TSTP Solution File: MGT026+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 05:21:57 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 02:53:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(greater_type, type, (
% 0.19/0.41 greater: ( $i * $i ) > $o)).
% 0.19/0.41 tff(critical_point_type, type, (
% 0.19/0.41 critical_point: $i > $i)).
% 0.19/0.41 tff(tptp_fun_E_1_type, type, (
% 0.19/0.41 tptp_fun_E_1: $i)).
% 0.19/0.41 tff(subpopulations_type, type, (
% 0.19/0.41 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.41 tff(efficient_producers_type, type, (
% 0.19/0.41 efficient_producers: $i)).
% 0.19/0.41 tff(first_movers_type, type, (
% 0.19/0.41 first_movers: $i)).
% 0.19/0.41 tff(growth_rate_type, type, (
% 0.19/0.41 growth_rate: ( $i * $i ) > $i)).
% 0.19/0.41 tff(environment_type, type, (
% 0.19/0.41 environment: $i > $o)).
% 0.19/0.41 tff(tptp_fun_T_0_type, type, (
% 0.19/0.41 tptp_fun_T_0: $i)).
% 0.19/0.41 tff(in_environment_type, type, (
% 0.19/0.41 in_environment: ( $i * $i ) > $o)).
% 0.19/0.41 tff(selection_favors_type, type, (
% 0.19/0.41 selection_favors: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(zero_type, type, (
% 0.19/0.41 zero: $i)).
% 0.19/0.41 tff(cardinality_at_time_type, type, (
% 0.19/0.41 cardinality_at_time: ( $i * $i ) > $i)).
% 0.19/0.41 tff(greater_or_equal_type, type, (
% 0.19/0.41 greater_or_equal: ( $i * $i ) > $o)).
% 0.19/0.41 tff(appear_type, type, (
% 0.19/0.41 appear: ( $i * $i ) > $i)).
% 0.19/0.41 tff(subpopulation_type, type, (
% 0.19/0.41 subpopulation: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 ((~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 ((~![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T))) <=> (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(3,axiom,(~![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(T, critical_point(E))) => selection_favors(efficient_producers, first_movers, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l8')).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (~![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(T, critical_point(E)))) | selection_favors(efficient_producers, first_movers, T))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.41 tff(11,plain,(
% 0.19/0.41 ~((~(environment(E!1) & in_environment(E!1, T!0) & greater(T!0, critical_point(E!1)))) | selection_favors(efficient_producers, first_movers, T!0))),
% 0.19/0.41 inference(skolemize,[status(sab)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (environment(E!1) & in_environment(E!1, T!0) & greater(T!0, critical_point(E!1))),
% 0.19/0.41 inference(or_elim,[status(thm)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (environment(E!1)),
% 0.19/0.41 inference(and_elim,[status(thm)],[12])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (^[E: $i, Tc: $i] : refl(((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (^[E: $i, Tc: $i] : rewrite(((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[E: $i, Tc: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & (Tc = critical_point(E))) <=> (~((~environment(E)) | (~(Tc = critical_point(E)))))), ((~(environment(E) & (Tc = critical_point(E)))) <=> (~(~((~environment(E)) | (~(Tc = critical_point(E)))))))), rewrite((~(~((~environment(E)) | (~(Tc = critical_point(E)))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))))), ((~(environment(E) & (Tc = critical_point(E)))) <=> ((~environment(E)) | (~(Tc = critical_point(E)))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), rewrite((((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))) <=> ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))), (((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))), rewrite(((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))) <=> (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))), (((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))), (((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~(Tc = critical_point(E)))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))))), rewrite((((~environment(E)) | (~(Tc = critical_point(E)))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc))))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))), (((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (^[E: $i, Tc: $i] : trans(monotonicity(rewrite(((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))) <=> ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))), (((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))))), rewrite(((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), (((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (![E: $i, Tc: $i] : ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T))))) <=> ![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.42 tff(24,axiom,(![E: $i, Tc: $i] : ((environment(E) & (Tc = critical_point(E))) => ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc)) => greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1')).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.42 tff(27,plain,(
% 0.19/0.42 ![E: $i, Tc: $i] : ((~(environment(E) & (Tc = critical_point(E)))) | ((~greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc))) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater(T, Tc))) | greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[26])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))) <=> ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | (~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (((~environment(E!1)) | $false | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))))) <=> ((~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 ((~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))))) <=> (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 ((~$true) <=> $false),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((critical_point(E!1) = critical_point(E!1)) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 ((~(critical_point(E!1) = critical_point(E!1))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~(critical_point(E!1) = critical_point(E!1))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1)))))))) <=> ((~environment(E!1)) | $false | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[36, 32])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1)))))))) <=> ((~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[37, 31])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))))))) <=> ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))))))) <=> ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | (~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[39, 30])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | ((~environment(E!1)) | (~(critical_point(E!1) = critical_point(E!1))) | (~(greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 ((~![E: $i, Tc: $i] : ((~environment(E)) | (~(Tc = critical_point(E))) | (~(greater(growth_rate(efficient_producers, Tc), growth_rate(first_movers, Tc)) | (~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater(T, Tc)))))))) | (~environment(E!1)) | (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (~((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[42, 29, 13])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | greater(growth_rate(efficient_producers, critical_point(E!1)), growth_rate(first_movers, critical_point(E!1)))) | ![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl((greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : rewrite((greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.43 tff(51,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')).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.43 tff(54,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[53])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(T!0, appear(efficient_producers, E!1)) <=> ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (greater_or_equal(T!0, appear(efficient_producers, E!1)) <=> ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.43 tff(58,assumption,(~greater(T!0, appear(efficient_producers, E!1))), introduced(assumption)).
% 0.19/0.43 tff(59,assumption,(critical_point(E!1) = appear(efficient_producers, E!1)), introduced(assumption)).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (greater(T!0, critical_point(E!1)) <=> greater(T!0, appear(efficient_producers, E!1))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (greater(T!0, appear(efficient_producers, E!1)) <=> greater(T!0, critical_point(E!1))),
% 0.19/0.43 inference(symmetry,[status(thm)],[60])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 ((~greater(T!0, appear(efficient_producers, E!1))) <=> (~greater(T!0, critical_point(E!1)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (~greater(T!0, critical_point(E!1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[58, 62])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (greater(T!0, critical_point(E!1))),
% 0.19/0.43 inference(and_elim,[status(thm)],[12])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.43 tff(66,plain,((~(critical_point(E!1) = appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (~(critical_point(E!1) = appear(efficient_producers, E!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[66, 58])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[68, 55])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (^[E: $i] : refl(((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (^[E: $i] : rewrite((environment(E) => greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (![E: $i] : (environment(E) => greater_or_equal(critical_point(E), appear(efficient_producers, E))) <=> ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.43 tff(75,axiom,(![E: $i] : (environment(E) => greater_or_equal(critical_point(E), appear(efficient_producers, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_critical_point_after_EP')).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.43 tff(78,plain,(
% 0.19/0.43 ![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[77])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 (((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | ((~environment(E!1)) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))) <=> ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | (~environment(E!1)) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | ((~environment(E!1)) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 ((~![E: $i] : ((~environment(E)) | greater_or_equal(critical_point(E), appear(efficient_producers, E)))) | (~environment(E!1)) | greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[82, 79, 13])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 ((~(greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))) | (~greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1))) | ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 ((~(greater_or_equal(critical_point(E!1), appear(efficient_producers, E!1)) <=> ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))))) | ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[85, 69])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 ((~((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1)))) | (critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 ((critical_point(E!1) = appear(efficient_producers, E!1)) | greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (greater(critical_point(E!1), appear(efficient_producers, E!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[88, 67])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(X, Y) & greater(Y, Z)) <=> (~((~greater(X, Y)) | (~greater(Y, Z))))), ((~(greater(X, Y) & greater(Y, Z))) <=> (~(~((~greater(X, Y)) | (~greater(Y, Z))))))), rewrite((~(~((~greater(X, Y)) | (~greater(Y, Z))))) <=> ((~greater(X, Y)) | (~greater(Y, Z)))), ((~(greater(X, Y) & greater(Y, Z))) <=> ((~greater(X, Y)) | (~greater(Y, Z))))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)))), rewrite((((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (^[X: $i, Y: $i, Z: $i] : rewrite(((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.44 tff(96,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_greater_transitivity')).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.44 tff(99,plain,(
% 0.19/0.44 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.19/0.44 inference(skolemize,[status(sab)],[98])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 ((greater(T!0, appear(efficient_producers, E!1)) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1)))) <=> ((~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(T!0, appear(efficient_producers, E!1)) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(T!0, appear(efficient_producers, E!1)) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[104, 102])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(T!0, appear(efficient_producers, E!1)) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(T!0, critical_point(E!1))) | (~greater(critical_point(E!1), appear(efficient_producers, E!1))) | greater(T!0, appear(efficient_producers, E!1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[107, 101, 64, 89, 58])).
% 0.19/0.44 tff(109,plain,(greater(T!0, appear(efficient_producers, E!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))) | (~greater(T!0, appear(efficient_producers, E!1)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 ((~(greater_or_equal(T!0, appear(efficient_producers, E!1)) <=> ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))))) | greater_or_equal(T!0, appear(efficient_producers, E!1)) | (~((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 ((~(greater_or_equal(T!0, appear(efficient_producers, E!1)) <=> ((T!0 = appear(efficient_producers, E!1)) | greater(T!0, appear(efficient_producers, E!1))))) | greater_or_equal(T!0, appear(efficient_producers, E!1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 (greater_or_equal(T!0, appear(efficient_producers, E!1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[113, 57])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 (in_environment(E!1, T!0)),
% 0.19/0.44 inference(and_elim,[status(thm)],[12])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 (^[E: $i, T: $i] : refl((greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) <=> ![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[116])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.44 tff(123,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6')).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.19/0.44 tff(126,plain,(
% 0.19/0.44 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.19/0.44 inference(skolemize,[status(sab)],[125])).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[127, 117])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (greater(cardinality_at_time(efficient_producers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))))) <=> ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | greater(cardinality_at_time(efficient_producers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (greater(cardinality_at_time(efficient_producers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | greater(cardinality_at_time(efficient_producers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater_or_equal(T!0, appear(efficient_producers, E!1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 (greater(cardinality_at_time(efficient_producers, T!0), zero) | (~greater_or_equal(T!0, appear(efficient_producers, E!1)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[131, 128, 13, 115])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 (greater(cardinality_at_time(efficient_producers, T!0), zero)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[132, 114])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), rewrite((subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)) <=> (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))), (((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> (((~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))))), rewrite((((~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))), (((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 (^[E: $i, T: $i] : rewrite(((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[139])).
% 0.19/0.45 tff(141,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_subpopulations')).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.19/0.45 tff(144,plain,(
% 0.19/0.45 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[143])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[145, 135])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (~((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[149, 146, 13, 115])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 (((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))) | subpopulation(efficient_producers, E!1, T!0)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 (subpopulation(efficient_producers, E!1, T!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 (((~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0))) | subpopulation(first_movers, E!1, T!0)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 (subpopulation(first_movers, E!1, T!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 (~selection_favors(efficient_producers, first_movers, T!0)),
% 0.19/0.45 inference(or_elim,[status(thm)],[11])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))) <=> (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero)) <=> (~((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))), ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) <=> (~(~((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))))), rewrite((~(~((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))) <=> ((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))), ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) <=> ((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))))), (((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> (((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)))), rewrite((((~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))), (((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[158])).
% 0.19/0.45 tff(160,plain,
% 0.19/0.45 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T))), ((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) <=> ((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)))), rewrite(((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero))), ((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero)))), (((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) <=> ((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)))), rewrite(((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))), (((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) <=> (environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero)))), ((((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)) <=> ((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)))), rewrite(((environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)) <=> ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))), ((((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)) <=> ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (![E: $i, S1: $i, S2: $i, T: $i] : (((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[161])).
% 0.19/0.45 tff(163,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((((environment(E) & subpopulation(S1, E, T)) & subpopulation(S2, E, T)) & greater(cardinality_at_time(S1, T), zero)) & (cardinality_at_time(S2, T) = zero)) => selection_favors(S1, S2, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp2_favour_members')).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.19/0.45 tff(166,plain,(
% 0.19/0.45 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulation(S1, E, T) & subpopulation(S2, E, T) & greater(cardinality_at_time(S1, T), zero) & (cardinality_at_time(S2, T) = zero))) | selection_favors(S1, S2, T))),
% 0.19/0.45 inference(skolemize,[status(sab)],[165])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 ((selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero))) <=> (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[170])).
% 0.19/0.46 tff(172,plain,
% 0.19/0.46 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[171, 169])).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~subpopulation(first_movers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(174,plain,
% 0.19/0.46 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S1, S2, T) | (~environment(E)) | (~subpopulation(S1, E, T)) | (~subpopulation(S2, E, T)) | (~greater(cardinality_at_time(S1, T), zero)) | (~(cardinality_at_time(S2, T) = zero)))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulation(first_movers, E!1, T!0)) | (~subpopulation(efficient_producers, E!1, T!0)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 ((~greater(cardinality_at_time(efficient_producers, T!0), zero)) | (~(cardinality_at_time(first_movers, T!0) = zero))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[174, 168, 13, 155, 154, 152])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 (~(cardinality_at_time(first_movers, T!0) = zero)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[175, 133])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) <=> ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) <=> ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[177, 55])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 (^[E: $i, T: $i] : refl((greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T))) <=> (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(180,plain,
% 0.19/0.46 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T))) <=> ![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), (((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> (((~environment(E)) | (~in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)))), rewrite((((~environment(E)) | (~in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))), (((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(182,plain,
% 0.19/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> ![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 (^[E: $i, T: $i] : rewrite(((environment(E) & in_environment(E, T)) => greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(cardinality_at_time(first_movers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.46 tff(186,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => greater_or_equal(cardinality_at_time(first_movers, T), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_first_movers_exist')).
% 0.19/0.46 tff(187,plain,
% 0.19/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.46 tff(188,plain,
% 0.19/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.19/0.46 tff(189,plain,(
% 0.19/0.46 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | greater_or_equal(cardinality_at_time(first_movers, T), zero))),
% 0.19/0.46 inference(skolemize,[status(sab)],[188])).
% 0.19/0.46 tff(190,plain,
% 0.19/0.46 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.19/0.46 tff(191,plain,
% 0.19/0.46 (![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[190, 180])).
% 0.19/0.46 tff(192,plain,
% 0.19/0.46 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(193,plain,
% 0.19/0.46 ((greater_or_equal(cardinality_at_time(first_movers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0))) <=> ((~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(194,plain,
% 0.19/0.46 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[193])).
% 0.19/0.46 tff(195,plain,
% 0.19/0.46 (((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)))) <=> ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero))),
% 0.19/0.46 inference(transitivity,[status(thm)],[194, 192])).
% 0.19/0.46 tff(196,plain,
% 0.19/0.46 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater_or_equal(cardinality_at_time(first_movers, T!0), zero) | (~environment(E!1)) | (~in_environment(E!1, T!0)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(197,plain,
% 0.19/0.46 ((~![E: $i, T: $i] : (greater_or_equal(cardinality_at_time(first_movers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | greater_or_equal(cardinality_at_time(first_movers, T!0), zero)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.46 tff(198,plain,
% 0.19/0.46 (greater_or_equal(cardinality_at_time(first_movers, T!0), zero)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[197, 191, 13, 115])).
% 0.19/0.46 tff(199,plain,
% 0.19/0.46 ((~(greater_or_equal(cardinality_at_time(first_movers, T!0), zero) <=> ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)))) | (~greater_or_equal(cardinality_at_time(first_movers, T!0), zero)) | ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(200,plain,
% 0.19/0.46 ((~(greater_or_equal(cardinality_at_time(first_movers, T!0), zero) <=> ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)))) | ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.19/0.46 tff(201,plain,
% 0.19/0.46 ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[200, 178])).
% 0.19/0.46 tff(202,plain,
% 0.19/0.46 ((~((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero))) | (cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(203,plain,
% 0.19/0.46 ((cardinality_at_time(first_movers, T!0) = zero) | greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.19/0.46 tff(204,plain,
% 0.19/0.46 (greater(cardinality_at_time(first_movers, T!0), zero)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[203, 176])).
% 0.19/0.46 tff(205,plain,
% 0.19/0.46 (^[E: $i, T: $i] : refl((subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(206,plain,
% 0.19/0.46 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.46 tff(207,plain,
% 0.19/0.46 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))), ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))), ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))), (((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))), (((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[207])).
% 0.19/0.46 tff(209,plain,
% 0.19/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))), (((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)))), rewrite(((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))), (((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (![E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.47 tff(212,axiom,(![E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_non_empty_fm_and_ep')).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.19/0.47 tff(215,plain,(
% 0.19/0.47 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.19/0.47 inference(skolemize,[status(sab)],[214])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[216, 206])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 ((subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))) <=> ((~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | ((~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[220, 218])).
% 0.19/0.47 tff(222,plain,
% 0.19/0.47 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(223,plain,
% 0.19/0.47 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.47 tff(224,plain,
% 0.19/0.47 (subpopulations(first_movers, efficient_producers, E!1, T!0) | (~greater(cardinality_at_time(first_movers, T!0), zero)) | (~greater(cardinality_at_time(efficient_producers, T!0), zero))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[223, 217, 13, 115])).
% 0.19/0.47 tff(225,plain,
% 0.19/0.47 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[224, 204, 133])).
% 0.19/0.47 tff(226,plain,
% 0.19/0.47 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(227,plain,
% 0.19/0.47 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[226])).
% 0.19/0.47 tff(228,plain,
% 0.19/0.47 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(229,plain,
% 0.19/0.47 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[228])).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(231,plain,
% 0.19/0.47 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) <=> (environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)))), rewrite(((environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(232,plain,
% 0.19/0.47 (![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[231])).
% 0.19/0.47 tff(233,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(growth_rate(S2, T), growth_rate(S1, T))) => selection_favors(S2, S1, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp1_high_growth_rates')).
% 0.19/0.47 tff(234,plain,
% 0.19/0.47 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.19/0.47 tff(235,plain,
% 0.19/0.47 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.19/0.47 tff(236,plain,(
% 0.19/0.47 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(growth_rate(S2, T), growth_rate(S1, T)))) | selection_favors(S2, S1, T))),
% 0.19/0.47 inference(skolemize,[status(sab)],[235])).
% 0.19/0.47 tff(237,plain,
% 0.19/0.47 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.19/0.47 tff(238,plain,
% 0.19/0.47 (![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[237, 227])).
% 0.19/0.47 tff(239,plain,
% 0.19/0.47 (((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(240,plain,
% 0.19/0.47 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | (selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(241,plain,
% 0.19/0.47 ((~![E: $i, S1: $i, S2: $i, T: $i] : (selection_favors(S2, S1, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(growth_rate(S2, T), growth_rate(S1, T))))) | selection_favors(efficient_producers, first_movers, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.19/0.47 tff(242,plain,
% 0.19/0.47 (~greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[241, 238, 13, 155, 225])).
% 0.19/0.47 tff(243,plain,
% 0.19/0.47 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | ((~greater(T!0, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | (~greater(T!0, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(244,plain,
% 0.19/0.47 ((greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(T!0, critical_point(E!1)))) <=> ((~greater(T!0, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(245,plain,
% 0.19/0.47 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | (greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(T!0, critical_point(E!1))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | ((~greater(T!0, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[244])).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 (((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | (greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(T!0, critical_point(E!1))))) <=> ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | (~greater(T!0, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[245, 243])).
% 0.19/0.48 tff(247,plain,
% 0.19/0.48 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | (greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(T!0, critical_point(E!1))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(248,plain,
% 0.19/0.48 ((~![T: $i] : (greater(growth_rate(efficient_producers, T), growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!1, T)) | (~greater(T, critical_point(E!1))))) | (~greater(T!0, critical_point(E!1))) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater(growth_rate(efficient_producers, T!0), growth_rate(first_movers, T!0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.19/0.48 tff(249,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[248, 64, 225, 242, 45])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------