TSTP Solution File: MGT037+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT037+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 05:22:05 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : MGT037+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:33:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(constant_type, type, (
% 0.20/0.40 constant: $i > $o)).
% 0.20/0.40 tff(number_of_organizations_type, type, (
% 0.20/0.40 number_of_organizations: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_To_0_type, type, (
% 0.20/0.40 tptp_fun_To_0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_E_3_type, type, (
% 0.20/0.40 tptp_fun_E_3: $i)).
% 0.20/0.40 tff(tptp_fun_T_2_type, type, (
% 0.20/0.40 tptp_fun_T_2: $i)).
% 0.20/0.40 tff(resources_type, type, (
% 0.20/0.40 resources: ( $i * $i ) > $i)).
% 0.20/0.40 tff(greater_type, type, (
% 0.20/0.40 greater: ( $i * $i ) > $o)).
% 0.20/0.40 tff(equilibrium_type, type, (
% 0.20/0.40 equilibrium: $i > $i)).
% 0.20/0.40 tff(decreases_type, type, (
% 0.20/0.40 decreases: $i > $o)).
% 0.20/0.40 tff(growth_rate_type, type, (
% 0.20/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X_1_type, type, (
% 0.20/0.40 tptp_fun_X_1: ( $i * $i ) > $i)).
% 0.20/0.40 tff(zero_type, type, (
% 0.20/0.40 zero: $i)).
% 0.20/0.40 tff(cardinality_at_time_type, type, (
% 0.20/0.40 cardinality_at_time: ( $i * $i ) > $i)).
% 0.20/0.40 tff(subpopulation_type, type, (
% 0.20/0.40 subpopulation: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(efficient_producers_type, type, (
% 0.20/0.40 efficient_producers: $i)).
% 0.20/0.40 tff(first_movers_type, type, (
% 0.20/0.40 first_movers: $i)).
% 0.20/0.40 tff(resilience_type, type, (
% 0.20/0.40 resilience: $i > $i)).
% 0.20/0.40 tff(in_environment_type, type, (
% 0.20/0.40 in_environment: ( $i * $i ) > $o)).
% 0.20/0.40 tff(appear_type, type, (
% 0.20/0.40 appear: ( $i * $i ) > $i)).
% 0.20/0.40 tff(greater_or_equal_type, type, (
% 0.20/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.20/0.40 tff(environment_type, type, (
% 0.20/0.40 environment: $i > $o)).
% 0.20/0.40 tff(an_organisation_type, type, (
% 0.20/0.40 an_organisation: $i)).
% 0.20/0.40 tff(1,assumption,(~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))) | (~greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (~greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 ((~![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 ((~![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,axiom,(~![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t6')).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (~![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))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~![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))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![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))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![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))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![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))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (~![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))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~![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))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.20/0.40 tff(14,plain,(
% 0.20/0.40 ~((~(environment(E!3) & in_environment(E!3, T!2) & greater_or_equal(T!2, appear(efficient_producers, E!3)))) | greater(cardinality_at_time(efficient_producers, T!2), zero))),
% 0.20/0.40 inference(skolemize,[status(sab)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (~greater(cardinality_at_time(efficient_producers, T!2), zero)),
% 0.20/0.40 inference(or_elim,[status(thm)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (environment(E!3) & in_environment(E!3, T!2) & greater_or_equal(T!2, appear(efficient_producers, E!3))),
% 0.20/0.40 inference(or_elim,[status(thm)],[14])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (in_environment(E!3, T!2)),
% 0.20/0.40 inference(and_elim,[status(thm)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (environment(E!3)),
% 0.20/0.40 inference(and_elim,[status(thm)],[16])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (^[E: $i, T: $i] : refl(((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T))) <=> ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), (((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | ((~environment(E)) | (~in_environment(E, T)))))), rewrite(((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | ((~environment(E)) | (~in_environment(E, T)))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))), (((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))) <=> ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))) <=> ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (^[E: $i, T: $i] : rewrite(((environment(E) & in_environment(E, T)) => ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.41 tff(26,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_efficient_producers_exist')).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.41 tff(29,plain,(
% 0.20/0.41 ![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))) <=> ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (((cardinality_at_time(efficient_producers, T!2) = zero) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (~environment(E!3)) | (~in_environment(E!3, T!2))) <=> (greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((cardinality_at_time(efficient_producers, T!2) = zero) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))) <=> ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | (greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((cardinality_at_time(efficient_producers, T!2) = zero) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))) <=> ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[34, 32])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | ((cardinality_at_time(efficient_producers, T!2) = zero) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (~environment(E!3)) | (~in_environment(E!3, T!2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~![E: $i, T: $i] : ((cardinality_at_time(efficient_producers, T) = zero) | greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)))) | greater(cardinality_at_time(efficient_producers, T!2), zero) | (cardinality_at_time(efficient_producers, T!2) = zero) | (~environment(E!3)) | (~in_environment(E!3, T!2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (cardinality_at_time(efficient_producers, T!2) = zero),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[37, 31, 18, 17, 15])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (greater_or_equal(T!2, appear(efficient_producers, E!3))),
% 0.20/0.41 inference(and_elim,[status(thm)],[16])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (^[E: $i, T: $i] : refl(((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero)) <=> (~((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))))), ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) <=> (~(~((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))))))), rewrite((~(~((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)))), ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))))), rewrite((greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))) <=> (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))), (((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | (greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))) <=> (((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))))), rewrite((((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero))) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))), (((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | (greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))) <=> ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | (greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))) <=> ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) <=> (environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))), quant_intro(proof_bind(^[To: $i] : trans(monotonicity(rewrite(((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) <=> (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To))), ((((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))) <=> ((greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))))), rewrite(((greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))) <=> (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))), ((((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))) <=> (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))))), (?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))) <=> ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))), ((((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To)))) <=> ((environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))))), rewrite(((environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To)))) <=> ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))), ((((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To)))) <=> ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![E: $i, T: $i] : (((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To)))) <=> ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42 tff(47,axiom,(![E: $i, T: $i] : (((environment(E) & greater_or_equal(T, appear(efficient_producers, E))) & (cardinality_at_time(efficient_producers, T) = zero)) => ?[To: $i] : (((greater(To, appear(efficient_producers, E)) & in_environment(E, To)) & greater(T, To)) & greater(zero, growth_rate(efficient_producers, To))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_previous_negative_growth')).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & in_environment(E, To) & greater(T, To) & greater(zero, growth_rate(efficient_producers, To))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.42 tff(50,plain,(
% 0.20/0.42 ![E: $i, T: $i] : ((~(environment(E) & greater_or_equal(T, appear(efficient_producers, E)) & (cardinality_at_time(efficient_producers, T) = zero))) | (greater(tptp_fun_To_0(T, E), appear(efficient_producers, E)) & in_environment(E, tptp_fun_To_0(T, E)) & greater(T, tptp_fun_To_0(T, E)) & greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[49])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (((~![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))) | ((~environment(E!3)) | (~greater_or_equal(T!2, appear(efficient_producers, E!3))) | (~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))) | (~environment(E!3)) | (~greater_or_equal(T!2, appear(efficient_producers, E!3))) | (~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 ((~![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))) | ((~environment(E!3)) | (~greater_or_equal(T!2, appear(efficient_producers, E!3))) | (~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ((~![E: $i, T: $i] : ((~environment(E)) | (~greater_or_equal(T, appear(efficient_producers, E))) | (~(cardinality_at_time(efficient_producers, T) = zero)) | (~((~greater(tptp_fun_To_0(T, E), appear(efficient_producers, E))) | (~in_environment(E, tptp_fun_To_0(T, E))) | (~greater(T, tptp_fun_To_0(T, E))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T, E)))))))) | (~environment(E!3)) | (~greater_or_equal(T!2, appear(efficient_producers, E!3))) | (~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~(cardinality_at_time(efficient_producers, T!2) = zero)) | (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 52, 18, 39])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (~((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[56, 38])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))) | greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~greater(tptp_fun_To_0(T!2, E!3), appear(efficient_producers, E!3))) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(T!2, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))) | in_environment(E!3, tptp_fun_To_0(T!2, E!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (in_environment(E!3, tptp_fun_To_0(T!2, E!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))) <=> ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))) <=> (~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))), ((~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))) <=> (~(~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))))), rewrite((~(~(greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))) <=> (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))), ((~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1)))) <=> (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1)))))), (((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ((~greater(zero, growth_rate(S2, T))) | (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))))), rewrite(((~greater(zero, growth_rate(S2, T))) | (greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) <=> ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))), (((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | (~(environment(E) & in_environment(E, T) & (~greater(zero, growth_rate(S1, T))) & greater(resilience(S2), resilience(S1))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (^[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)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.42 tff(69,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')).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.43 tff(72,plain,(
% 0.20/0.43 ![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)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[71])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (((~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3))))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | ((~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~greater(zero, growth_rate(S2, T))) | greater(zero, growth_rate(S1, T)) | (~environment(E)) | (~in_environment(E, T)) | (~greater(resilience(S2), resilience(S1))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) | (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[80, 74, 18, 61, 59, 3])).
% 0.20/0.43 tff(82,assumption,(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers), introduced(assumption)).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)) = resilience(first_movers)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3))) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[84])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(87,axiom,(greater(resilience(efficient_producers), resilience(first_movers))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a2')).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (greater(resilience(efficient_producers), resilience(first_movers))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.20/0.43 tff(90,assumption,(~greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))), introduced(assumption)).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.43 tff(92,plain,((~(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers)) | greater(resilience(efficient_producers), resilience(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (~(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[92, 81])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))) | greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[94, 1])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))) | subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[96, 1])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (^[E: $i, X: $i, T: $i] : refl(((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))) <=> ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))) <=> ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (^[E: $i, X: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) <=> (~((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))), ((~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) <=> (~(~((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))))), rewrite((~(~((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))) <=> ((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))), ((~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))) <=> ((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero))))), (((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))) <=> ((X = first_movers) | (X = efficient_producers) | ((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))))), rewrite(((X = first_movers) | (X = efficient_producers) | ((~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) <=> ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))), (((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))) <=> ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))) <=> ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)))) <=> ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (^[E: $i, X: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) <=> (environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))), ((((environment(E) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => ((X = efficient_producers) | (X = first_movers))) <=> ((environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) => ((X = efficient_producers) | (X = first_movers))))), rewrite(((environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) => ((X = efficient_producers) | (X = first_movers))) <=> ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))), ((((environment(E) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => ((X = efficient_producers) | (X = first_movers))) <=> ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (![E: $i, X: $i, T: $i] : (((environment(E) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => ((X = efficient_producers) | (X = first_movers))) <=> ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.44 tff(105,axiom,(![E: $i, X: $i, T: $i] : (((environment(E) & subpopulation(X, E, T)) & greater(cardinality_at_time(X, T), zero)) => ((X = efficient_producers) | (X = first_movers)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a9')).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.44 tff(108,plain,(
% 0.20/0.44 ![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~(environment(E) & subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[107])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers))) <=> ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero))) <=> ((~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)))) <=> ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)))) <=> ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers))),
% 0.20/0.44 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | ((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 ((~![E: $i, X: $i, T: $i] : ((X = first_movers) | (X = efficient_producers) | (~environment(E)) | (~subpopulation(X, E, T)) | (~greater(cardinality_at_time(X, T), zero)))) | (~environment(E!3)) | (~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 ((tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = first_movers) | (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 110, 18, 97, 95])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3) = efficient_producers),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[117, 93])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)) = growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))) <=> greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))) <=> greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.44 inference(symmetry,[status(thm)],[120])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[59, 121])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[3, 122])).
% 0.20/0.44 tff(124,plain,((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (^[E: $i, T: $i] : refl((decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> ![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T)))) <=> (~(decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) <=> (~(~(decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~(decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))))), rewrite((subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))) <=> (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))), (((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | (subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> ((decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))))), rewrite(((decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T))) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))), (((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | (subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | (subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T))))) <=> ![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) <=> (environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))), quant_intro(proof_bind(^[X: $i] : rewrite(((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T)))) <=> (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))), (?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T)))) <=> ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))), ((((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T))))) <=> ((environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T))))))), rewrite(((environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T))))) <=> ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))), ((((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T))))) <=> ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.45 tff(132,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & (~decreases(number_of_organizations(E, T)))) => ?[X: $i] : ((subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero)) & (~greater(zero, growth_rate(X, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_non_decreasing')).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | ?[X: $i] : (subpopulation(X, E, T) & greater(cardinality_at_time(X, T), zero) & (~greater(zero, growth_rate(X, T)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.20/0.45 tff(135,plain,(
% 0.20/0.45 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & (~decreases(number_of_organizations(E, T))))) | (subpopulation(tptp_fun_X_1(T, E), E, T) & greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero) & (~greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[134])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))) <=> ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))) <=> ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))) <=> ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[140, 138])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 ((~![E: $i, T: $i] : (decreases(number_of_organizations(E, T)) | (~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(tptp_fun_X_1(T, E), E, T)) | (~greater(cardinality_at_time(tptp_fun_X_1(T, E), T), zero)) | greater(zero, growth_rate(tptp_fun_X_1(T, E), T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(cardinality_at_time(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)), zero)) | greater(zero, growth_rate(tptp_fun_X_1(tptp_fun_To_0(T!2, E!3), E!3), tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[143, 137, 18, 61])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[144, 124])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (^[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((((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))) <=> (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))), (((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> (((~environment(E)) | (~in_environment(E, T))) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))))), rewrite((((~environment(E)) | (~in_environment(E, T))) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))), (((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[148])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T)))) <=> (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))), (((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ((environment(E) & in_environment(E, T)) => (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))))), rewrite(((environment(E) & in_environment(E, T)) => (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T)))))) <=> ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))), (((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.46 tff(153,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => ((decreases(resources(E, T)) => (~decreases(number_of_organizations(E, T)))) & (constant(resources(E, T)) => constant(number_of_organizations(E, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a6')).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.20/0.46 tff(156,plain,(
% 0.20/0.46 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T)))) & (constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[155])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~((~decreases(number_of_organizations(E, T))) | (~decreases(resources(E, T))))) | (~(constant(number_of_organizations(E, T)) | (~constant(resources(E, T))))))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (~((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[161, 158, 18, 61])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 (((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))))) | ((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 ((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 ((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 ((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[166, 145])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (^[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))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (![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)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), rewrite((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)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (![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)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.46 tff(175,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_subpopulations')).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.20/0.46 tff(178,plain,(
% 0.20/0.46 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T))) | (subpopulation(first_movers, E, T) & subpopulation(efficient_producers, E, T)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[177])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[179, 169])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~((~subpopulation(first_movers, E, T)) | (~subpopulation(efficient_producers, E, T)))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (~((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[183, 180, 18, 61])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 (((~subpopulation(first_movers, E!3, tptp_fun_To_0(T!2, E!3))) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3)))) | subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (^[S: $i, T: $i] : refl(((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))) <=> ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))) <=> ![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[187])).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))) <=> ![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 (^[S: $i, T: $i] : rewrite(((cardinality_at_time(S, T) = zero) => (~greater(zero, growth_rate(S, T)))) <=> ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 (![S: $i, T: $i] : ((cardinality_at_time(S, T) = zero) => (~greater(zero, growth_rate(S, T)))) <=> ![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[190])).
% 0.20/0.47 tff(192,axiom,(![S: $i, T: $i] : ((cardinality_at_time(S, T) = zero) => (~greater(zero, growth_rate(S, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_empty_not_decreasing')).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.20/0.47 tff(195,plain,(
% 0.20/0.47 ![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[194])).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 (![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (((~![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))) | ((~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))) <=> ((~![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))) | (~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 ((~![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))) | ((~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 ((~![S: $i, T: $i] : ((~(cardinality_at_time(S, T) = zero)) | (~greater(zero, growth_rate(S, T))))) | (~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)) | (~greater(zero, growth_rate(efficient_producers, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 (~(cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[199, 196, 59])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 (^[E: $i, T: $i, X: $i] : refl(((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))) <=> ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 (![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))) <=> ![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[201])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 (^[E: $i, T: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))), ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))), ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))))), (((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))), (((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> ![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[203])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 (![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero)) <=> ![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 (^[E: $i, T: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) <=> (environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero))), ((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) <=> ((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)))), rewrite(((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) <=> (environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))), ((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) <=> (environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T)))), (((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)) <=> ((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)))), rewrite(((environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)) <=> ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))), (((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)) <=> ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 (![E: $i, T: $i, X: $i] : ((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero)) <=> ![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[206])).
% 0.20/0.47 tff(208,axiom,(![E: $i, T: $i, X: $i] : ((((environment(E) & in_environment(E, T)) & (number_of_organizations(E, T) = zero)) & subpopulation(X, E, T)) => (cardinality_at_time(X, T) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_no_members')).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 (![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 (![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.20/0.47 tff(211,plain,(
% 0.20/0.47 ![E: $i, T: $i, X: $i] : ((~(environment(E) & in_environment(E, T) & (number_of_organizations(E, T) = zero) & subpopulation(X, E, T))) | (cardinality_at_time(X, T) = zero))),
% 0.20/0.47 inference(skolemize,[status(sab)],[210])).
% 0.20/0.47 tff(212,plain,
% 0.20/0.47 (![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.20/0.47 tff(213,plain,
% 0.20/0.47 (![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[212, 202])).
% 0.20/0.47 tff(214,plain,
% 0.20/0.47 (((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)))) <=> ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(215,plain,
% 0.20/0.47 (((cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3)))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 (((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.47 tff(217,plain,
% 0.20/0.47 (((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[216, 214])).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | ((cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 ((~![E: $i, T: $i, X: $i] : ((cardinality_at_time(X, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~(number_of_organizations(E, T) = zero)) | (~subpopulation(X, E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (cardinality_at_time(efficient_producers, tptp_fun_To_0(T!2, E!3)) = zero) | (~subpopulation(efficient_producers, E!3, tptp_fun_To_0(T!2, E!3))) | (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.47 tff(220,plain,
% 0.20/0.47 (~(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[219, 213, 18, 61, 200, 186])).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 (^[E: $i, T: $i] : refl(((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))) <=> ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))) <=> ![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))), ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))), ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))))), (((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))), (((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> ![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[223])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) <=> (environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))), ((((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)) <=> ((environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)))), rewrite(((environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)) <=> ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))), ((((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)) <=> ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.47 tff(228,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(appear(an_organisation, E), T)) => (number_of_organizations(E, T) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_start_of_organizations')).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.20/0.48 tff(231,plain,(
% 0.20/0.48 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(appear(an_organisation, E), T))) | (number_of_organizations(E, T) = zero))),
% 0.20/0.48 inference(skolemize,[status(sab)],[230])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[232, 222])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 (((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[235])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[236, 234])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | ((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 ((~![E: $i, T: $i] : ((number_of_organizations(E, T) = zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater(appear(an_organisation, E), T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 ((number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)) = zero) | (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[239, 233, 18, 61])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 (~greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[240, 220])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (^[E: $i, T: $i] : refl((greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T))) <=> ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[242])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T)) <=> (~((~environment(E)) | (~in_environment(E, T))))), ((~(environment(E) & in_environment(E, T))) <=> (~(~((~environment(E)) | (~in_environment(E, T))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T))))) <=> ((~environment(E)) | (~in_environment(E, T)))), ((~(environment(E) & in_environment(E, T))) <=> ((~environment(E)) | (~in_environment(E, T))))), ((greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T)))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | ((~environment(E)) | (~in_environment(E, T)))))), rewrite((greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | ((~environment(E)) | (~in_environment(E, T)))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))), ((greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T)))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T)))) <=> ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[244])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T)))) <=> ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (^[E: $i, T: $i] : trans(monotonicity(rewrite((greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T)) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)))), (((environment(E) & in_environment(E, T)) => (greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T))) <=> ((environment(E) & in_environment(E, T)) => (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)))))), rewrite(((environment(E) & in_environment(E, T)) => (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))), (((environment(E) & in_environment(E, T)) => (greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T))) <=> (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T))) <=> ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[247])).
% 0.20/0.48 tff(249,axiom,(![E: $i, T: $i] : ((environment(E) & in_environment(E, T)) => (greater_or_equal(T, appear(an_organisation, E)) | greater(appear(an_organisation, E), T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_environment_inequality')).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.20/0.48 tff(252,plain,(
% 0.20/0.48 ![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~(environment(E) & in_environment(E, T))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[251])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[252, 245])).
% 0.20/0.48 tff(254,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[253, 243])).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))) <=> ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(256,plain,
% 0.20/0.48 ((greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3)))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))))) <=> ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[257, 255])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3)) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 ((~![E: $i, T: $i] : (greater(appear(an_organisation, E), T) | greater_or_equal(T, appear(an_organisation, E)) | (~environment(E)) | (~in_environment(E, T)))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 (greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)) | greater(appear(an_organisation, E!3), tptp_fun_To_0(T!2, E!3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[260, 254, 18, 61])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 (greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[261, 241])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (^[E: $i, T: $i] : refl((greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))) <=> ![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[263])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E))) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[265])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) <=> (environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)) <=> ((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[268])).
% 0.20/0.48 tff(270,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(an_organisation, E))) => greater(number_of_organizations(E, T), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a1')).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.20/0.48 tff(273,plain,(
% 0.20/0.48 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(an_organisation, E)))) | greater(number_of_organizations(E, T), zero))),
% 0.20/0.48 inference(skolemize,[status(sab)],[272])).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.20/0.48 tff(275,plain,
% 0.20/0.48 (![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[274, 264])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 ((greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(278,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[277])).
% 0.20/0.48 tff(279,plain,
% 0.20/0.48 (((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))) <=> ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[278, 276])).
% 0.20/0.49 tff(280,plain,
% 0.20/0.49 ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(281,plain,
% 0.20/0.49 ((~![E: $i, T: $i] : (greater(number_of_organizations(E, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(an_organisation, E))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.20/0.49 tff(282,plain,
% 0.20/0.49 (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero) | (~greater_or_equal(tptp_fun_To_0(T!2, E!3), appear(an_organisation, E!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[281, 275, 18, 61])).
% 0.20/0.49 tff(283,plain,
% 0.20/0.49 (greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[282, 262])).
% 0.20/0.49 tff(284,plain,
% 0.20/0.49 (^[E: $i, T: $i] : refl(((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(285,plain,
% 0.20/0.49 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[284])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))), ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)))), ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))))), trans(monotonicity(rewrite(((~greater(equilibrium(E), T)) | decreases(resources(E, T))) <=> ((~greater(equilibrium(E), T)) | decreases(resources(E, T)))), ((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))) <=> (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))), rewrite((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))) <=> (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))), ((((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))) <=> (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))), (((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero))) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))), (((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[286])).
% 0.20/0.49 tff(288,plain,
% 0.20/0.49 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(289,plain,
% 0.20/0.49 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))), rewrite(((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T)))) <=> (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))), ((((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) => (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))))), rewrite(((environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero)) => (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T)))) <=> ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))), ((((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T))))) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[289])).
% 0.20/0.49 tff(291,axiom,(![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater(number_of_organizations(E, T), zero)) => ((greater(equilibrium(E), T) => decreases(resources(E, T))) & ((~greater(equilibrium(E), T)) => constant(resources(E, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a3')).
% 0.20/0.49 tff(292,plain,
% 0.20/0.49 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.49 tff(293,plain,
% 0.20/0.49 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.20/0.49 tff(294,plain,(
% 0.20/0.49 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(number_of_organizations(E, T), zero))) | (((~greater(equilibrium(E), T)) | decreases(resources(E, T))) & (constant(resources(E, T)) | greater(equilibrium(E), T))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[293])).
% 0.20/0.49 tff(295,plain,
% 0.20/0.49 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.20/0.49 tff(296,plain,
% 0.20/0.49 (![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[295, 285])).
% 0.20/0.49 tff(297,plain,
% 0.20/0.49 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(298,plain,
% 0.20/0.49 (((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~((~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))) | (~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))) <=> ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~((~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))) | (~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[298])).
% 0.20/0.49 tff(300,plain,
% 0.20/0.49 (((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~((~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))) | (~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[299, 297])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | ((~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~((~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))))) | (~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(302,plain,
% 0.20/0.49 ((~![E: $i, T: $i] : ((~environment(E)) | (~in_environment(E, T)) | (~greater(number_of_organizations(E, T), zero)) | (~((~((~greater(equilibrium(E), T)) | decreases(resources(E, T)))) | (~(constant(resources(E, T)) | greater(equilibrium(E), T))))))) | (~environment(E!3)) | (~in_environment(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.20/0.49 tff(303,plain,
% 0.20/0.49 ((~greater(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)), zero)) | (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[302, 296, 18, 61])).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 (~((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[303, 283])).
% 0.20/0.49 tff(305,plain,
% 0.20/0.49 (((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))) | (decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(306,plain,
% 0.20/0.49 (decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[305, 304])).
% 0.20/0.49 tff(307,plain,
% 0.20/0.49 ((~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))))) | decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(308,plain,
% 0.20/0.49 (decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[307, 306])).
% 0.20/0.49 tff(309,plain,
% 0.20/0.49 (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[308, 167])).
% 0.20/0.49 tff(310,plain,
% 0.20/0.49 (((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | (~(decreases(resources(E!3, tptp_fun_To_0(T!2, E!3))) | (~greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))))) | (constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(311,plain,
% 0.20/0.49 (constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[310, 304])).
% 0.20/0.49 tff(312,plain,
% 0.20/0.49 ((~(constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3)))) | constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(313,plain,
% 0.20/0.49 (constant(resources(E!3, tptp_fun_To_0(T!2, E!3))) | greater(equilibrium(E!3), tptp_fun_To_0(T!2, E!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[312, 311])).
% 0.20/0.49 tff(314,plain,
% 0.20/0.50 (constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[313, 309])).
% 0.20/0.50 tff(315,plain,
% 0.20/0.50 (((~((~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | (~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))))) | (constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(316,plain,
% 0.20/0.50 (constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[315, 162])).
% 0.20/0.50 tff(317,plain,
% 0.20/0.50 ((~(constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3)))))) | constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(318,plain,
% 0.20/0.50 (constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))) | (~constant(resources(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[317, 316])).
% 0.20/0.50 tff(319,plain,
% 0.20/0.50 (constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[318, 314])).
% 0.20/0.50 tff(320,plain,
% 0.20/0.50 (^[X: $i] : refl(((~constant(X)) | (~decreases(X))) <=> ((~constant(X)) | (~decreases(X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(321,plain,
% 0.20/0.50 (![X: $i] : ((~constant(X)) | (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[320])).
% 0.20/0.50 tff(322,plain,
% 0.20/0.50 (![X: $i] : ((~constant(X)) | (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(323,plain,
% 0.20/0.50 (^[X: $i] : rewrite((constant(X) => (~decreases(X))) <=> ((~constant(X)) | (~decreases(X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(324,plain,
% 0.20/0.50 (![X: $i] : (constant(X) => (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[323])).
% 0.20/0.50 tff(325,axiom,(![X: $i] : (constant(X) => (~decreases(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_constant_not_decrease')).
% 0.20/0.50 tff(326,plain,
% 0.20/0.50 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.20/0.50 tff(327,plain,
% 0.20/0.50 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.20/0.50 tff(328,plain,(
% 0.20/0.50 ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[327])).
% 0.20/0.50 tff(329,plain,
% 0.20/0.50 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[328, 321])).
% 0.20/0.50 tff(330,plain,
% 0.20/0.50 (((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | ((~constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))))) <=> ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | (~constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(331,plain,
% 0.20/0.50 ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | ((~constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(332,plain,
% 0.20/0.50 ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | (~constant(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3)))) | (~decreases(number_of_organizations(E!3, tptp_fun_To_0(T!2, E!3))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.20/0.50 tff(333,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[332, 329, 145, 319])).
% 0.20/0.50 % SZS output end Proof
%------------------------------------------------------------------------------