TSTP Solution File: MGT020+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT020+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 05:21:53 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT020+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:44:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(greater_or_equal_type, type, (
% 0.13/0.39 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.39 tff(initial_FM_EP_type, type, (
% 0.13/0.39 initial_FM_EP: $i > $i)).
% 0.13/0.39 tff(tptp_fun_E_1_type, type, (
% 0.13/0.39 tptp_fun_E_1: $i)).
% 0.13/0.39 tff(subpopulations_type, type, (
% 0.13/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.39 tff(efficient_producers_type, type, (
% 0.13/0.39 efficient_producers: $i)).
% 0.13/0.39 tff(first_movers_type, type, (
% 0.13/0.39 first_movers: $i)).
% 0.13/0.39 tff(in_environment_type, type, (
% 0.13/0.39 in_environment: ( $i * $i ) > $o)).
% 0.13/0.39 tff(environment_type, type, (
% 0.13/0.39 environment: $i > $o)).
% 0.13/0.39 tff(tptp_fun_T_0_type, type, (
% 0.13/0.39 tptp_fun_T_0: $i)).
% 0.13/0.39 tff(greater_type, type, (
% 0.13/0.39 greater: ( $i * $i ) > $o)).
% 0.13/0.39 tff(disbanding_rate_type, type, (
% 0.13/0.39 disbanding_rate: ( $i * $i ) > $i)).
% 0.13/0.39 tff(start_time_type, type, (
% 0.13/0.39 start_time: $i > $i)).
% 0.13/0.39 tff(decreases_type, type, (
% 0.13/0.39 decreases: $i > $o)).
% 0.13/0.39 tff(difference_type, type, (
% 0.13/0.39 difference: ( $i * $i ) > $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) <=> (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) <=> (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,axiom,(~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l2')).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | greater(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.39 tff(11,plain,(
% 0.13/0.39 ~((~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0))) | greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (environment(E!1)),
% 0.13/0.39 inference(and_elim,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (^[E: $i, T: $i] : refl(((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))))) <=> ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (^[E: $i, T: $i] : rewrite(((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))) <=> ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![E: $i, T: $i] : ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![E: $i, T: $i] : ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((in_environment(E, initial_FM_EP(E)) => subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & (subpopulations(first_movers, efficient_producers, E, T) => greater_or_equal(T, initial_FM_EP(E)))) <=> (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))), ((environment(E) => ((in_environment(E, initial_FM_EP(E)) => subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & (subpopulations(first_movers, efficient_producers, E, T) => greater_or_equal(T, initial_FM_EP(E))))) <=> (environment(E) => (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))))), rewrite((environment(E) => (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E))))) <=> ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))), ((environment(E) => ((in_environment(E, initial_FM_EP(E)) => subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & (subpopulations(first_movers, efficient_producers, E, T) => greater_or_equal(T, initial_FM_EP(E))))) <=> ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![E: $i, T: $i] : (environment(E) => ((in_environment(E, initial_FM_EP(E)) => subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & (subpopulations(first_movers, efficient_producers, E, T) => greater_or_equal(T, initial_FM_EP(E))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.39 tff(21,axiom,(![E: $i, T: $i] : (environment(E) => ((in_environment(E, initial_FM_EP(E)) => subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & (subpopulations(first_movers, efficient_producers, E, T) => greater_or_equal(T, initial_FM_EP(E)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_point')).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![E: $i, T: $i] : ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![E: $i, T: $i] : ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.13/0.39 tff(24,plain,(
% 0.13/0.39 ![E: $i, T: $i] : ((~environment(E)) | (((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E))) & ((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[23])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (((~![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))) | ((~environment(E!1)) | (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))) | (~environment(E!1)) | (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))) | ((~environment(E!1)) | (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))) | (~environment(E!1)) | (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))))) | ((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.40 tff(33,assumption,(~in_environment(E!1, initial_FM_EP(E!1))), introduced(assumption)).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![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))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (^[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)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (![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))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.40 tff(41,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_time_point_occurs')).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.13/0.40 tff(44,plain,(
% 0.13/0.40 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.13/0.40 inference(skolemize,[status(sab)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 ((in_environment(E!1, initial_FM_EP(E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) <=> ((~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, initial_FM_EP(E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[48])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, initial_FM_EP(E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[49, 47])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, initial_FM_EP(E!1)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[52, 46, 13, 33])).
% 0.13/0.40 tff(54,assumption,(T!0 = initial_FM_EP(E!1)), introduced(assumption)).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (subpopulations(first_movers, efficient_producers, E!1, T!0) <=> subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[54])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)) <=> subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.40 inference(symmetry,[status(thm)],[55])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 ((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) <=> (~subpopulations(first_movers, efficient_producers, E!1, T!0))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[56])).
% 0.13/0.40 tff(58,assumption,(~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))), introduced(assumption)).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (~subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.40 inference(and_elim,[status(thm)],[12])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.13/0.40 tff(62,plain,((~(T!0 = initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (~(T!0 = initial_FM_EP(E!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[62, 53])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (((~![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))) | ((~environment(E!1)) | (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))) | (~environment(E!1)) | (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1)))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))) | ((~environment(E!1)) | (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 ((~![E: $i, T: $i] : ((~environment(E)) | (~((~((~in_environment(E, initial_FM_EP(E))) | subpopulations(first_movers, efficient_producers, E, initial_FM_EP(E)))) | (~((~subpopulations(first_movers, efficient_producers, E, T)) | greater_or_equal(T, initial_FM_EP(E)))))))) | (~environment(E!1)) | (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (~((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1)))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[66, 26, 13])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1))))) | ((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 ((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 ((~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1)))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 ((~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1)))) | greater_or_equal(T!0, initial_FM_EP(E!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[70, 60])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 (greater_or_equal(T!0, initial_FM_EP(E!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[71, 69])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : refl(((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y))) <=> ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[73])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((greater(X, Y) | (X = Y)) <=> ((X = Y) | greater(X, Y))), ((greater_or_equal(X, Y) => (greater(X, Y) | (X = Y))) <=> (greater_or_equal(X, Y) => ((X = Y) | greater(X, Y))))), rewrite((greater_or_equal(X, Y) => ((X = Y) | greater(X, Y))) <=> ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))), ((greater_or_equal(X, Y) => (greater(X, Y) | (X = Y))) <=> ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (greater_or_equal(X, Y) => (greater(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.13/0.41 tff(78,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) => (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_or_equal')).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.13/0.41 tff(80,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.13/0.41 tff(81,plain,(
% 0.13/0.41 ![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[80])).
% 0.13/0.41 tff(82,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.13/0.41 tff(83,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))) | ((~greater_or_equal(T!0, initial_FM_EP(E!1))) | (T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | (T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(84,plain,
% 0.13/0.41 (((T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1)) | (~greater_or_equal(T!0, initial_FM_EP(E!1)))) <=> ((~greater_or_equal(T!0, initial_FM_EP(E!1))) | (T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(85,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))) | ((T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))) | ((~greater_or_equal(T!0, initial_FM_EP(E!1))) | (T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[84])).
% 0.13/0.41 tff(86,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))) | ((T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | (T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[85, 83])).
% 0.13/0.41 tff(87,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))) | ((T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(88,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : ((X = Y) | greater(X, Y) | (~greater_or_equal(X, Y)))) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | (T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.13/0.41 tff(89,plain,
% 0.13/0.41 ((T!0 = initial_FM_EP(E!1)) | greater(T!0, initial_FM_EP(E!1))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[88, 82, 72])).
% 0.13/0.41 tff(90,plain,
% 0.13/0.41 (greater(T!0, initial_FM_EP(E!1))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[89, 63])).
% 0.13/0.41 tff(91,plain,
% 0.13/0.41 (^[E: $i] : refl(((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E))) <=> ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(92,plain,
% 0.13/0.41 (![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[91])).
% 0.13/0.41 tff(93,plain,
% 0.13/0.41 (![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(94,plain,
% 0.13/0.41 (^[E: $i] : rewrite((environment(E) => greater_or_equal(initial_FM_EP(E), start_time(E))) <=> ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(95,plain,
% 0.13/0.41 (![E: $i] : (environment(E) => greater_or_equal(initial_FM_EP(E), start_time(E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[94])).
% 0.13/0.41 tff(96,axiom,(![E: $i] : (environment(E) => greater_or_equal(initial_FM_EP(E), start_time(E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_initial_time')).
% 0.13/0.41 tff(97,plain,
% 0.13/0.41 (![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.13/0.41 tff(98,plain,
% 0.13/0.41 (![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.13/0.41 tff(99,plain,(
% 0.13/0.41 ![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[98])).
% 0.13/0.41 tff(100,plain,
% 0.13/0.41 (![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.13/0.41 tff(101,plain,
% 0.13/0.41 (((~![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))) | ((~environment(E!1)) | greater_or_equal(initial_FM_EP(E!1), start_time(E!1)))) <=> ((~![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))) | (~environment(E!1)) | greater_or_equal(initial_FM_EP(E!1), start_time(E!1)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(102,plain,
% 0.13/0.41 ((~![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))) | ((~environment(E!1)) | greater_or_equal(initial_FM_EP(E!1), start_time(E!1)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(103,plain,
% 0.13/0.41 ((~![E: $i] : ((~environment(E)) | greater_or_equal(initial_FM_EP(E), start_time(E)))) | (~environment(E!1)) | greater_or_equal(initial_FM_EP(E!1), start_time(E!1))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.13/0.41 tff(104,plain,
% 0.13/0.41 (greater_or_equal(initial_FM_EP(E!1), start_time(E!1))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[103, 100, 13])).
% 0.13/0.41 tff(105,plain,
% 0.13/0.41 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(106,plain,
% 0.13/0.41 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(107,plain,
% 0.13/0.41 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.13/0.41 tff(108,plain,
% 0.13/0.41 (in_environment(E!1, T!0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[107, 46, 13, 60])).
% 0.13/0.41 tff(109,plain,
% 0.13/0.41 (^[E: $i, T1: $i, T2: $i] : refl((in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))) <=> (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(110,plain,
% 0.13/0.41 (![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))) <=> ![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.13/0.41 tff(111,plain,
% 0.13/0.41 (^[E: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2)) <=> (~((~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))))), ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) <=> (~(~((~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))))))), rewrite((~(~((~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))))) <=> ((~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))), ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) <=> ((~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))))), (((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1)) <=> (((~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))) | in_environment(E, T1)))), rewrite((((~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2))) | in_environment(E, T1)) <=> (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))), (((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1)) <=> (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(112,plain,
% 0.13/0.41 (![E: $i, T1: $i, T2: $i] : ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1)) <=> ![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.13/0.41 tff(113,plain,
% 0.13/0.41 (![E: $i, T1: $i, T2: $i] : ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1)) <=> ![E: $i, T1: $i, T2: $i] : ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(114,plain,
% 0.13/0.41 (^[E: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & greater_or_equal(T1, start_time(E))) & greater(T2, T1)) <=> (environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1))), ((((environment(E) & greater_or_equal(T1, start_time(E))) & greater(T2, T1)) & in_environment(E, T2)) <=> ((environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1)) & in_environment(E, T2)))), rewrite(((environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1)) & in_environment(E, T2)) <=> (environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))), ((((environment(E) & greater_or_equal(T1, start_time(E))) & greater(T2, T1)) & in_environment(E, T2)) <=> (environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2)))), (((((environment(E) & greater_or_equal(T1, start_time(E))) & greater(T2, T1)) & in_environment(E, T2)) => in_environment(E, T1)) <=> ((environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2)) => in_environment(E, T1)))), rewrite(((environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2)) => in_environment(E, T1)) <=> ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1))), (((((environment(E) & greater_or_equal(T1, start_time(E))) & greater(T2, T1)) & in_environment(E, T2)) => in_environment(E, T1)) <=> ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(115,plain,
% 0.13/0.41 (![E: $i, T1: $i, T2: $i] : ((((environment(E) & greater_or_equal(T1, start_time(E))) & greater(T2, T1)) & in_environment(E, T2)) => in_environment(E, T1)) <=> ![E: $i, T1: $i, T2: $i] : ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[114])).
% 0.13/0.41 tff(116,axiom,(![E: $i, T1: $i, T2: $i] : ((((environment(E) & greater_or_equal(T1, start_time(E))) & greater(T2, T1)) & in_environment(E, T2)) => in_environment(E, T1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_times_in_order')).
% 0.13/0.41 tff(117,plain,
% 0.13/0.41 (![E: $i, T1: $i, T2: $i] : ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.13/0.41 tff(118,plain,
% 0.13/0.41 (![E: $i, T1: $i, T2: $i] : ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.13/0.41 tff(119,plain,(
% 0.13/0.41 ![E: $i, T1: $i, T2: $i] : ((~(environment(E) & greater_or_equal(T1, start_time(E)) & greater(T2, T1) & in_environment(E, T2))) | in_environment(E, T1))),
% 0.13/0.41 inference(skolemize,[status(sab)],[118])).
% 0.13/0.41 tff(120,plain,
% 0.13/0.41 (![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.13/0.41 tff(121,plain,
% 0.13/0.41 (![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.13/0.41 tff(122,plain,
% 0.13/0.41 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))) | ((~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0)))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))) | (~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(123,plain,
% 0.13/0.41 ((in_environment(E!1, initial_FM_EP(E!1)) | (~environment(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0))) <=> ((~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))) | (in_environment(E!1, initial_FM_EP(E!1)) | (~environment(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0)))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))) | ((~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))) | (in_environment(E!1, initial_FM_EP(E!1)) | (~environment(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0)))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))) | (~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[124, 122])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))) | (in_environment(E!1, initial_FM_EP(E!1)) | (~environment(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T1) | (~environment(E)) | (~greater_or_equal(T1, start_time(E))) | (~greater(T2, T1)) | (~in_environment(E, T2)))) | (~environment(E!1)) | in_environment(E!1, initial_FM_EP(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), start_time(E!1))) | (~greater(T!0, initial_FM_EP(E!1))) | (~in_environment(E!1, T!0))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[127, 121, 13, 108, 33, 104, 90])).
% 0.21/0.41 tff(129,plain,(in_environment(E!1, initial_FM_EP(E!1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 (((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~((~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(T!0, initial_FM_EP(E!1))))) | ((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 ((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[130, 67])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 ((~((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) | (~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 ((~in_environment(E!1, initial_FM_EP(E!1))) | subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 (subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[133, 129])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 ((~((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 ((~((~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))) | greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 (greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[136, 32])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (^[E: $i, T: $i] : refl(((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[138])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[140])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[143])).
% 0.21/0.42 tff(145,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l3')).
% 0.21/0.42 tff(146,plain,
% 0.21/0.42 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.21/0.42 tff(148,plain,(
% 0.21/0.42 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[147])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 (![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[149, 139])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(152,plain,
% 0.21/0.42 (((~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1)))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(153,plain,
% 0.21/0.42 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[152])).
% 0.21/0.42 tff(154,plain,
% 0.21/0.42 (((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))) <=> ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[153, 151])).
% 0.21/0.42 tff(155,plain,
% 0.21/0.42 ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(156,plain,
% 0.21/0.42 ((~![E: $i, T: $i] : ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, initial_FM_EP(E!1))) | (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.42 tff(157,plain,
% 0.21/0.42 (~decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[156, 150, 13, 134])).
% 0.21/0.42 tff(158,plain,
% 0.21/0.42 (^[E: $i] : refl(((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E)))) <=> ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(159,plain,
% 0.21/0.42 (![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E)))) <=> ![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[158])).
% 0.21/0.42 tff(160,plain,
% 0.21/0.42 (![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E)))) <=> ![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(161,plain,
% 0.21/0.42 (^[E: $i] : rewrite((environment(E) => greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E)))) <=> ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(162,plain,
% 0.21/0.42 (![E: $i] : (environment(E) => greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E)))) <=> ![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[161])).
% 0.21/0.42 tff(163,axiom,(![E: $i] : (environment(E) => greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a8')).
% 0.21/0.42 tff(164,plain,
% 0.21/0.42 (![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.42 tff(165,plain,
% 0.21/0.42 (![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.21/0.42 tff(166,plain,(
% 0.21/0.42 ![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[165])).
% 0.21/0.42 tff(167,plain,
% 0.21/0.42 (![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.21/0.42 tff(168,plain,
% 0.21/0.42 (((~![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))) | ((~environment(E!1)) | greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))) <=> ((~![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))) | (~environment(E!1)) | greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(169,plain,
% 0.21/0.42 ((~![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))) | ((~environment(E!1)) | greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(170,plain,
% 0.21/0.42 ((~![E: $i] : ((~environment(E)) | greater(disbanding_rate(first_movers, initial_FM_EP(E)), disbanding_rate(efficient_producers, initial_FM_EP(E))))) | (~environment(E!1)) | greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.42 tff(171,plain,
% 0.21/0.42 (greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[170, 167, 13])).
% 0.21/0.42 tff(172,plain,
% 0.21/0.42 (~greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))),
% 0.21/0.42 inference(or_elim,[status(thm)],[11])).
% 0.21/0.42 tff(173,plain,
% 0.21/0.42 (^[E: $i, T: $i, T1: $i, T2: $i] : refl((greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))) <=> (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(174,plain,
% 0.21/0.42 (![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))) <=> ![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.42 tff(175,plain,
% 0.21/0.42 (^[E: $i, T: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) <=> (~((~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))), ((~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))) <=> (~(~((~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))))), rewrite((~(~((~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))) <=> ((~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))), ((~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))) <=> ((~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))), ((greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) <=> (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | ((~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))))), rewrite((greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | ((~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) <=> (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))), ((greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) <=> (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(176,plain,
% 0.21/0.43 (![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) <=> ![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[175])).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 (![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) <=> ![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(178,plain,
% 0.21/0.43 (^[E: $i, T: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) <=> (environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T))), ((((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) <=> ((environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)))), rewrite(((environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) <=> (environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2))), ((((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) <=> (environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2)))), (((((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) <=> ((environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2)) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))), rewrite(((environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2)) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) <=> (environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))), (((((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) <=> (environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))), rewrite(((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) => greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2))) <=> (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)))), ((((((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) => ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) => greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)))) <=> ((environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) => (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)))))), rewrite(((environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) => (decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)))) <=> (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))), ((((((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) => ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) => greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)))) <=> (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(179,plain,
% 0.21/0.43 (![E: $i, T: $i, T1: $i, T2: $i] : (((((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) => ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) => greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)))) <=> ![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[178])).
% 0.21/0.43 tff(180,axiom,(![E: $i, T: $i, T1: $i, T2: $i] : (((((environment(E) & greater_or_equal(T, T1)) & greater_or_equal(T2, T)) & subpopulations(first_movers, efficient_producers, E, T2)) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))) => ((~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) => greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_positive_function_difference')).
% 0.21/0.43 tff(181,plain,
% 0.21/0.43 (![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.21/0.43 tff(182,plain,
% 0.21/0.43 (![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.21/0.43 tff(183,plain,(
% 0.21/0.43 ![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~(environment(E) & greater_or_equal(T, T1) & greater_or_equal(T2, T) & subpopulations(first_movers, efficient_producers, E, T2) & greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[182])).
% 0.21/0.43 tff(184,plain,
% 0.21/0.43 (![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.21/0.43 tff(185,plain,
% 0.21/0.43 (![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[184, 174])).
% 0.21/0.43 tff(186,plain,
% 0.21/0.43 (((~![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) | (greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))))) <=> ((~![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) | greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(187,plain,
% 0.21/0.43 ((greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~environment(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1))))) <=> (greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(188,plain,
% 0.21/0.44 (((~![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) | (greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~environment(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))))) <=> ((~![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) | (greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[187])).
% 0.21/0.44 tff(189,plain,
% 0.21/0.44 (((~![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) | (greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~environment(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))))) <=> ((~![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) | greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[188, 186])).
% 0.21/0.44 tff(190,plain,
% 0.21/0.44 ((~![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) | (greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~environment(E!1)) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1))) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(191,plain,
% 0.21/0.44 ((~![E: $i, T: $i, T1: $i, T2: $i] : (greater(disbanding_rate(first_movers, T2), disbanding_rate(efficient_producers, T2)) | decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~environment(E)) | (~greater_or_equal(T, T1)) | (~greater_or_equal(T2, T)) | (~subpopulations(first_movers, efficient_producers, E, T2)) | (~greater(disbanding_rate(first_movers, T1), disbanding_rate(efficient_producers, T1))))) | greater(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater_or_equal(T!0, initial_FM_EP(E!1))) | decreases(difference(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater(disbanding_rate(first_movers, initial_FM_EP(E!1)), disbanding_rate(efficient_producers, initial_FM_EP(E!1)))) | (~greater_or_equal(initial_FM_EP(E!1), initial_FM_EP(E!1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.21/0.44 tff(192,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[191, 185, 13, 60, 172, 72, 171, 157, 137])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------