TSTP Solution File: MGT025+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT025+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:21:56 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT025+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 02:05:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(greater_type, type, (
% 0.12/0.39 greater: ( $i * $i ) > $o)).
% 0.12/0.39 tff(growth_rate_type, type, (
% 0.12/0.39 growth_rate: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_T_0_type, type, (
% 0.12/0.39 tptp_fun_T_0: $i)).
% 0.12/0.39 tff(efficient_producers_type, type, (
% 0.12/0.39 efficient_producers: $i)).
% 0.12/0.39 tff(zero_type, type, (
% 0.12/0.39 zero: $i)).
% 0.12/0.39 tff(decreases_type, type, (
% 0.12/0.39 decreases: $i > $o)).
% 0.12/0.39 tff(cardinality_at_time_type, type, (
% 0.12/0.39 cardinality_at_time: ( $i * $i ) > $i)).
% 0.12/0.39 tff(increases_type, type, (
% 0.12/0.39 increases: $i > $o)).
% 0.12/0.39 tff(first_movers_type, type, (
% 0.12/0.39 first_movers: $i)).
% 0.12/0.39 tff(constant_type, type, (
% 0.12/0.39 constant: $i > $o)).
% 0.12/0.39 tff(subpopulation_type, type, (
% 0.12/0.39 subpopulation: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_E_1_type, type, (
% 0.12/0.39 tptp_fun_E_1: $i)).
% 0.12/0.39 tff(in_environment_type, type, (
% 0.12/0.39 in_environment: ( $i * $i ) > $o)).
% 0.12/0.39 tff(subpopulations_type, type, (
% 0.12/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.39 tff(number_of_organizations_type, type, (
% 0.12/0.39 number_of_organizations: ( $i * $i ) > $i)).
% 0.12/0.39 tff(environment_type, type, (
% 0.12/0.39 environment: $i > $o)).
% 0.12/0.39 tff(sum_type, type, (
% 0.12/0.39 sum: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,assumption,(~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0)))) | decreases(cardinality_at_time(first_movers, T!0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (decreases(cardinality_at_time(first_movers, T!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 ((~((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) | (greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) | ((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & constant(number_of_organizations(E!1, T!0)))))) <=> (~((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) | (greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) | ((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & constant(number_of_organizations(E!1, T!0))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 ((~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))) <=> (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 ((~![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & constant(number_of_organizations(E, T))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))) <=> (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(7,axiom,(~![E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & constant(number_of_organizations(E, T))) => ((((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))) | (greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l7')).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (~![E: $i, T: $i] : ((greater(growth_rate(efficient_producers, T), zero) & greater(zero, growth_rate(first_movers, T))) | (greater(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) | ((growth_rate(first_movers, T) = zero) & (growth_rate(efficient_producers, T) = zero)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & constant(number_of_organizations(E, T)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.19/0.40 tff(15,plain,(
% 0.19/0.40 ~((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) | (greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) | ((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & constant(number_of_organizations(E!1, T!0)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[14])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (~((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) | (greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) | ((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & constant(number_of_organizations(E!1, T!0)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & constant(number_of_organizations(E!1, T!0))),
% 0.19/0.40 inference(or_elim,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.19/0.40 inference(and_elim,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (environment(E!1)),
% 0.19/0.40 inference(and_elim,[status(thm)],[17])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (^[E: $i, T: $i] : refl((in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.40 tff(27,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_time_point_occur')).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.40 tff(30,plain,(
% 0.19/0.40 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.40 inference(skolemize,[status(sab)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 ((in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.19/0.40 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (in_environment(E!1, T!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 32, 19, 18])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.41 tff(47,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_subpopulations')).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.41 tff(50,plain,(
% 0.19/0.41 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[49])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[55, 52, 19, 39])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))) | subpopulation(first_movers, E!1, T!0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (subpopulation(first_movers, E!1, T!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (^[E: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), rewrite((greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.41 tff(66,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_non_zero_producers')).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.41 tff(69,plain,(
% 0.19/0.41 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~((~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (~((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 71, 19, 18])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) | greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (^[X: $i, E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))) <=> ![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (^[X: $i, E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))), ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))), ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))), rewrite((((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))) <=> (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))), (((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> (((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))), (((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> ![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> ![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (^[X: $i, E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) <=> (environment(E) & in_environment(E, T) & subpopulation(X, E, T))), ((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) <=> ((environment(E) & in_environment(E, T) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) <=> (environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))), ((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) <=> (environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))), trans(monotonicity(rewrite(((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) <=> (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)))), rewrite((decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T))) <=> ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))), ((((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T)))) <=> ((((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))), rewrite(((((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))) <=> (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))), ((((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T)))) <=> (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))), (((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => (((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T))))) <=> ((environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) => (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))))), rewrite(((environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) => (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T))))) <=> ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))), (((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => (((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T))))) <=> ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![X: $i, E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => (((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T))))) <=> ![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.42 tff(85,axiom,(![X: $i, E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => (((constant(cardinality_at_time(X, T)) => (growth_rate(X, T) = zero)) & (increases(cardinality_at_time(X, T)) => greater(growth_rate(X, T), zero))) & (decreases(cardinality_at_time(X, T)) => greater(zero, growth_rate(X, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_growth_rate')).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.42 tff(88,plain,(
% 0.19/0.42 ![X: $i, E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) | (((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero)) & ((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero)) & ((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[87])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))))))) <=> ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (~((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[93, 90, 19, 77, 39, 58])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))))) | ((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0)))) | (~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 ((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (greater(zero, growth_rate(first_movers, T!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[98, 3])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0)))) | increases(cardinality_at_time(efficient_producers, T!0))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (increases(cardinality_at_time(efficient_producers, T!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[100, 1])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))) | subpopulation(efficient_producers, E!1, T!0)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (subpopulation(efficient_producers, E!1, T!0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[102, 56])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (((~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) | greater(cardinality_at_time(efficient_producers, T!0), zero)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (greater(cardinality_at_time(efficient_producers, T!0), zero)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 75])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))))))) <=> ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 ((~![X: $i, E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)) | (~((~((~constant(cardinality_at_time(X, T))) | (growth_rate(X, T) = zero))) | (~((~increases(cardinality_at_time(X, T))) | greater(growth_rate(X, T), zero))) | (~((~decreases(cardinality_at_time(X, T))) | greater(zero, growth_rate(X, T)))))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (~((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[108, 90, 19, 105, 39, 103])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))))) | ((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 ((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 ((~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (greater(growth_rate(efficient_producers, T!0), zero)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[113, 101])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~(~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))))) <=> ((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 ((greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0))) <=> (~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~(greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0)))) <=> (~(~((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[116])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 ((~(greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0)))) <=> ((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[117, 115])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (~(greater(growth_rate(efficient_producers, T!0), zero) & greater(zero, growth_rate(first_movers, T!0)))),
% 0.19/0.43 inference(or_elim,[status(thm)],[16])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 ((~greater(growth_rate(efficient_producers, T!0), zero)) | (~greater(zero, growth_rate(first_movers, T!0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[120, 114, 99])).
% 0.19/0.43 tff(122,plain,((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(123,assumption,(~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))), introduced(assumption)).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))) | constant(cardinality_at_time(efficient_producers, T!0))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (constant(cardinality_at_time(efficient_producers, T!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))))) | ((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 ((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[126, 109])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 ((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 ((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (growth_rate(efficient_producers, T!0) = zero),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[129, 125])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))) | constant(cardinality_at_time(first_movers, T!0))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 (constant(cardinality_at_time(first_movers, T!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[131, 123])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))))) | ((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 ((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[133, 94])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 ((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 ((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 (growth_rate(first_movers, T!0) = zero),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[136, 132])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 ((~(~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))))) <=> ((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 (((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero)) <=> (~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 ((~((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero))) <=> (~(~((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[139])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 ((~((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero))) <=> ((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[140, 138])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 (~((growth_rate(first_movers, T!0) = zero) & (growth_rate(efficient_producers, T!0) = zero))),
% 0.19/0.44 inference(or_elim,[status(thm)],[16])).
% 0.19/0.44 tff(143,plain,
% 0.19/0.44 ((~(growth_rate(first_movers, T!0) = zero)) | (~(growth_rate(efficient_producers, T!0) = zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.44 tff(144,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[143, 137, 130])).
% 0.19/0.44 tff(145,plain,((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(146,plain,
% 0.19/0.44 (^[E: $i, X: $i, T: $i] : refl(((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) <=> ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(147,plain,
% 0.19/0.44 (![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) <=> ![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.44 tff(148,plain,
% 0.19/0.44 (^[E: $i, X: $i, T: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))) <=> ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))), ((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) <=> (environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), rewrite((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) <=> (~((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))), ((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) <=> (~((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))))), ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) <=> (~(~((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))))), rewrite((~(~((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))) <=> ((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) <=> ((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))))), (((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> (((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))))), rewrite((((~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), (((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(149,plain,
% 0.19/0.44 (![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.44 tff(150,plain,
% 0.19/0.44 (![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(151,plain,
% 0.19/0.44 (^[E: $i, X: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers))) <=> ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))), (((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) <=> ((environment(E) & subpopulation(X, E, T)) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), rewrite(((environment(E) & subpopulation(X, E, T)) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) <=> (environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))), (((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) <=> (environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))), ((((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))))), rewrite(((environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))), ((((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(152,plain,
% 0.19/0.44 (![E: $i, X: $i, T: $i] : (((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T)))) <=> ![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.44 tff(153,axiom,(![E: $i, X: $i, T: $i] : (((environment(E) & subpopulation(X, E, T)) & (greater(cardinality_at_time(X, T), zero) => ((X = efficient_producers) | (X = first_movers)))) => (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_only_members')).
% 0.19/0.44 tff(154,plain,
% 0.19/0.44 (![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.44 tff(155,plain,
% 0.19/0.44 (![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.19/0.44 tff(156,plain,(
% 0.19/0.44 ![E: $i, X: $i, T: $i] : ((~(environment(E) & subpopulation(X, E, T) & ((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero))))) | (number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[155])).
% 0.19/0.44 tff(157,plain,
% 0.19/0.44 (![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.19/0.44 tff(158,plain,
% 0.19/0.44 (![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 (((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))) <=> ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 (((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | $false) <=> ((~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 ((~$true) <=> $false),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (((efficient_producers = first_movers) | $true | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(163,plain,
% 0.19/0.45 ((efficient_producers = efficient_producers) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) <=> ((efficient_producers = first_movers) | $true | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[163])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 (((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) <=> $true),
% 0.19/0.45 inference(transitivity,[status(thm)],[164, 162])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 ((~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> (~$true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[165])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 ((~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[166, 161])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 (((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))))) <=> ((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | $false)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.45 tff(169,plain,
% 0.19/0.45 (((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))))) <=> ((~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[168, 160])).
% 0.19/0.45 tff(170,plain,
% 0.19/0.45 (((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))) <=> ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.45 tff(171,plain,
% 0.19/0.45 (((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))) <=> ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[170, 159])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | ((number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~((efficient_producers = first_movers) | (efficient_producers = efficient_producers) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 ((~![E: $i, X: $i, T: $i] : ((number_of_organizations(E, T) = sum(cardinality_at_time(first_movers, T), cardinality_at_time(efficient_producers, T))) | (~environment(E)) | (~subpopulation(X, E, T)) | (~((X = first_movers) | (X = efficient_producers) | (~greater(cardinality_at_time(X, T), zero)))))) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (number_of_organizations(E!1, T!0) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[173, 158, 19, 103])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = number_of_organizations(E!1, T!0)),
% 0.19/0.45 inference(symmetry,[status(thm)],[174])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) <=> constant(number_of_organizations(E!1, T!0))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[175])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (constant(number_of_organizations(E!1, T!0)) <=> constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))),
% 0.19/0.45 inference(symmetry,[status(thm)],[176])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 (constant(number_of_organizations(E!1, T!0))),
% 0.19/0.45 inference(and_elim,[status(thm)],[17])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 (constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : refl(((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A))) <=> ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[180])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((decreases(B) & increases(C)) <=> (~((~decreases(B)) | (~increases(C))))), rewrite((increases(B) & decreases(C)) <=> (~((~increases(B)) | (~decreases(C))))), rewrite((constant(B) & constant(C)) <=> (~((~constant(B)) | (~constant(C))))), trans(monotonicity(rewrite(((A = sum(B, C)) & constant(A)) <=> (~((~(A = sum(B, C))) | (~constant(A))))), ((~((A = sum(B, C)) & constant(A))) <=> (~(~((~(A = sum(B, C))) | (~constant(A))))))), rewrite((~(~((~(A = sum(B, C))) | (~constant(A))))) <=> ((~(A = sum(B, C))) | (~constant(A)))), ((~((A = sum(B, C)) & constant(A))) <=> ((~(A = sum(B, C))) | (~constant(A))))), (((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A)))) <=> ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | ((~(A = sum(B, C))) | (~constant(A)))))), rewrite(((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | ((~(A = sum(B, C))) | (~constant(A)))) <=> ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))), (((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A)))) <=> ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(183,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A)))) <=> ![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[182])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A)))) <=> ![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C))) <=> ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))), ((((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C)))) <=> (((A = sum(B, C)) & constant(A)) => ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))))), rewrite((((A = sum(B, C)) & constant(A)) => ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)))) <=> ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))), ((((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C)))) <=> ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : (((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C)))) <=> ![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.45 tff(187,axiom,(![A: $i, B: $i, C: $i] : (((A = sum(B, C)) & constant(A)) => (((constant(B) & constant(C)) | (increases(B) & decreases(C))) | (decreases(B) & increases(C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_abc_sum_increase')).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.45 tff(189,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.19/0.45 tff(190,plain,(
% 0.19/0.45 ![A: $i, B: $i, C: $i] : ((decreases(B) & increases(C)) | (increases(B) & decreases(C)) | (constant(B) & constant(C)) | (~((A = sum(B, C)) & constant(A))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[189])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[191, 181])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))) | ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 (((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))) | $false | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))) <=> ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(195,plain,
% 0.19/0.45 ((sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))) <=> $true),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 ((~(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) <=> (~$true)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[195])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 ((~(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) <=> $false),
% 0.19/0.45 inference(transitivity,[status(thm)],[196, 161])).
% 0.19/0.45 tff(198,plain,
% 0.19/0.45 ((~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))) <=> (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 ((~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) <=> (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 (((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))) | (~(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))) <=> ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))) | $false | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[199, 198, 197])).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 (((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))) | (~(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0))))) <=> ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[200, 194])).
% 0.19/0.45 tff(202,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))) | ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))) | (~(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))) | ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[201])).
% 0.19/0.45 tff(203,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))) | ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))) | (~(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[202, 193])).
% 0.19/0.45 tff(204,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))) | ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | (~decreases(cardinality_at_time(efficient_producers, T!0))))) | (~((~constant(cardinality_at_time(first_movers, T!0))) | (~constant(cardinality_at_time(efficient_producers, T!0))))) | (~(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)) = sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : ((~((~decreases(B)) | (~increases(C)))) | (~((~increases(B)) | (~decreases(C)))) | (~((~constant(B)) | (~constant(C)))) | (~(A = sum(B, C))) | (~constant(A)))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.46 tff(206,plain,
% 0.19/0.46 ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~constant(sum(cardinality_at_time(first_movers, T!0), cardinality_at_time(efficient_producers, T!0)))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[205, 192])).
% 0.19/0.46 tff(207,plain,
% 0.19/0.46 ((~((~decreases(cardinality_at_time(first_movers, T!0))) | (~increases(cardinality_at_time(efficient_producers, T!0))))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))) | (~((~constant(cardinality_at_time(efficient_producers, T!0))) | (~constant(cardinality_at_time(first_movers, T!0)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[206, 179])).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[207, 145, 122])).
% 0.19/0.46 tff(209,plain,
% 0.19/0.46 (((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0)))) | decreases(cardinality_at_time(efficient_producers, T!0))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(210,plain,
% 0.19/0.46 (decreases(cardinality_at_time(efficient_producers, T!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.19/0.46 tff(211,plain,
% 0.19/0.46 (((~((~constant(cardinality_at_time(efficient_producers, T!0))) | (growth_rate(efficient_producers, T!0) = zero))) | (~((~increases(cardinality_at_time(efficient_producers, T!0))) | greater(growth_rate(efficient_producers, T!0), zero))) | (~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))))) | ((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(212,plain,
% 0.19/0.46 ((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[211, 109])).
% 0.19/0.46 tff(213,plain,
% 0.19/0.46 ((~((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0)))) | (~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(214,plain,
% 0.19/0.46 ((~decreases(cardinality_at_time(efficient_producers, T!0))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.19/0.46 tff(215,plain,
% 0.19/0.46 (greater(zero, growth_rate(efficient_producers, T!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[214, 210])).
% 0.19/0.46 tff(216,plain,
% 0.19/0.46 (((~decreases(cardinality_at_time(efficient_producers, T!0))) | (~increases(cardinality_at_time(first_movers, T!0)))) | increases(cardinality_at_time(first_movers, T!0))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(217,plain,
% 0.19/0.46 (increases(cardinality_at_time(first_movers, T!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[216, 208])).
% 0.19/0.46 tff(218,plain,
% 0.19/0.46 (((~((~constant(cardinality_at_time(first_movers, T!0))) | (growth_rate(first_movers, T!0) = zero))) | (~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~((~decreases(cardinality_at_time(first_movers, T!0))) | greater(zero, growth_rate(first_movers, T!0))))) | ((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(219,plain,
% 0.19/0.46 ((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[218, 94])).
% 0.19/0.46 tff(220,plain,
% 0.19/0.46 ((~((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero))) | (~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(221,plain,
% 0.19/0.46 ((~increases(cardinality_at_time(first_movers, T!0))) | greater(growth_rate(first_movers, T!0), zero)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.19/0.46 tff(222,plain,
% 0.19/0.46 (greater(growth_rate(first_movers, T!0), zero)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[221, 217])).
% 0.19/0.46 tff(223,plain,
% 0.19/0.46 ((~(~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))))) <=> ((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(224,plain,
% 0.19/0.46 ((greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))) <=> (~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(225,plain,
% 0.19/0.46 ((~(greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0)))) <=> (~(~((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[224])).
% 0.19/0.46 tff(226,plain,
% 0.19/0.46 ((~(greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0)))) <=> ((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[225, 223])).
% 0.19/0.46 tff(227,plain,
% 0.19/0.46 (~(greater(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.19/0.46 inference(or_elim,[status(thm)],[16])).
% 0.19/0.46 tff(228,plain,
% 0.19/0.46 ((~greater(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.19/0.46 tff(229,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[228, 222, 215])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------