[179])).
% 0.12/0.44 tff(181,plain,
% 0.12/0.44 (![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(182,plain,
% 0.12/0.44 (^[B: $i, C: $i] : rewrite(((~constant(sum(B, C))) | (decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C))) <=> ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C)))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(183,plain,
% 0.12/0.44 (![B: $i, C: $i] : ((~constant(sum(B, C))) | (decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C))) <=> ![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[182])).
% 0.12/0.44 tff(184,plain,
% 0.12/0.44 (![A: $i, B: $i, C: $i] : ((~constant(sum(B, C))) | (decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C))) <=> ![B: $i, C: $i] : ((~constant(sum(B, C))) | (decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))),
% 0.12/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.44 tff(185,plain,
% 0.12/0.44 (![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A)))) <=> ![A: $i, B: $i, C: $i] : ((~constant(sum(B, C))) | (decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))),
% 0.12/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.44 tff(186,plain,
% 0.12/0.44 (![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A)))) <=> ![B: $i, C: $i] : ((~constant(sum(B, C))) | (decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))),
% 0.12/0.44 inference(transitivity,[status(thm)],[185, 184])).
% 0.12/0.44 tff(187,plain,
% 0.12/0.44 (![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A)))) <=> ![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C))))),
% 0.12/0.44 inference(transitivity,[status(thm)],[186, 183])).
% 0.12/0.44 tff(188,plain,
% 0.12/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C))) <=> ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))), ((((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C)))) <=> (((A = sum(B, C)) & constant(A)) => ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))))), rewrite((((A = sum(B, C)) & constant(A)) => ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))) <=> ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))), ((((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C)))) <=> ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(189,plain,
% 0.12/0.45 (![A: $i, B: $i, C: $i] : (((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C)))) <=> ![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[188])).
% 0.12/0.45 tff(190,plain,
% 0.12/0.45 (![A: $i, B: $i, C: $i] : (((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C)))) <=> ![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[189, 187])).
% 0.12/0.45 tff(191,axiom,(![A: $i, B: $i, C: $i] : (((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_abc_sum_increase')).
% 0.12/0.45 tff(192,plain,
% 0.12/0.45 (![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.12/0.45 tff(193,plain,
% 0.12/0.45 (![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[192, 181])).
% 0.12/0.45 tff(194,plain,(
% 0.12/0.45 ![B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(skolemize,[status(sab)],[193])).
% 0.12/0.45 tff(195,plain,
% 0.12/0.45 (![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[194, 180])).
% 0.12/0.45 tff(196,plain,
% 0.12/0.45 (![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[195, 178])).
% 0.12/0.45 tff(197,plain,
% 0.12/0.45 (((~![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))) | ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))) <=> ((~![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(198,plain,
% 0.12/0.45 (((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))) <=> ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(199,plain,
% 0.12/0.45 ((~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))) <=> (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(200,plain,
% 0.12/0.45 ((~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) <=> (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0)))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(201,plain,
% 0.12/0.45 (((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0)))))) <=> ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.12/0.45 inference(monotonicity,[status(thm)],[200, 199])).
% 0.12/0.45 tff(202,plain,
% 0.12/0.45 (((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0)))))) <=> ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[201, 198])).
% 0.12/0.45 tff(203,plain,
% 0.12/0.45 (((~![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))) | ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))))) <=> ((~![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))) | ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))))),
% 0.12/0.45 inference(monotonicity,[status(thm)],[202])).
% 0.12/0.45 tff(204,plain,
% 0.12/0.45 (((~![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))) | ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))))) <=> ((~![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[203, 197])).
% 0.12/0.45 tff(205,plain,
% 0.12/0.45 ((~![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))) | ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))))),
% 0.12/0.45 inference(quant_inst,[status(thm)],[])).
% 0.12/0.45 tff(206,plain,
% 0.12/0.45 ((~![B: $i, C: $i] : ((~constant(sum(B, C))) | (~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.12/0.45 tff(207,plain,
% 0.12/0.45 ((~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[206, 196])).
% 0.12/0.45 tff(208,plain,
% 0.12/0.45 ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[207, 176])).
% 0.12/0.45 tff(209,plain,
% 0.12/0.45 (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[208, 142, 119])).
% 0.12/0.45 tff(210,plain,
% 0.12/0.45 (((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0)))) | decreases(cardinality_at_time(efficient_producers, T!0))),
% 0.12/0.45 inference(tautology,[status(thm)],[])).
% 0.12/0.45 tff(211,plain,
% 0.12/0.45 (decreases(cardinality_at_time(efficient_producers, T!0))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.12/0.45 tff(212,plain,
% 0.12/0.45 (((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))))) | ((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.12/0.45 inference(tautology,[status(thm)],[])).
% 0.12/0.45 tff(213,plain,
% 0.12/0.45 ((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[212, 106])).
% 0.12/0.45 tff(214,plain,
% 0.12/0.45 ((~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))) | (~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.12/0.45 inference(tautology,[status(thm)],[])).
% 0.12/0.45 tff(215,plain,
% 0.12/0.45 ((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.12/0.45 tff(216,plain,
% 0.12/0.45 (greater(zero, growth_rate(efficient_producers, T!0))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[215, 211])).
% 0.12/0.45 tff(217,plain,
% 0.12/0.45 (((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0)))) | increases(cardinality_at_time(first_movers, T!0))),
% 0.12/0.45 inference(tautology,[status(thm)],[])).
% 0.12/0.45 tff(218,plain,
% 0.12/0.45 (increases(cardinality_at_time(first_movers, T!0))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[217, 209])).
% 0.12/0.45 tff(219,plain,
% 0.12/0.45 (((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))))) | ((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))),
% 0.12/0.45 inference(tautology,[status(thm)],[])).
% 0.12/0.45 tff(220,plain,
% 0.12/0.45 ((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero)),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[219, 91])).
% 0.12/0.45 tff(221,plain,
% 0.12/0.45 ((~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero)),
% 0.12/0.45 inference(tautology,[status(thm)],[])).
% 0.12/0.45 tff(222,plain,
% 0.12/0.45 ((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero)),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.12/0.45 tff(223,plain,
% 0.12/0.45 (greater(growth_rate(first_movers, T!0), zero)),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[222, 218])).
% 0.12/0.45 tff(224,plain,
% 0.12/0.45 ((~(~((~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))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(225,plain,
% 0.12/0.45 ((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)))))),
% 0.12/0.46 inference(rewrite,[status(thm)],[])).
% 0.12/0.46 tff(226,plain,
% 0.12/0.46 ((~(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))))))),
% 0.12/0.46 inference(monotonicity,[status(thm)],[225])).
% 0.12/0.46 tff(227,plain,
% 0.12/0.46 ((~(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))))),
% 0.12/0.46 inference(transitivity,[status(thm)],[226, 224])).
% 0.12/0.46 tff(228,plain,
% 0.12/0.46 (~(greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.12/0.46 inference(or_elim,[status(thm)],[13])).
% 0.12/0.46 tff(229,plain,
% 0.12/0.46 ((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.12/0.46 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.12/0.46 tff(230,plain,
% 0.12/0.46 ($false),
% 0.12/0.46 inference(unit_resolution,[status(thm)],[229, 223, 216])).
% 0.12/0.46 % SZS output end Proof
% 0.12/0.46 % E exiting
%------------------------------------------------------------------------------