TSTP Solution File: MGT036+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 05:22:04 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 02:39:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(greater_type, type, (
% 0.12/0.38 greater: ( $i * $i ) > $o)).
% 0.12/0.38 tff(growth_rate_type, type, (
% 0.12/0.38 growth_rate: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_T_0_type, type, (
% 0.12/0.38 tptp_fun_T_0: $i)).
% 0.12/0.38 tff(efficient_producers_type, type, (
% 0.12/0.38 efficient_producers: $i)).
% 0.12/0.38 tff(zero_type, type, (
% 0.12/0.38 zero: $i)).
% 0.12/0.38 tff(greater_or_equal_type, type, (
% 0.12/0.38 greater_or_equal: ( $i * $i ) > $o)).
% 0.12/0.38 tff(first_movers_type, type, (
% 0.12/0.38 first_movers: $i)).
% 0.12/0.38 tff(outcompetes_type, type, (
% 0.12/0.38 outcompetes: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(subpopulations_type, type, (
% 0.12/0.38 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_E_1_type, type, (
% 0.12/0.38 tptp_fun_E_1: $i)).
% 0.12/0.38 tff(environment_type, type, (
% 0.12/0.38 environment: $i > $o)).
% 0.12/0.38 tff(in_environment_type, type, (
% 0.12/0.38 in_environment: ( $i * $i ) > $o)).
% 0.12/0.38 tff(resilience_type, type, (
% 0.12/0.38 resilience: $i > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))) <=> (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~outcompetes(first_movers, efficient_producers, T)))) <=> (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => (~outcompetes(first_movers, efficient_producers, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t5')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![E: $i, T: $i] : ((~outcompetes(first_movers, efficient_producers, T)) | (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.38 tff(11,plain,(
% 0.12/0.38 ~((~outcompetes(first_movers, efficient_producers, T!0)) | (~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.12/0.38 inference(or_elim,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (environment(E!1)),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[E: $i, T: $i] : refl((subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.38 tff(22,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => subpopulations(efficient_producers, first_movers, E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_symmetry_of_FM_and_EP')).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.12/0.38 tff(25,plain,(
% 0.12/0.38 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | subpopulations(efficient_producers, first_movers, E, T))),
% 0.12/0.38 inference(skolemize,[status(sab)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.12/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~![E: $i, T: $i] : (subpopulations(efficient_producers, first_movers, E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 27, 14, 13])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T)) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T))))), rewrite(((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T))) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T))))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T))) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.39 tff(42,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2')).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.12/0.39 tff(45,plain,(
% 0.12/0.39 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[44])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | ((~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) <=> outcompetes(first_movers, efficient_producers, T!0)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | ((~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | ((~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater(zero, growth_rate(S1, T))) | (~greater_or_equal(growth_rate(S2, T), zero)))) <=> outcompetes(S2, S1, T)))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | ((~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) <=> outcompetes(first_movers, efficient_producers, T!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) <=> outcompetes(first_movers, efficient_producers, T!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 47, 14, 34])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (outcompetes(first_movers, efficient_producers, T!0)),
% 0.19/0.39 inference(or_elim,[status(thm)],[11])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~((~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) <=> outcompetes(first_movers, efficient_producers, T!0))) | (~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) | (~outcompetes(first_movers, efficient_producers, T!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~((~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))) <=> outcompetes(first_movers, efficient_producers, T!0))) | (~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (~((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) | greater(zero, growth_rate(efficient_producers, T!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (greater(zero, growth_rate(efficient_producers, T!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (^[E: $i, T: $i] : refl((in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)))), rewrite((((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))), (((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (^[E: $i, T: $i] : rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T)) <=> ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.39 tff(65,axiom,(![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => in_environment(E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_time_point_occur')).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.39 tff(68,plain,(
% 0.19/0.39 ![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | in_environment(E, T))),
% 0.19/0.39 inference(skolemize,[status(sab)],[67])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0))),
% 0.19/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (in_environment(E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![E: $i, T: $i] : (in_environment(E, T) | (~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | in_environment(E!1, T!0)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (in_environment(E!1, T!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 70, 14, 13])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T)))) <=> ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite((((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite((((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.40 tff(85,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) => greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_growth_rate_relationships')).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.40 tff(88,plain,(
% 0.19/0.40 ![E: $i, S1: $i, S2: $i, T: $i] : (((~(environment(E) & subpopulations(S1, S2, E, T))) | greater_or_equal(growth_rate(S1, T), zero)) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[87])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))) | (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) <=> (~greater(zero, growth_rate(first_movers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))) | (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) <=> (~greater(zero, growth_rate(first_movers, T!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (((greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> (~greater(zero, growth_rate(first_movers, T!0)))) <=> (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) <=> (~greater(zero, growth_rate(first_movers, T!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))) | ((greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> (~greater(zero, growth_rate(first_movers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))) | (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) <=> (~greater(zero, growth_rate(first_movers, T!0)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))) | ((greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> (~greater(zero, growth_rate(first_movers, T!0))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))) | (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) <=> (~greater(zero, growth_rate(first_movers, T!0)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[93, 91])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))) | ((greater_or_equal(growth_rate(first_movers, T!0), zero) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> (~greater(zero, growth_rate(first_movers, T!0))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((greater_or_equal(growth_rate(S1, T), zero) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (~greater(zero, growth_rate(S1, T))))) | (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) <=> (~greater(zero, growth_rate(first_movers, T!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) <=> (~greater(zero, growth_rate(first_movers, T!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[96, 90])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (((~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))) | greater_or_equal(growth_rate(first_movers, T!0), zero)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (greater_or_equal(growth_rate(first_movers, T!0), zero)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 55])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater_or_equal(growth_rate(first_movers, T!0), zero))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((~(((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero)) <=> (~greater(zero, growth_rate(first_movers, T!0))))) | (~((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | greater_or_equal(growth_rate(first_movers, T!0), zero))) | (~greater(zero, growth_rate(first_movers, T!0)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (~greater(zero, growth_rate(first_movers, T!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[102, 101, 97])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(105,axiom,(greater(resilience(efficient_producers), resilience(first_movers))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a2')).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (greater(resilience(efficient_producers), resilience(first_movers))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))) <=> (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) <=> (~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))), ((~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))) <=> (~(~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))))), rewrite((~(~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))) <=> (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))), ((~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))) <=> (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))), (((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ((~greater(zero, growth_rate(S2, T))) | (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))))), rewrite(((~greater(zero, growth_rate(S2, T))) | (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) <=> (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))), (((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))))), ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> ((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))))), rewrite(((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))), ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) <=> (environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))), (((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))))), rewrite(((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))), (((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.41 tff(114,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & (~greater(zero, growth_rate(S1, T)))) & greater(resilience(S2), resilience(S1))) => (~greater(zero, growth_rate(S2, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a12')).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.41 tff(117,plain,(
% 0.19/0.41 ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[116])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[118, 108])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 ((greater(zero, growth_rate(first_movers, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers)))) <=> ((~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (greater(zero, growth_rate(first_movers, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (greater(zero, growth_rate(first_movers, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (greater(zero, growth_rate(first_movers, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~environment(E!1)) | (~in_environment(E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![E: $i, S1: $i, S2: $i, T: $i] : (greater(zero, growth_rate(S1, T)) | (~greater(zero, growth_rate(S2, T))) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!1)) | greater(zero, growth_rate(first_movers, T!0)) | (~in_environment(E!1, T!0)) | (~greater(zero, growth_rate(efficient_producers, T!0))) | (~greater(resilience(efficient_producers), resilience(first_movers)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 119, 106, 14, 103, 77, 57])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------