%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n012.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 06:23:58 AM UTC 2026
% Result : Theorem 0.03s 0.32s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.01 % Command : run_E %s %d THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 7 12:02:58 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.32 % SZS status Theorem
% 0.03/0.32 % SZS output start Proof
% 0.03/0.32 tff(greater_type, type, (
% 0.03/0.32 greater: ( $i * $i ) > $o)).
% 0.03/0.32 tff(tptp_fun_T_0_type, type, (
% 0.03/0.32 tptp_fun_T_0: $i)).
% 0.03/0.32 tff(equilibrium_type, type, (
% 0.03/0.32 equilibrium: $i > $i)).
% 0.03/0.32 tff(tptp_fun_E_1_type, type, (
% 0.03/0.32 tptp_fun_E_1: $i)).
% 0.03/0.32 tff(decreases_type, type, (
% 0.03/0.32 decreases: $i > $o)).
% 0.03/0.32 tff(resources_type, type, (
% 0.03/0.32 resources: ( $i * $i ) > $i)).
% 0.03/0.32 tff(constant_type, type, (
% 0.03/0.32 constant: $i > $o)).
% 0.03/0.32 tff(zero_type, type, (
% 0.03/0.32 zero: $i)).
% 0.03/0.32 tff(number_of_organizations_type, type, (
% 0.03/0.32 number_of_organizations: ( $i * $i ) > $i)).
% 0.03/0.32 tff(subpopulations_type, type, (
% 0.03/0.32 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.03/0.32 tff(efficient_producers_type, type, (
% 0.03/0.32 efficient_producers: $i)).
% 0.03/0.32 tff(first_movers_type, type, (
% 0.03/0.32 first_movers: $i)).
% 0.03/0.32 tff(environment_type, type, (
% 0.03/0.32 environment: $i > $o)).
% 0.03/0.32 tff(difference_type, type, (
% 0.03/0.32 difference: ( $i * $i ) > $i)).
% 0.03/0.32 tff(disbanding_rate_type, type, (
% 0.03/0.32 disbanding_rate: ( $i * $i ) > $i)).
% 0.03/0.32 tff(in_environment_type, type, (
% 0.03/0.32 in_environment: ( $i * $i ) > $o)).
% 0.03/0.32 tff(increases_type, type, (
% 0.03/0.32 increases: $i > $o)).
% 0.03/0.32 tff(1,plain,
% 0.03/0.32 ((~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))) <=> (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(2,plain,
% 0.03/0.32 ((~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))) <=> (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(3,axiom,(~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l3')).
% 0.03/0.32 tff(4,plain,
% 0.03/0.32 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.03/0.32 tff(5,plain,
% 0.03/0.32 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.03/0.32 tff(6,plain,
% 0.03/0.32 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.03/0.32 tff(7,plain,
% 0.03/0.32 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.03/0.32 tff(8,plain,(
% 0.03/0.32 ~((~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.03/0.32 inference(skolemize,[status(sab)],[7])).
% 0.03/0.32 tff(9,plain,
% 0.03/0.32 (environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.03/0.32 inference(or_elim,[status(thm)],[8])).
% 0.03/0.32 tff(10,plain,
% 0.03/0.32 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.03/0.32 inference(and_elim,[status(thm)],[9])).
% 0.03/0.32 tff(11,plain,
% 0.03/0.32 (environment(E!1)),
% 0.03/0.32 inference(and_elim,[status(thm)],[9])).
% 0.03/0.32 tff(12,plain,
% 0.03/0.32 (^[E: $i, T: $i] : refl((greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.03/0.32 inference(bind,[status(th)],[])).
% 0.03/0.32 tff(13,plain,
% 0.03/0.32 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.03/0.32 inference(quant_intro,[status(thm)],[12])).
% 0.03/0.32 tff(14,plain,
% 0.03/0.32 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.03/0.32 inference(bind,[status(th)],[])).
% 0.03/0.32 tff(15,plain,
% 0.03/0.32 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.03/0.32 inference(quant_intro,[status(thm)],[14])).
% 0.03/0.32 tff(16,plain,
% 0.03/0.32 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(17,plain,
% 0.03/0.32 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater(number_of_organizations(E, T), zero)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero)))),
% 0.03/0.32 inference(bind,[status(th)],[])).
% 0.03/0.32 tff(18,plain,
% 0.03/0.32 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.03/0.32 inference(quant_intro,[status(thm)],[17])).
% 0.03/0.32 tff(19,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater(number_of_organizations(E, T), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_environment_not_empty')).
% 0.03/0.32 tff(20,plain,
% 0.03/0.32 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.03/0.32 tff(21,plain,
% 0.03/0.32 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.03/0.32 tff(22,plain,(
% 0.03/0.32 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(number_of_organizations(E, T), zero))),
% 0.03/0.32 inference(skolemize,[status(sab)],[21])).
% 0.03/0.32 tff(23,plain,
% 0.03/0.32 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.03/0.32 tff(24,plain,
% 0.03/0.32 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.03/0.32 tff(25,plain,
% 0.03/0.32 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero))),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(26,plain,
% 0.03/0.32 ((greater(number_of_organizations(E!1, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero))),
% 0.03/0.32 inference(rewrite,[status(thm)],[])).
% 0.03/0.32 tff(27,plain,
% 0.03/0.32 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(number_of_organizations(E!1, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero)))),
% 0.03/0.32 inference(monotonicity,[status(thm)],[26])).
% 0.03/0.32 tff(28,plain,
% 0.03/0.32 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(number_of_organizations(E!1, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero))),
% 0.03/0.32 inference(transitivity,[status(thm)],[27, 25])).
% 0.03/0.32 tff(29,plain,
% 0.03/0.32 ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (greater(number_of_organizations(E!1, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.03/0.32 inference(quant_inst,[status(thm)],[])).
% 0.03/0.32 tff(30,plain,
% 0.03/0.32 ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(number_of_organizations(E!1, T!0), zero)),
% 0.03/0.32 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.03/0.32 tff(31,plain,
% 0.03/0.32 (greater(number_of_organizations(E!1, T!0), zero)),
% 0.03/0.32 inference(unit_resolution,[status(thm)],[30, 24, 11, 10])).
% 0.03/0.32 tff(32,plain,
% 0.03/0.32 (^[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))))),
% 0.03/0.33 inference(bind,[status(th)],[])).
% 0.03/0.33 tff(33,plain,
% 0.03/0.33 (![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)))),
% 0.03/0.33 inference(quant_intro,[status(thm)],[32])).
% 0.03/0.33 tff(34,plain,
% 0.03/0.33 (^[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)))))),
% 0.03/0.33 inference(bind,[status(th)],[])).
% 0.03/0.33 tff(35,plain,
% 0.03/0.33 (![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)))),
% 0.03/0.33 inference(quant_intro,[status(thm)],[34])).
% 0.03/0.33 tff(36,plain,
% 0.03/0.33 (![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))),
% 0.03/0.33 inference(rewrite,[status(thm)],[])).
% 0.03/0.33 tff(37,plain,
% 0.03/0.33 (^[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)))),
% 0.03/0.33 inference(bind,[status(th)],[])).
% 0.03/0.33 tff(38,plain,
% 0.03/0.33 (![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))),
% 0.03/0.33 inference(quant_intro,[status(thm)],[37])).
% 0.03/0.33 tff(39,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_in_environment')).
% 0.03/0.33 tff(40,plain,
% 0.03/0.33 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.03/0.33 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.03/0.33 tff(41,plain,
% 0.03/0.33 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.03/0.33 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.03/0.33 tff(42,plain,(
% 0.03/0.33 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.03/0.33 inference(skolemize,[status(sab)],[41])).
% 0.03/0.33 tff(43,plain,
% 0.03/0.33 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.03/0.33 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.03/0.33 tff(44,plain,
% 0.03/0.33 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.03/0.33 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.03/0.33 tff(45,plain,
% 0.03/0.33 (((~![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))),
% 0.03/0.33 inference(rewrite,[status(thm)],[])).
% 0.03/0.33 tff(46,plain,
% 0.03/0.33 ((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))),
% 0.03/0.33 inference(rewrite,[status(thm)],[])).
% 0.03/0.33 tff(47,plain,
% 0.03/0.33 (((~![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)))),
% 0.03/0.33 inference(monotonicity,[status(thm)],[46])).
% 0.03/0.33 tff(48,plain,
% 0.03/0.33 (((~![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))),
% 0.03/0.33 inference(transitivity,[status(thm)],[47, 45])).
% 0.03/0.33 tff(49,plain,
% 0.03/0.33 ((~![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)))),
% 0.03/0.33 inference(quant_inst,[status(thm)],[])).
% 0.03/0.33 tff(50,plain,
% 0.03/0.33 ((~![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)),
% 0.03/0.33 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.03/0.33 tff(51,plain,
% 0.03/0.33 (in_environment(E!1, T!0)),
% 0.03/0.33 inference(unit_resolution,[status(thm)],[50, 44, 11, 10])).
% 0.03/0.33 tff(52,plain,
% 0.03/0.33 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))))),
% 0.03/0.33 inference(bind,[status(th)],[])).
% 0.03/0.33 tff(53,plain,
% 0.03/0.33 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.09/0.33 inference(quant_intro,[status(thm)],[52])).
% 0.09/0.33 tff(54,plain,
% 0.09/0.33 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))), ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)))), ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))), trans(monotonicity(rewrite(((~greater(equilibrium(E), T)) | decreases(resources(E, T))) <=> ((~greater(equilibrium(E), T)) | decreases(resources(E, T)))), ((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))) <=> (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))), rewrite((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))) <=> (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))), ((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))) <=> (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))), (((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))), (((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))))),
% 0.09/0.33 inference(bind,[status(th)],[])).
% 0.09/0.33 tff(55,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.09/0.33 inference(quant_intro,[status(thm)],[54])).
% 0.09/0.33 tff(56,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.09/0.33 inference(rewrite,[status(thm)],[])).
% 0.09/0.33 tff(57,plain,
% 0.09/0.33 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))), rewrite(((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T)))) <=> (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))), ((((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) => (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))))), rewrite(((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) => (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))), ((((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.09/0.33 inference(bind,[status(th)],[])).
% 0.09/0.33 tff(58,plain,
% 0.09/0.33 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.09/0.33 inference(quant_intro,[status(thm)],[57])).
% 0.09/0.33 tff(59,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a3')).
% 0.09/0.33 tff(60,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.09/0.33 tff(61,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.09/0.33 tff(62,plain,(
% 0.09/0.33 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.09/0.33 inference(skolemize,[status(sab)],[61])).
% 0.09/0.33 tff(63,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.09/0.33 tff(64,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.09/0.33 tff(65,plain,
% 0.09/0.33 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0)))))))),
% 0.09/0.33 inference(rewrite,[status(thm)],[])).
% 0.09/0.33 tff(66,plain,
% 0.09/0.33 (((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0)))))) <=> ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0)))))))),
% 0.09/0.33 inference(rewrite,[status(thm)],[])).
% 0.09/0.33 tff(67,plain,
% 0.09/0.33 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0))))))))),
% 0.09/0.33 inference(monotonicity,[status(thm)],[66])).
% 0.09/0.33 tff(68,plain,
% 0.09/0.33 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0)))))))),
% 0.09/0.33 inference(transitivity,[status(thm)],[67, 65])).
% 0.09/0.33 tff(69,plain,
% 0.09/0.33 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~((~greater(equilibrium(E!1), T!0)) | decreases(resources(E!1, T!0)))) | (~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))))))),
% 0.09/0.33 inference(quant_inst,[status(thm)],[])).
% 0.09/0.33 tff(70,plain,
% 0.09/0.33 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(number_of_organizations(E!1, T!0), zero)) | (~((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0))))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.09/0.33 tff(71,plain,
% 0.09/0.33 (~((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0)))))),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[70, 64, 11, 51, 31])).
% 0.09/0.33 tff(72,plain,
% 0.09/0.33 (((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0))))) | (decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0)))),
% 0.09/0.33 inference(tautology,[status(thm)],[])).
% 0.09/0.33 tff(73,plain,
% 0.09/0.33 (decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0))),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.09/0.33 tff(74,plain,
% 0.09/0.33 (((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | (~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0))))) | (constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))),
% 0.09/0.33 inference(tautology,[status(thm)],[])).
% 0.09/0.33 tff(75,plain,
% 0.09/0.33 (constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0)),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.09/0.33 tff(76,plain,
% 0.09/0.33 (^[E: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))))),
% 0.09/0.33 inference(bind,[status(th)],[])).
% 0.09/0.33 tff(77,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))),
% 0.09/0.33 inference(quant_intro,[status(thm)],[76])).
% 0.09/0.33 tff(78,plain,
% 0.09/0.33 (^[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(((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))) <=> (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))))),
% 0.09/0.33 inference(bind,[status(th)],[])).
% 0.09/0.33 tff(79,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))),
% 0.09/0.33 inference(quant_intro,[status(thm)],[78])).
% 0.09/0.33 tff(80,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.09/0.33 inference(rewrite,[status(thm)],[])).
% 0.09/0.33 tff(81,plain,
% 0.09/0.33 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((decreases(resources(E, T)) => increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) & (constant(resources(E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))) <=> ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))), (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) & (constant(resources(E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))), (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) & (constant(resources(E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))),
% 0.09/0.33 inference(bind,[status(th)],[])).
% 0.09/0.33 tff(82,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) & (constant(resources(E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.09/0.33 inference(quant_intro,[status(thm)],[81])).
% 0.09/0.33 tff(83,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) & (constant(resources(E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l4')).
% 0.09/0.33 tff(84,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.09/0.33 tff(85,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.09/0.33 tff(86,plain,(
% 0.09/0.33 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.09/0.33 inference(skolemize,[status(sab)],[85])).
% 0.09/0.33 tff(87,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.09/0.33 tff(88,plain,
% 0.09/0.33 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.09/0.33 tff(89,plain,
% 0.09/0.33 (((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))))))),
% 0.09/0.33 inference(rewrite,[status(thm)],[])).
% 0.09/0.33 tff(90,plain,
% 0.09/0.33 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))))))),
% 0.09/0.33 inference(quant_inst,[status(thm)],[])).
% 0.09/0.33 tff(91,plain,
% 0.09/0.33 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~(increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T))))) | (~((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.09/0.33 tff(92,plain,
% 0.09/0.33 (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))))),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[91, 88, 11, 10])).
% 0.09/0.33 tff(93,plain,
% 0.09/0.33 (((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))) | ((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.09/0.33 inference(tautology,[status(thm)],[])).
% 0.09/0.33 tff(94,plain,
% 0.09/0.33 ((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.09/0.33 tff(95,plain,
% 0.09/0.33 (decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))),
% 0.09/0.33 inference(or_elim,[status(thm)],[8])).
% 0.09/0.33 tff(96,plain,
% 0.09/0.33 ((~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))) | (~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))),
% 0.09/0.33 inference(tautology,[status(thm)],[])).
% 0.09/0.33 tff(97,plain,
% 0.09/0.33 ((~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))) | (~constant(resources(E!1, T!0)))),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.09/0.33 tff(98,plain,
% 0.09/0.33 (~constant(resources(E!1, T!0))),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.09/0.33 tff(99,plain,
% 0.09/0.33 ((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0)),
% 0.09/0.33 inference(tautology,[status(thm)],[])).
% 0.09/0.33 tff(100,plain,
% 0.09/0.33 ((~(constant(resources(E!1, T!0)) | greater(equilibrium(E!1), T!0))) | greater(equilibrium(E!1), T!0)),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.09/0.33 tff(101,plain,
% 0.09/0.33 (greater(equilibrium(E!1), T!0)),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[100, 75])).
% 0.09/0.33 tff(102,plain,
% 0.09/0.33 (((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))) | (increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))),
% 0.09/0.33 inference(tautology,[status(thm)],[])).
% 0.09/0.33 tff(103,plain,
% 0.09/0.33 (increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0)))),
% 0.09/0.33 inference(unit_resolution,[status(thm)],[102, 92])).
% 0.09/0.33 tff(104,plain,
% 0.09/0.33 (^[X: $i] : refl(((~decreases(X)) | (~increases(X))) <=> ((~decreases(X)) | (~increases(X))))),
% 0.09/0.33 inference(bind,[status(th)],[])).
% 0.09/0.33 tff(105,plain,
% 0.09/0.33 (![X: $i] : ((~decreases(X)) | (~increases(X))) <=> ![X: $i] : ((~decreases(X)) | (~increases(X)))),
% 0.09/0.33 inference(quant_intro,[status(thm)],[104])).
% 0.09/0.33 tff(106,plain,
% 0.09/0.33 (![X: $i] : ((~decreases(X)) | (~increases(X))) <=> ![X: $i] : ((~decreases(X)) | (~increases(X)))),
% 0.09/0.33 inference(rewrite,[status(thm)],[])).
% 0.09/0.33 tff(107,plain,
% 0.09/0.33 (^[X: $i] : rewrite((increases(X) => (~decreases(X))) <=> ((~decreases(X)) | (~increases(X))))),
% 0.09/0.33 inference(bind,[status(th)],[])).
% 0.09/0.33 tff(108,plain,
% 0.09/0.33 (![X: $i] : (increases(X) => (~decreases(X))) <=> ![X: $i] : ((~decreases(X)) | (~increases(X)))),
% 0.09/0.33 inference(quant_intro,[status(thm)],[107])).
% 0.09/0.33 tff(109,axiom,(![X: $i] : (increases(X) => (~decreases(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_increase_not_decrease')).
% 0.09/0.33 tff(110,plain,
% 0.09/0.33 (![X: $i] : ((~decreases(X)) | (~increases(X)))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.09/0.33 tff(111,plain,
% 0.09/0.33 (![X: $i] : ((~decreases(X)) | (~increases(X)))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.09/0.33 tff(112,plain,(
% 0.09/0.33 ![X: $i] : ((~decreases(X)) | (~increases(X)))),
% 0.09/0.33 inference(skolemize,[status(sab)],[111])).
% 0.09/0.33 tff(113,plain,
% 0.09/0.33 (![X: $i] : ((~decreases(X)) | (~increases(X)))),
% 0.09/0.33 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.09/0.33 tff(114,plain,
% 0.09/0.33 (((~![X: $i] : ((~decreases(X)) | (~increases(X)))) | ((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))) <=> ((~![X: $i] : ((~decreases(X)) | (~increases(X)))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.09/0.33 inference(rewrite,[status(thm)],[])).
% 0.09/0.33 tff(115,plain,
% 0.09/0.33 ((~![X: $i] : ((~decreases(X)) | (~increases(X)))) | ((~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.09/0.33 inference(quant_inst,[status(thm)],[])).
% 0.09/0.33 tff(116,plain,
% 0.09/0.33 ((~![X: $i] : ((~decreases(X)) | (~increases(X)))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))),
% 0.09/0.34 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.09/0.34 tff(117,plain,
% 0.09/0.34 (~increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))),
% 0.09/0.34 inference(unit_resolution,[status(thm)],[116, 113, 95])).
% 0.09/0.34 tff(118,plain,
% 0.09/0.34 ((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0)))),
% 0.09/0.34 inference(tautology,[status(thm)],[])).
% 0.09/0.34 tff(119,plain,
% 0.09/0.34 (~decreases(resources(E!1, T!0))),
% 0.09/0.34 inference(unit_resolution,[status(thm)],[118, 117, 103])).
% 0.09/0.34 tff(120,plain,
% 0.09/0.34 ((~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0)))) | decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0))),
% 0.09/0.34 inference(tautology,[status(thm)],[])).
% 0.09/0.34 tff(121,plain,
% 0.09/0.34 ((~(decreases(resources(E!1, T!0)) | (~greater(equilibrium(E!1), T!0)))) | (~greater(equilibrium(E!1), T!0))),
% 0.09/0.34 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.09/0.34 tff(122,plain,
% 0.09/0.34 ($false),
% 0.09/0.34 inference(unit_resolution,[status(thm)],[121, 101, 73])).
% 0.09/0.34 % SZS output end Proof
% 0.09/0.34 % E exiting
%------------------------------------------------------------------------------