%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT037+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:03 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT037+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 12:43:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start Proof
% 0.13/0.42 tff(constant_type, type, (
% 0.13/0.42 constant: $i > $o)).
% 0.13/0.42 tff(number_of_organizations_type, type, (
% 0.13/0.42 number_of_organizations: ( $i * $i ) > $i)).
% 0.13/0.42 tff(tptp_fun_To_0_type, type, (
% 0.13/0.42 tptp_fun_To_0: ( $i * $i ) > $i)).
% 0.13/0.42 tff(tptp_fun_E_3_type, type, (
% 0.13/0.42 tptp_fun_E_3: $i)).
% 0.13/0.42 tff(tptp_fun_T_2_type, type, (
% 0.13/0.42 tptp_fun_T_2: $i)).
% 0.13/0.42 tff(resources_type, type, (
% 0.13/0.42 resources: ( $i * $i ) > $i)).
% 0.13/0.42 tff(greater_type, type, (
% 0.13/0.42 greater: ( $i * $i ) > $o)).
% 0.13/0.42 tff(equilibrium_type, type, (
% 0.13/0.42 equilibrium: $i > $i)).
% 0.13/0.42 tff(decreases_type, type, (
% 0.13/0.42 decreases: $i > $o)).
% 0.13/0.42 tff(growth_rate_type, type, (
% 0.13/0.42 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.42 tff(tptp_fun_X_1_type, type, (
% 0.13/0.42 tptp_fun_X_1: ( $i * $i ) > $i)).
% 0.13/0.42 tff(zero_type, type, (
% 0.13/0.42 zero: $i)).
% 0.13/0.42 tff(cardinality_at_time_type, type, (
% 0.13/0.42 cardinality_at_time: ( $i * $i ) > $i)).
% 0.13/0.42 tff(subpopulation_type, type, (
% 0.13/0.42 subpopulation: ( $i * $i * $i ) > $o)).
% 0.13/0.42 tff(efficient_producers_type, type, (
% 0.13/0.42 efficient_producers: $i)).
% 0.13/0.42 tff(first_movers_type, type, (
% 0.13/0.42 first_movers: $i)).
% 0.13/0.42 tff(resilience_type, type, (
% 0.13/0.42 resilience: $i > $i)).
% 0.13/0.42 tff(in_environment_type, type, (
% 0.13/0.42 in_environment: ( $i * $i ) > $o)).
% 0.13/0.42 tff(appear_type, type, (
% 0.13/0.42 appear: ( $i * $i ) > $i)).
% 0.13/0.42 tff(greater_or_equal_type, type, (
% 0.13/0.42 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.42 tff(environment_type, type, (
% 0.13/0.42 environment: $i > $o)).
% 0.13/0.42 tff(an_organisation_type, type, (
% 0.13/0.42 an_organisation: $i)).
% 0.13/0.42 tff(1,assumption,(~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))), introduced(assumption)).
% 0.13/0.42 tff(2,plain,
% 0.13/0.42 (((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))) | (~greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(3,plain,
% 0.13/0.42 (~greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.13/0.42 tff(4,plain,
% 0.13/0.42 ((~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(5,plain,
% 0.13/0.42 ((~![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(6,axiom,(~![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t6')).
% 0.13/0.42 tff(7,plain,
% 0.13/0.42 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.42 tff(8,plain,
% 0.13/0.42 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.13/0.42 tff(9,plain,
% 0.13/0.42 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.42 tff(10,plain,
% 0.13/0.42 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.13/0.42 tff(11,plain,(
% 0.13/0.42 ~((~(environment(E!3) & in_environment(E!3, T!2) & greater_or_equal(T!2, appear(efficient_producers, E!3)))) | greater(cardinality_at_time(efficient_producers, T!2), zero))),
% 0.13/0.42 inference(skolemize,[status(sab)],[10])).
% 0.13/0.42 tff(12,plain,
% 0.13/0.42 (~greater(cardinality_at_time(efficient_producers, T!2), zero)),
% 0.13/0.42 inference(or_elim,[status(thm)],[11])).
% 0.13/0.42 tff(13,plain,
% 0.13/0.42 (environment(E!3) & in_environment(E!3, T!2) & greater_or_equal(T!2, appear(efficient_producers, E!3))),
% 0.13/0.42 inference(or_elim,[status(thm)],[11])).
% 0.13/0.42 tff(14,plain,
% 0.13/0.42 (in_environment(E!3, T!2)),
% 0.13/0.42 inference(and_elim,[status(thm)],[13])).
% 0.13/0.42 tff(15,plain,
% 0.13/0.42 (environment(E!3)),
% 0.13/0.42 inference(and_elim,[status(thm)],[13])).
% 0.13/0.42 tff(16,plain,
% 0.13/0.42 (^[E: $i, T: $i] : refl(((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(17,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T))) <=> ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.42 tff(18,plain,
% 0.13/0.42 (^[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))))), (((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | ((~environment(E)) | (~in_environment(E, T)))))), rewrite(((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | ((~environment(E)) | (~in_environment(E, T)))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))), (((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(19,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))) <=> ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.42 tff(20,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))) <=> ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(21,plain,
% 0.13/0.42 (^[E: $i, T: $i] : rewrite(((environment(E) & in_environment(E, T)) => ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(22,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.42 tff(23,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_efficient_producers_exist')).
% 0.13/0.42 tff(24,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.42 tff(25,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.42 tff(26,plain,(
% 0.13/0.42 ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[25])).
% 0.13/0.42 tff(27,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.13/0.42 tff(28,plain,
% 0.13/0.42 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.13/0.42 tff(29,plain,
% 0.13/0.42 (((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))) <=> ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(30,plain,
% 0.13/0.42 (((cardinality_at_time(efficient_producers, T!2) = zero) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (~environment(E!3)) | (~in_environment(E!3, T!2))) <=> (greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(31,plain,
% 0.13/0.42 (((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((cardinality_at_time(efficient_producers, T!2) = zero) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))) <=> ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[30])).
% 0.13/0.43 tff(32,plain,
% 0.13/0.43 (((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((cardinality_at_time(efficient_producers, T!2) = zero) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))) <=> ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))),
% 0.13/0.43 inference(transitivity,[status(thm)],[31, 29])).
% 0.13/0.43 tff(33,plain,
% 0.13/0.43 ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((cardinality_at_time(efficient_producers, T!2) = zero) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(34,plain,
% 0.13/0.43 ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.43 tff(35,plain,
% 0.13/0.43 (cardinality_at_time(efficient_producers, T!2) = zero),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[34, 28, 15, 14, 12])).
% 0.13/0.43 tff(36,plain,
% 0.13/0.43 (greater_or_equal(T!2, appear(efficient_producers, E!3))),
% 0.13/0.43 inference(and_elim,[status(thm)],[13])).
% 0.13/0.43 tff(37,plain,
% 0.13/0.43 (^[E: $i, T: $i] : refl(((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(38,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.13/0.43 tff(39,plain,
% 0.13/0.43 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero)) <=> (~((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))))), ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) <=> (~(~((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))))))), rewrite((~(~((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)))), ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))))), rewrite((greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))) <=> (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))), (((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | (greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))) <=> (((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))))), rewrite((((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))), (((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | (greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(40,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | (greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.43 tff(41,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))) <=> ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(42,plain,
% 0.13/0.43 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) <=> (environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))), quant_intro(proof_bind(^[To: $i] : trans(monotonicity(rewrite(((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) <=> (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To))), ((((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))) <=> ((greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))))), rewrite(((greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))) <=> (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))), ((((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))) <=> (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))))), (?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))) <=> ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))), ((((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To)))) <=> ((environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))))), rewrite(((environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))) <=> ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))), ((((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To)))) <=> ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(43,plain,
% 0.13/0.43 (![E: $i, T: $i] : (((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To)))) <=> ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.13/0.43 tff(44,axiom,(![E: $i, T: $i] : (((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_previous_negative_growth')).
% 0.13/0.43 tff(45,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.13/0.43 tff(46,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.13/0.43 tff(47,plain,(
% 0.13/0.43 ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | (greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))),
% 0.13/0.43 inference(skolemize,[status(sab)],[46])).
% 0.13/0.43 tff(48,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.13/0.43 tff(49,plain,
% 0.13/0.43 (![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.13/0.43 tff(50,plain,
% 0.13/0.43 (((~![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))) | ((~environment(E!3)) | (~greater_or_equal(T!2, appear(efficient_producers, E!3))) | (~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))) | (~environment(E!3)) | (~greater_or_equal(T!2, appear(efficient_producers, E!3))) | (~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(51,plain,
% 0.13/0.43 ((~![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))) | ((~environment(E!3)) | (~greater_or_equal(T!2, appear(efficient_producers, E!3))) | (~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(52,plain,
% 0.13/0.43 ((~![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))) | (~environment(E!3)) | (~greater_or_equal(T!2, appear(efficient_producers, E!3))) | (~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.43 tff(53,plain,
% 0.13/0.43 ((~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[52, 49, 15, 36])).
% 0.13/0.43 tff(54,plain,
% 0.13/0.43 (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[53, 35])).
% 0.13/0.43 tff(55,plain,
% 0.13/0.43 (((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))) | greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(56,plain,
% 0.13/0.44 (greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.13/0.44 tff(57,plain,
% 0.13/0.44 (((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))) | in_environment(E!3, tptp_fun_To_0(T!2, E!3))),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(58,plain,
% 0.13/0.44 (in_environment(E!3, tptp_fun_To_0(T!2, E!3))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.13/0.44 tff(59,plain,
% 0.13/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))) <=> ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(60,plain,
% 0.13/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[59])).
% 0.13/0.44 tff(61,plain,
% 0.13/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) <=> (~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))), ((~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))) <=> (~(~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))))), rewrite((~(~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))) <=> (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))), ((~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))) <=> (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))), (((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ((~greater(zero, growth_rate(S2, T))) | (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))))), rewrite(((~greater(zero, growth_rate(S2, T))) | (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) <=> ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))), (((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(62,plain,
% 0.13/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[61])).
% 0.13/0.44 tff(63,plain,
% 0.13/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(64,plain,
% 0.13/0.44 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))))), ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> ((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))))), rewrite(((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))), ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))), (((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))))), rewrite(((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))), (((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(65,plain,
% 0.13/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[64])).
% 0.13/0.44 tff(66,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a12')).
% 0.13/0.44 tff(67,plain,
% 0.13/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.13/0.44 tff(68,plain,
% 0.13/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.13/0.44 tff(69,plain,(
% 0.13/0.44 ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.13/0.44 inference(skolemize,[status(sab)],[68])).
% 0.13/0.44 tff(70,plain,
% 0.13/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.13/0.44 tff(71,plain,
% 0.13/0.44 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.13/0.44 tff(72,plain,
% 0.13/0.44 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(73,plain,
% 0.13/0.44 (((~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3))))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(74,plain,
% 0.13/0.44 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3))))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[73])).
% 0.13/0.44 tff(75,plain,
% 0.13/0.44 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[74, 72])).
% 0.13/0.44 tff(76,plain,
% 0.13/0.44 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(77,plain,
% 0.13/0.44 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.13/0.44 tff(78,plain,
% 0.13/0.44 (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[77, 71, 15, 58, 56, 3])).
% 0.13/0.44 tff(79,assumption,(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers), introduced(assumption)).
% 0.13/0.44 tff(80,plain,
% 0.13/0.44 (resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)) = resilience(first_movers)),
% 0.13/0.44 inference(monotonicity,[status(thm)],[79])).
% 0.13/0.44 tff(81,plain,
% 0.13/0.44 (greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3))) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[80])).
% 0.13/0.44 tff(82,plain,
% 0.13/0.44 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))),
% 0.13/0.44 inference(symmetry,[status(thm)],[81])).
% 0.13/0.44 tff(83,plain,
% 0.13/0.44 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(84,axiom,(greater(resilience(efficient_producers), resilience(first_movers))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a2')).
% 0.13/0.44 tff(85,plain,
% 0.13/0.44 (greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.13/0.44 tff(86,plain,
% 0.13/0.44 (greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.13/0.44 tff(87,assumption,(~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))), introduced(assumption)).
% 0.13/0.44 tff(88,plain,
% 0.13/0.44 ($false),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.13/0.45 tff(89,plain,((~(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers)) | greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(90,plain,
% 0.13/0.45 (~(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers)),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[89, 78])).
% 0.13/0.45 tff(91,plain,
% 0.13/0.45 (((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))) | greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(92,plain,
% 0.13/0.45 (greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[91, 1])).
% 0.13/0.45 tff(93,plain,
% 0.13/0.45 (((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))) | subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))),
% 0.13/0.45 inference(tautology,[status(thm)],[])).
% 0.13/0.45 tff(94,plain,
% 0.13/0.45 (subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[93, 1])).
% 0.13/0.45 tff(95,plain,
% 0.13/0.45 (^[E: $i, X: $i, T: $i] : refl(((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))) <=> ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(96,plain,
% 0.13/0.45 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))) <=> ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[95])).
% 0.13/0.45 tff(97,plain,
% 0.13/0.45 (^[E: $i, X: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) <=> (~((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))), ((~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) <=> (~(~((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))))), rewrite((~(~((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))) <=> ((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))), ((~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) <=> ((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))), (((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))) <=> ((X = first_movers) | (X = efficient_producers) | ((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))))), rewrite(((X = first_movers) | (X = efficient_producers) | ((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) <=> ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))), (((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))) <=> ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(98,plain,
% 0.13/0.45 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))) <=> ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[97])).
% 0.13/0.45 tff(99,plain,
% 0.13/0.45 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))) <=> ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(100,plain,
% 0.13/0.45 (^[E: $i, X: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) <=> (environment(E) & subpopulation(X, E, T) & 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) & greater(cardinality_at_time(X, T), zero)) => ((X = efficient_producers) | (X = first_movers))))), rewrite(((environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) => ((X = efficient_producers) | (X = first_movers))) <=> ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & 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))) <=> ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(101,plain,
% 0.13/0.45 (![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))) <=> ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[100])).
% 0.13/0.45 tff(102,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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a9')).
% 0.13/0.45 tff(103,plain,
% 0.13/0.45 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.13/0.45 tff(104,plain,
% 0.13/0.45 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.13/0.45 tff(105,plain,(
% 0.13/0.45 ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.13/0.45 inference(skolemize,[status(sab)],[104])).
% 0.13/0.45 tff(106,plain,
% 0.13/0.45 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.13/0.45 tff(107,plain,
% 0.13/0.45 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.13/0.45 tff(108,plain,
% 0.13/0.45 (((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers))) <=> ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(109,plain,
% 0.13/0.45 (((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero))) <=> ((~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(110,plain,
% 0.13/0.45 (((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)))) <=> ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers)))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[109])).
% 0.13/0.45 tff(111,plain,
% 0.13/0.45 (((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)))) <=> ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers))),
% 0.13/0.45 inference(transitivity,[status(thm)],[110, 108])).
% 0.13/0.45 tff(112,plain,
% 0.13/0.45 ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(113,plain,
% 0.13/0.45 ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers)),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.13/0.45 tff(114,plain,
% 0.13/0.45 ((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers)),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[113, 107, 15, 94, 92])).
% 0.13/0.45 tff(115,plain,
% 0.13/0.45 (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[114, 90])).
% 0.13/0.45 tff(116,plain,
% 0.13/0.45 (growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)) = growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[115])).
% 0.13/0.45 tff(117,plain,
% 0.13/0.45 (greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) <=> greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[116])).
% 0.13/0.45 tff(118,plain,
% 0.13/0.45 (greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))) <=> greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.13/0.45 inference(symmetry,[status(thm)],[117])).
% 0.13/0.45 tff(119,plain,
% 0.13/0.45 (greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[56, 118])).
% 0.13/0.45 tff(120,plain,
% 0.13/0.45 ($false),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[3, 119])).
% 0.13/0.45 tff(121,plain,((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.45 tff(122,plain,
% 0.13/0.45 (^[E: $i, T: $i] : refl((decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(123,plain,
% 0.13/0.45 (![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> ![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[122])).
% 0.13/0.45 tff(124,plain,
% 0.13/0.45 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T)))) <=> (~(decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) <=> (~(~(decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~(decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))))), rewrite((subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))) <=> (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))), (((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | (subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> ((decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))))), rewrite(((decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))), (((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | (subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(125,plain,
% 0.13/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | (subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> ![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[124])).
% 0.13/0.45 tff(126,plain,
% 0.13/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(127,plain,
% 0.13/0.45 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) <=> (environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))), quant_intro(proof_bind(^[X: $i] : rewrite(((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T)))) <=> (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))), (?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T)))) <=> ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))), ((((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T))))) <=> ((environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T))))))), rewrite(((environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T))))) <=> ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))), ((((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T))))) <=> ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))))),
% 0.13/0.46 inference(bind,[status(th)],[])).
% 0.13/0.46 tff(128,plain,
% 0.13/0.46 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))),
% 0.13/0.46 inference(quant_intro,[status(thm)],[127])).
% 0.13/0.46 tff(129,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_non_decreasing')).
% 0.13/0.46 tff(130,plain,
% 0.13/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.13/0.46 tff(131,plain,
% 0.13/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.13/0.46 tff(132,plain,(
% 0.13/0.46 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | (subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.13/0.46 inference(skolemize,[status(sab)],[131])).
% 0.13/0.46 tff(133,plain,
% 0.13/0.46 (![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.13/0.46 tff(134,plain,
% 0.13/0.46 (![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.23/0.46 tff(135,plain,
% 0.23/0.46 (((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))) <=> ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(136,plain,
% 0.23/0.46 ((decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(137,plain,
% 0.23/0.46 (((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))) <=> ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[136])).
% 0.23/0.46 tff(138,plain,
% 0.23/0.46 (((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))) <=> ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[137, 135])).
% 0.23/0.46 tff(139,plain,
% 0.23/0.46 ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(140,plain,
% 0.23/0.46 ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.23/0.46 tff(141,plain,
% 0.23/0.46 (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[140, 134, 15, 58])).
% 0.23/0.46 tff(142,plain,
% 0.23/0.46 (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[141, 121])).
% 0.23/0.46 tff(143,plain,
% 0.23/0.46 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(144,plain,
% 0.23/0.46 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[143])).
% 0.23/0.46 tff(145,plain,
% 0.23/0.46 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), rewrite((((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))) <=> (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))), (((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> (((~environment(E)) | (~in_environment(E, T))) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))))), rewrite((((~environment(E)) | (~in_environment(E, T))) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))), (((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(146,plain,
% 0.23/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[145])).
% 0.23/0.46 tff(147,plain,
% 0.23/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(148,plain,
% 0.23/0.46 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T)))) <=> (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))), (((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ((environment(E) & in_environment(E, T)) => (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))), rewrite(((environment(E) & in_environment(E, T)) => (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))), (((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(149,plain,
% 0.23/0.46 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[148])).
% 0.23/0.46 tff(150,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a6')).
% 0.23/0.46 tff(151,plain,
% 0.23/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.23/0.46 tff(152,plain,
% 0.23/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.23/0.46 tff(153,plain,(
% 0.23/0.46 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.23/0.46 inference(skolemize,[status(sab)],[152])).
% 0.23/0.46 tff(154,plain,
% 0.23/0.46 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.23/0.46 tff(155,plain,
% 0.23/0.46 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.23/0.46 tff(156,plain,
% 0.23/0.46 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(157,plain,
% 0.23/0.47 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(158,plain,
% 0.23/0.47 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.23/0.47 tff(159,plain,
% 0.23/0.47 (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[158, 155, 15, 58])).
% 0.23/0.47 tff(160,plain,
% 0.23/0.47 (((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))))) | ((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(161,plain,
% 0.23/0.47 ((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.23/0.47 tff(162,plain,
% 0.23/0.47 ((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(163,plain,
% 0.23/0.47 ((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.23/0.47 tff(164,plain,
% 0.23/0.47 (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[163, 142])).
% 0.23/0.47 tff(165,plain,
% 0.23/0.47 (^[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))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(166,plain,
% 0.23/0.47 (![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)))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[165])).
% 0.23/0.47 tff(167,plain,
% 0.23/0.47 (^[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)))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(168,plain,
% 0.23/0.47 (![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)))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[167])).
% 0.23/0.47 tff(169,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(170,plain,
% 0.23/0.47 (^[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))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(171,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[170])).
% 0.23/0.47 tff(172,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_subpopulations')).
% 0.23/0.47 tff(173,plain,
% 0.23/0.47 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.23/0.47 tff(174,plain,
% 0.23/0.47 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.23/0.47 tff(175,plain,(
% 0.23/0.47 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.23/0.47 inference(skolemize,[status(sab)],[174])).
% 0.23/0.47 tff(176,plain,
% 0.23/0.47 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.23/0.47 tff(177,plain,
% 0.23/0.47 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[176, 166])).
% 0.23/0.47 tff(178,plain,
% 0.23/0.47 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(179,plain,
% 0.23/0.47 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(180,plain,
% 0.23/0.47 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.23/0.47 tff(181,plain,
% 0.23/0.47 (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[180, 177, 15, 58])).
% 0.23/0.47 tff(182,plain,
% 0.23/0.47 (((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3)))) | subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(183,plain,
% 0.23/0.47 (subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.23/0.47 tff(184,plain,
% 0.23/0.47 (^[S: $i, T: $i] : refl(((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))) <=> ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(185,plain,
% 0.23/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))) <=> ![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[184])).
% 0.23/0.47 tff(186,plain,
% 0.23/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))) <=> ![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(187,plain,
% 0.23/0.47 (^[S: $i, T: $i] : rewrite(((cardinality_at_time(S, T) = zero) => (~greater(zero, growth_rate(S, T)))) <=> ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(188,plain,
% 0.23/0.47 (![S: $i, T: $i] : ((cardinality_at_time(S, T) = zero) => (~greater(zero, growth_rate(S, T)))) <=> ![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[187])).
% 0.23/0.47 tff(189,axiom,(![S: $i, T: $i] : ((cardinality_at_time(S, T) = zero) => (~greater(zero, growth_rate(S, T))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_empty_not_decreasing')).
% 0.23/0.47 tff(190,plain,
% 0.23/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.23/0.47 tff(191,plain,
% 0.23/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.23/0.47 tff(192,plain,(
% 0.23/0.47 ![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.23/0.47 inference(skolemize,[status(sab)],[191])).
% 0.23/0.47 tff(193,plain,
% 0.23/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.23/0.47 tff(194,plain,
% 0.23/0.47 (((~![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))) | ((~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))) <=> ((~![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))) | (~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(195,plain,
% 0.23/0.47 ((~![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))) | ((~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(196,plain,
% 0.23/0.47 ((~![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))) | (~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.23/0.47 tff(197,plain,
% 0.23/0.47 (~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[196, 193, 56])).
% 0.23/0.47 tff(198,plain,
% 0.23/0.47 (^[E: $i, T: $i, X: $i] : refl(((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))) <=> ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(199,plain,
% 0.23/0.47 (![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))) <=> ![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[198])).
% 0.23/0.47 tff(200,plain,
% 0.23/0.47 (^[E: $i, T: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))), ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))), ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))), (((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))), (((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(201,plain,
% 0.23/0.47 (![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> ![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[200])).
% 0.23/0.47 tff(202,plain,
% 0.23/0.47 (![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> ![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(203,plain,
% 0.23/0.47 (^[E: $i, T: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) <=> (environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero))), ((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) <=> ((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)))), rewrite(((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) <=> (environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))), ((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) <=> (environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T)))), (((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)) <=> ((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)))), rewrite(((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)) <=> ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))), (((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)) <=> ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(204,plain,
% 0.23/0.47 (![E: $i, T: $i, X: $i] : ((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)) <=> ![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[203])).
% 0.23/0.47 tff(205,axiom,(![E: $i, T: $i, X: $i] : ((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_no_members')).
% 0.23/0.47 tff(206,plain,
% 0.23/0.47 (![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.23/0.47 tff(207,plain,
% 0.23/0.47 (![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.23/0.47 tff(208,plain,(
% 0.23/0.47 ![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.23/0.47 inference(skolemize,[status(sab)],[207])).
% 0.23/0.47 tff(209,plain,
% 0.23/0.47 (![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[208, 201])).
% 0.23/0.47 tff(210,plain,
% 0.23/0.47 (![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[209, 199])).
% 0.23/0.47 tff(211,plain,
% 0.23/0.47 (((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)))) <=> ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(212,plain,
% 0.23/0.47 (((cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3)))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(213,plain,
% 0.23/0.47 (((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[212])).
% 0.23/0.48 tff(214,plain,
% 0.23/0.48 (((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[213, 211])).
% 0.23/0.48 tff(215,plain,
% 0.23/0.48 ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(216,plain,
% 0.23/0.48 ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.23/0.48 tff(217,plain,
% 0.23/0.48 (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[216, 210, 15, 58, 197, 183])).
% 0.23/0.48 tff(218,plain,
% 0.23/0.48 (^[E: $i, T: $i] : refl(((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))) <=> ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(219,plain,
% 0.23/0.48 (![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))) <=> ![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[218])).
% 0.23/0.48 tff(220,plain,
% 0.23/0.48 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))), ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))), ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))), (((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))), (((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(221,plain,
% 0.23/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> ![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[220])).
% 0.23/0.48 tff(222,plain,
% 0.23/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(223,plain,
% 0.23/0.48 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) <=> (environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))), ((((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)) <=> ((environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)))), rewrite(((environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)) <=> ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))), ((((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)) <=> ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(224,plain,
% 0.23/0.48 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[223])).
% 0.23/0.48 tff(225,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_start_of_organizations')).
% 0.23/0.48 tff(226,plain,
% 0.23/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.23/0.48 tff(227,plain,
% 0.23/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.23/0.48 tff(228,plain,(
% 0.23/0.48 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.23/0.48 inference(skolemize,[status(sab)],[227])).
% 0.23/0.48 tff(229,plain,
% 0.23/0.48 (![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.23/0.48 tff(230,plain,
% 0.23/0.48 (![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[229, 219])).
% 0.23/0.48 tff(231,plain,
% 0.23/0.48 (((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(232,plain,
% 0.23/0.48 (((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(233,plain,
% 0.23/0.48 (((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[232])).
% 0.23/0.48 tff(234,plain,
% 0.23/0.48 (((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[233, 231])).
% 0.23/0.48 tff(235,plain,
% 0.23/0.48 ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(236,plain,
% 0.23/0.48 ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.23/0.48 tff(237,plain,
% 0.23/0.48 ((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[236, 230, 15, 58])).
% 0.23/0.48 tff(238,plain,
% 0.23/0.48 (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[237, 217])).
% 0.23/0.48 tff(239,plain,
% 0.23/0.48 (^[E: $i, T: $i] : refl((greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(240,plain,
% 0.23/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T))) <=> ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[239])).
% 0.23/0.48 tff(241,plain,
% 0.23/0.48 (^[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))))), ((greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T)))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | ((~environment(E)) | (~in_environment(E, T)))))), rewrite((greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | ((~environment(E)) | (~in_environment(E, T)))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))), ((greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T)))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(242,plain,
% 0.23/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T)))) <=> ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[241])).
% 0.23/0.48 tff(243,plain,
% 0.23/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T)))) <=> ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(244,plain,
% 0.23/0.48 (^[E: $i, T: $i] : trans(monotonicity(rewrite((greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T)) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)))), (((environment(E) & in_environment(E, T)) => (greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T))) <=> ((environment(E) & in_environment(E, T)) => (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)))))), rewrite(((environment(E) & in_environment(E, T)) => (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))), (((environment(E) & in_environment(E, T)) => (greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(245,plain,
% 0.23/0.48 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T))) <=> ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[244])).
% 0.23/0.48 tff(246,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_environment_inequality')).
% 0.23/0.49 tff(247,plain,
% 0.23/0.49 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.23/0.49 tff(248,plain,
% 0.23/0.49 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.23/0.49 tff(249,plain,(
% 0.23/0.49 ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.23/0.49 inference(skolemize,[status(sab)],[248])).
% 0.23/0.49 tff(250,plain,
% 0.23/0.49 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.23/0.49 tff(251,plain,
% 0.23/0.49 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[250, 240])).
% 0.23/0.49 tff(252,plain,
% 0.23/0.49 (((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))) <=> ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(253,plain,
% 0.23/0.49 ((greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3)))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(254,plain,
% 0.23/0.49 (((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[253])).
% 0.23/0.49 tff(255,plain,
% 0.23/0.49 (((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[254, 252])).
% 0.23/0.49 tff(256,plain,
% 0.23/0.49 ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(257,plain,
% 0.23/0.49 ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.23/0.49 tff(258,plain,
% 0.23/0.49 (greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[257, 251, 15, 58])).
% 0.23/0.49 tff(259,plain,
% 0.23/0.49 (greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[258, 238])).
% 0.23/0.49 tff(260,plain,
% 0.23/0.49 (^[E: $i, T: $i] : refl((greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(261,plain,
% 0.23/0.49 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))) <=> ![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[260])).
% 0.23/0.49 tff(262,plain,
% 0.23/0.49 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E))) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(263,plain,
% 0.23/0.49 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[262])).
% 0.23/0.49 tff(264,plain,
% 0.23/0.49 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(265,plain,
% 0.23/0.49 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) <=> (environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)) <=> ((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(266,plain,
% 0.23/0.49 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[265])).
% 0.23/0.49 tff(267,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a1')).
% 0.23/0.49 tff(268,plain,
% 0.23/0.49 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.23/0.49 tff(269,plain,
% 0.23/0.49 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[268, 264])).
% 0.23/0.49 tff(270,plain,(
% 0.23/0.49 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.23/0.49 inference(skolemize,[status(sab)],[269])).
% 0.23/0.49 tff(271,plain,
% 0.23/0.49 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[270, 263])).
% 0.23/0.49 tff(272,plain,
% 0.23/0.49 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[271, 261])).
% 0.23/0.49 tff(273,plain,
% 0.23/0.49 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(274,plain,
% 0.23/0.49 ((greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(275,plain,
% 0.23/0.49 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[274])).
% 0.23/0.49 tff(276,plain,
% 0.23/0.49 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[275, 273])).
% 0.23/0.49 tff(277,plain,
% 0.23/0.49 ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(278,plain,
% 0.23/0.49 ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.23/0.49 tff(279,plain,
% 0.23/0.49 (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[278, 272, 15, 58])).
% 0.23/0.49 tff(280,plain,
% 0.23/0.49 (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[279, 259])).
% 0.23/0.49 tff(281,plain,
% 0.23/0.49 (^[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)))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(282,plain,
% 0.23/0.49 (![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))))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[281])).
% 0.23/0.49 tff(283,plain,
% 0.23/0.49 (^[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))))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(284,plain,
% 0.23/0.49 (![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))))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[283])).
% 0.23/0.49 tff(285,plain,
% 0.23/0.49 (![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))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(286,plain,
% 0.23/0.49 (^[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))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(287,plain,
% 0.23/0.49 (![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))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[286])).
% 0.23/0.50 tff(288,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/sandbox2/benchmark/theBenchmark.p','a3')).
% 0.23/0.50 tff(289,plain,
% 0.23/0.50 (![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))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.23/0.50 tff(290,plain,
% 0.23/0.50 (![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))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.23/0.50 tff(291,plain,(
% 0.23/0.50 ![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))))),
% 0.23/0.50 inference(skolemize,[status(sab)],[290])).
% 0.23/0.50 tff(292,plain,
% 0.23/0.50 (![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))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[291, 284])).
% 0.23/0.50 tff(293,plain,
% 0.23/0.50 (![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))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[292, 282])).
% 0.23/0.50 tff(294,plain,
% 0.23/0.50 (((~![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!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))))) <=> ((~![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!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(295,plain,
% 0.23/0.50 (((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~((~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))) | (~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(296,plain,
% 0.23/0.50 (((~![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!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~((~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))) | (~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))) <=> ((~![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!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[295])).
% 0.23/0.50 tff(297,plain,
% 0.23/0.50 (((~![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!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~((~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))) | (~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))) <=> ((~![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!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[296, 294])).
% 0.23/0.50 tff(298,plain,
% 0.23/0.50 ((~![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!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~((~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))) | (~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(299,plain,
% 0.23/0.50 ((~![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!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.23/0.50 tff(300,plain,
% 0.23/0.50 ((~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[299, 293, 15, 58])).
% 0.23/0.50 tff(301,plain,
% 0.23/0.50 (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[300, 280])).
% 0.23/0.50 tff(302,plain,
% 0.23/0.50 (((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))) | (decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(303,plain,
% 0.23/0.50 (decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.23/0.50 tff(304,plain,
% 0.23/0.50 ((~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(305,plain,
% 0.23/0.50 (decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.23/0.50 tff(306,plain,
% 0.23/0.50 (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[305, 164])).
% 0.23/0.50 tff(307,plain,
% 0.23/0.50 (((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))) | (constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(308,plain,
% 0.23/0.50 (constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[307, 301])).
% 0.23/0.50 tff(309,plain,
% 0.23/0.50 ((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(310,plain,
% 0.23/0.50 (constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[309, 308])).
% 0.23/0.50 tff(311,plain,
% 0.23/0.50 (constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[310, 306])).
% 0.23/0.50 tff(312,plain,
% 0.23/0.50 (((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))))) | (constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(313,plain,
% 0.23/0.50 (constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[312, 159])).
% 0.23/0.51 tff(314,plain,
% 0.23/0.51 ((~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(315,plain,
% 0.23/0.51 (constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[314, 313])).
% 0.23/0.51 tff(316,plain,
% 0.23/0.51 (constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[315, 311])).
% 0.23/0.51 tff(317,plain,
% 0.23/0.51 (^[X: $i] : refl(((~constant(X)) | (~decreases(X))) <=> ((~constant(X)) | (~decreases(X))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(318,plain,
% 0.23/0.51 (![X: $i] : ((~constant(X)) | (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[317])).
% 0.23/0.51 tff(319,plain,
% 0.23/0.51 (![X: $i] : ((~constant(X)) | (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(320,plain,
% 0.23/0.51 (^[X: $i] : rewrite((constant(X) => (~decreases(X))) <=> ((~constant(X)) | (~decreases(X))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(321,plain,
% 0.23/0.51 (![X: $i] : (constant(X) => (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[320])).
% 0.23/0.51 tff(322,axiom,(![X: $i] : (constant(X) => (~decreases(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_constant_not_decrease')).
% 0.23/0.51 tff(323,plain,
% 0.23/0.51 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.23/0.51 tff(324,plain,
% 0.23/0.51 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[323, 319])).
% 0.23/0.51 tff(325,plain,(
% 0.23/0.51 ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.23/0.51 inference(skolemize,[status(sab)],[324])).
% 0.23/0.51 tff(326,plain,
% 0.23/0.51 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[325, 318])).
% 0.23/0.51 tff(327,plain,
% 0.23/0.51 (((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | ((~constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))))) <=> ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | (~constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(328,plain,
% 0.23/0.51 ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | ((~constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(329,plain,
% 0.23/0.51 ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | (~constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.23/0.51 tff(330,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[329, 326, 142, 316])).
% 0.23/0.51 % SZS output end Proof
% 0.23/0.51 % E exiting
%------------------------------------------------------------------------------