TSTP Solution File: MGT027+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:21:57 EDT 2022
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 02:57:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(greater_type, type, (
% 0.18/0.38 greater: ( $i * $i ) > $o)).
% 0.18/0.38 tff(appear_type, type, (
% 0.18/0.38 appear: ( $i * $i ) > $i)).
% 0.18/0.38 tff(tptp_fun_E_2_type, type, (
% 0.18/0.38 tptp_fun_E_2: $i)).
% 0.18/0.38 tff(efficient_producers_type, type, (
% 0.18/0.38 efficient_producers: $i)).
% 0.18/0.38 tff(tptp_fun_T_0_type, type, (
% 0.18/0.38 tptp_fun_T_0: $i > $i)).
% 0.18/0.38 tff(tptp_fun_To_1_type, type, (
% 0.18/0.38 tptp_fun_To_1: $i > $i)).
% 0.18/0.38 tff(in_environment_type, type, (
% 0.18/0.38 in_environment: ( $i * $i ) > $o)).
% 0.18/0.38 tff(stable_type, type, (
% 0.18/0.38 stable: $i > $o)).
% 0.18/0.38 tff(contracts_from_type, type, (
% 0.18/0.38 contracts_from: ( $i * $i ) > $o)).
% 0.18/0.38 tff(first_movers_type, type, (
% 0.18/0.38 first_movers: $i)).
% 0.18/0.38 tff(environment_type, type, (
% 0.18/0.38 environment: $i > $o)).
% 0.18/0.38 tff(zero_type, type, (
% 0.18/0.38 zero: $i)).
% 0.18/0.38 tff(cardinality_at_time_type, type, (
% 0.18/0.38 cardinality_at_time: ( $i * $i ) > $i)).
% 0.18/0.38 tff(subpopulations_type, type, (
% 0.18/0.38 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.18/0.38 tff(greater_or_equal_type, type, (
% 0.18/0.38 greater_or_equal: ( $i * $i ) > $o)).
% 0.18/0.38 tff(growth_rate_type, type, (
% 0.18/0.38 growth_rate: ( $i * $i ) > $i)).
% 0.18/0.38 tff(1,assumption,(greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))), introduced(assumption)).
% 0.18/0.38 tff(2,assumption,(~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))), introduced(assumption)).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (((environment(E!2) & stable(E!2)) & ![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers)))) <=> (environment(E!2) & stable(E!2) & ![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 ((~(~(environment(E!2) & stable(E!2)))) <=> (environment(E!2) & stable(E!2))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (((~(~(environment(E!2) & stable(E!2)))) & ![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers)))) <=> ((environment(E!2) & stable(E!2)) & ![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[4])).
% 0.18/0.38 tff(6,plain,
% 0.18/0.38 (((~(~(environment(E!2) & stable(E!2)))) & ![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers)))) <=> (environment(E!2) & stable(E!2) & ![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[5, 3])).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 ((~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 ((~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))) <=> (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(9,axiom,(~![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l9')).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (~![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & contracts_from(To, first_movers)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (environment(E!2) & stable(E!2) & ![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (stable(E!2)),
% 0.18/0.39 inference(and_elim,[status(thm)],[17])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (environment(E!2)),
% 0.18/0.39 inference(and_elim,[status(thm)],[17])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (^[E: $i] : refl((in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E))) <=> (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E))) <=> ![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & stable(E)) <=> (~((~environment(E)) | (~stable(E))))), ((~(environment(E) & stable(E))) <=> (~(~((~environment(E)) | (~stable(E))))))), rewrite((~(~((~environment(E)) | (~stable(E))))) <=> ((~environment(E)) | (~stable(E)))), ((~(environment(E) & stable(E))) <=> ((~environment(E)) | (~stable(E))))), (((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E))) <=> (((~environment(E)) | (~stable(E))) | in_environment(E, appear(efficient_producers, E))))), rewrite((((~environment(E)) | (~stable(E))) | in_environment(E, appear(efficient_producers, E))) <=> (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))), (((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E))) <=> (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E))) <=> ![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (^[E: $i] : rewrite(((environment(E) & stable(E)) => in_environment(E, appear(efficient_producers, E))) <=> ((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![E: $i] : ((environment(E) & stable(E)) => in_environment(E, appear(efficient_producers, E))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.39 tff(27,axiom,(![E: $i] : ((environment(E) & stable(E)) => in_environment(E, appear(efficient_producers, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_EP_in_stable_environments')).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.39 tff(30,plain,(
% 0.18/0.39 ![E: $i] : ((~(environment(E) & stable(E))) | in_environment(E, appear(efficient_producers, E)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[29])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (((~![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))) | (in_environment(E!2, appear(efficient_producers, E!2)) | (~environment(E!2)) | (~stable(E!2)))) <=> ((~![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))) | in_environment(E!2, appear(efficient_producers, E!2)) | (~environment(E!2)) | (~stable(E!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 ((~![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))) | (in_environment(E!2, appear(efficient_producers, E!2)) | (~environment(E!2)) | (~stable(E!2)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 ((~![E: $i] : (in_environment(E, appear(efficient_producers, E)) | (~environment(E)) | (~stable(E)))) | in_environment(E!2, appear(efficient_producers, E!2)) | (~environment(E!2)) | (~stable(E!2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (in_environment(E!2, appear(efficient_producers, E!2))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[35, 32, 19, 18])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (^[E: $i, T1: $i, T2: $i] : refl((in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))) <=> (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))) <=> ![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (^[E: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1)) <=> (~((~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))))), ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) <=> (~(~((~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))))))), rewrite((~(~((~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))))) <=> ((~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))), ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) <=> ((~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))))), (((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2)) <=> (((~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))) | in_environment(E, T2)))), rewrite((((~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1))) | in_environment(E, T2)) <=> (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))), (((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2)) <=> (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (![E: $i, T1: $i, T2: $i] : ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2)) <=> ![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (![E: $i, T1: $i, T2: $i] : ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2)) <=> ![E: $i, T1: $i, T2: $i] : ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (^[E: $i, T1: $i, T2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & stable(E)) & in_environment(E, T1)) <=> (environment(E) & stable(E) & in_environment(E, T1))), ((((environment(E) & stable(E)) & in_environment(E, T1)) & greater(T2, T1)) <=> ((environment(E) & stable(E) & in_environment(E, T1)) & greater(T2, T1)))), rewrite(((environment(E) & stable(E) & in_environment(E, T1)) & greater(T2, T1)) <=> (environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))), ((((environment(E) & stable(E)) & in_environment(E, T1)) & greater(T2, T1)) <=> (environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1)))), (((((environment(E) & stable(E)) & in_environment(E, T1)) & greater(T2, T1)) => in_environment(E, T2)) <=> ((environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1)) => in_environment(E, T2)))), rewrite(((environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1)) => in_environment(E, T2)) <=> ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2))), (((((environment(E) & stable(E)) & in_environment(E, T1)) & greater(T2, T1)) => in_environment(E, T2)) <=> ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (![E: $i, T1: $i, T2: $i] : ((((environment(E) & stable(E)) & in_environment(E, T1)) & greater(T2, T1)) => in_environment(E, T2)) <=> ![E: $i, T1: $i, T2: $i] : ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.39 tff(44,axiom,(![E: $i, T1: $i, T2: $i] : ((((environment(E) & stable(E)) & in_environment(E, T1)) & greater(T2, T1)) => in_environment(E, T2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_long_stable_environments')).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (![E: $i, T1: $i, T2: $i] : ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 (![E: $i, T1: $i, T2: $i] : ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.18/0.39 tff(47,plain,(
% 0.18/0.39 ![E: $i, T1: $i, T2: $i] : ((~(environment(E) & stable(E) & in_environment(E, T1) & greater(T2, T1))) | in_environment(E, T2))),
% 0.18/0.39 inference(skolemize,[status(sab)],[46])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | ((~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 ((in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))) <=> ((~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | ((~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[52, 50])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[55, 49, 19, 18, 36, 2, 1])).
% 0.18/0.39 tff(57,plain,(in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[57, 1])).
% 0.18/0.39 tff(59,assumption,(~in_environment(E!2, tptp_fun_To_1(E!2))), introduced(assumption)).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (^[E: $i] : refl(((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (^[E: $i] : rewrite(((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[63, 61])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & stable(E)) <=> (~((~environment(E)) | (~stable(E))))), ((~(environment(E) & stable(E))) <=> (~(~((~environment(E)) | (~stable(E))))))), rewrite((~(~((~environment(E)) | (~stable(E))))) <=> ((~environment(E)) | (~stable(E)))), ((~(environment(E) & stable(E))) <=> ((~environment(E)) | (~stable(E))))), trans(monotonicity(quant_intro(proof_bind(^[T: $i] : trans(monotonicity(trans(monotonicity(rewrite((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E))) <=> (~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) <=> (~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))), rewrite((~(~((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))), ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) <=> ((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T))))), rewrite((((~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))), (((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))), (![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T))) <=> ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))), ((greater(tptp_fun_To_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T)))) <=> (greater(tptp_fun_To_1(E), appear(efficient_producers, E)) & ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))), rewrite((greater(tptp_fun_To_1(E), appear(efficient_producers, E)) & ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))) <=> (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))), ((greater(tptp_fun_To_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T)))) <=> (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))), (((~(environment(E) & stable(E))) | (greater(tptp_fun_To_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> (((~environment(E)) | (~stable(E))) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))))), rewrite((((~environment(E)) | (~stable(E))) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E)))))))) <=> ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))), (((~(environment(E) & stable(E))) | (greater(tptp_fun_To_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | (greater(tptp_fun_To_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[To: $i] : rewrite((greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))) <=> (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))), (?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))) <=> ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T))))) <=> ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))))), rewrite(((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))), (((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T))))) <=> ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T))))) <=> ![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.40 tff(70,axiom,(![E: $i] : ((environment(E) & stable(E)) => ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l10')).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (![E: $i] : ((~(environment(E) & stable(E))) | ?[To: $i] : (greater(To, appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.18/0.40 tff(73,plain,(
% 0.18/0.40 ![E: $i] : ((~(environment(E) & stable(E))) | (greater(tptp_fun_To_1(E), appear(efficient_producers, E)) & ![T: $i] : ((~(subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(T, tptp_fun_To_1(E)))) | greater(zero, growth_rate(first_movers, T)))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[72])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))))))) <=> ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))) | ((~environment(E!2)) | (~stable(E!2)) | (~((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 ((~![E: $i] : ((~environment(E)) | (~stable(E)) | (~((~greater(tptp_fun_To_1(E), appear(efficient_producers, E))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~greater_or_equal(T, tptp_fun_To_1(E))))))))) | (~environment(E!2)) | (~stable(E!2)) | (~((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2)))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (~((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[78, 75, 19, 18])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2)))))) | greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | ((~environment(E!2)) | (~stable(E!2)) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_To_1(E!2)))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (~environment(E!2)) | (~stable(E!2)) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_To_1(E!2)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 ((in_environment(E!2, tptp_fun_To_1(E!2)) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2)))) <=> ((~environment(E!2)) | (~stable(E!2)) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_To_1(E!2)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (in_environment(E!2, tptp_fun_To_1(E!2)) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | ((~environment(E!2)) | (~stable(E!2)) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_To_1(E!2))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (in_environment(E!2, tptp_fun_To_1(E!2)) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))))) <=> ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (~environment(E!2)) | (~stable(E!2)) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_To_1(E!2)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[84, 82])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (in_environment(E!2, tptp_fun_To_1(E!2)) | (~environment(E!2)) | (~stable(E!2)) | (~in_environment(E!2, appear(efficient_producers, E!2))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 ((~![E: $i, T1: $i, T2: $i] : (in_environment(E, T2) | (~environment(E)) | (~stable(E)) | (~in_environment(E, T1)) | (~greater(T2, T1)))) | (~environment(E!2)) | (~stable(E!2)) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~in_environment(E!2, appear(efficient_producers, E!2))) | in_environment(E!2, tptp_fun_To_1(E!2))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[87, 49, 19, 18, 36, 81, 59])).
% 0.18/0.41 tff(89,plain,(in_environment(E!2, tptp_fun_To_1(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 (^[To: $i] : refl(((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers))) <=> ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers))) <=> ![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (^[To: $i] : trans(monotonicity(rewrite((greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers)) <=> (~((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers))))), ((~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers))) <=> (~(~((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers))))))), rewrite((~(~((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers))))) <=> ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))), ((~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers))) <=> ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 (![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers))) <=> ![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 (![To: $i] : (~(greater(To, appear(efficient_producers, E!2)) & contracts_from(To, first_movers)))),
% 0.18/0.41 inference(and_elim,[status(thm)],[17])).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 (![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 (((~![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))) | ((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~contracts_from(tptp_fun_To_1(E!2), first_movers)))) <=> ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~contracts_from(tptp_fun_To_1(E!2), first_movers)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))) | ((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~contracts_from(tptp_fun_To_1(E!2), first_movers)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 ((~![To: $i] : ((~greater(To, appear(efficient_producers, E!2))) | (~contracts_from(To, first_movers)))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~contracts_from(tptp_fun_To_1(E!2), first_movers))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 (~contracts_from(tptp_fun_To_1(E!2), first_movers)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[99, 96, 81])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 (^[E: $i, To: $i] : refl((contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To))))) <=> (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 (![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To))))) <=> ![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 (^[E: $i, To: $i] : trans(monotonicity(rewrite((~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))))) <=> (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To))))), ((contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To)))))) <=> (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To))))))), rewrite((contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To))))) <=> (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))), ((contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To)))))) <=> (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To)))))) <=> ![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (^[E: $i, To: $i] : rewrite((((~environment(E)) | (~stable(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To)))))) | contracts_from(To, first_movers)) <=> (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (![E: $i, To: $i] : (((~environment(E)) | (~stable(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To)))))) | contracts_from(To, first_movers)) <=> ![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 (![E: $i, To: $i] : ((~(environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) | contracts_from(To, first_movers)) <=> ![E: $i, To: $i] : ((~(environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) | contracts_from(To, first_movers))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (^[E: $i, To: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & stable(E)) & in_environment(E, To)) <=> (environment(E) & stable(E) & in_environment(E, To))), quant_intro(proof_bind(^[T: $i] : rewrite(((greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T))) <=> ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))), (![T: $i] : ((greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T))) <=> ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))), ((((environment(E) & stable(E)) & in_environment(E, To)) & ![T: $i] : ((greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))) <=> ((environment(E) & stable(E) & in_environment(E, To)) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))), rewrite(((environment(E) & stable(E) & in_environment(E, To)) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))) <=> (environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))), ((((environment(E) & stable(E)) & in_environment(E, To)) & ![T: $i] : ((greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))) <=> (environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))))), (((((environment(E) & stable(E)) & in_environment(E, To)) & ![T: $i] : ((greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))) => contracts_from(To, first_movers)) <=> ((environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))) => contracts_from(To, first_movers)))), rewrite(((environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T)))) => contracts_from(To, first_movers)) <=> ((~(environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) | contracts_from(To, first_movers))), (((((environment(E) & stable(E)) & in_environment(E, To)) & ![T: $i] : ((greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))) => contracts_from(To, first_movers)) <=> ((~(environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) | contracts_from(To, first_movers))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (![E: $i, To: $i] : ((((environment(E) & stable(E)) & in_environment(E, To)) & ![T: $i] : ((greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))) => contracts_from(To, first_movers)) <=> ![E: $i, To: $i] : ((~(environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) | contracts_from(To, first_movers))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[108])).
% 0.18/0.41 tff(110,axiom,(![E: $i, To: $i] : ((((environment(E) & stable(E)) & in_environment(E, To)) & ![T: $i] : ((greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To)) => greater(zero, growth_rate(first_movers, T)))) => contracts_from(To, first_movers))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_contracts_from')).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 (![E: $i, To: $i] : ((~(environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) | contracts_from(To, first_movers))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (![E: $i, To: $i] : ((~(environment(E) & stable(E) & in_environment(E, To) & ![T: $i] : ((~(greater(cardinality_at_time(first_movers, T), zero) & greater_or_equal(T, To))) | greater(zero, growth_rate(first_movers, T))))) | contracts_from(To, first_movers))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.18/0.41 tff(113,plain,(
% 0.18/0.41 ![E: $i, To: $i] : (((~environment(E)) | (~stable(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To)))))) | contracts_from(To, first_movers))),
% 0.18/0.41 inference(skolemize,[status(sab)],[112])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 (![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~((~(greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero) & greater_or_equal(tptp_fun_T_0(To), To))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.18/0.42 tff(115,plain,
% 0.18/0.42 (![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[114, 104])).
% 0.18/0.42 tff(116,plain,
% 0.18/0.42 (![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[115, 102])).
% 0.18/0.42 tff(117,plain,
% 0.18/0.42 (((~![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))) | ((~environment(E!2)) | (~stable(E!2)) | contracts_from(tptp_fun_To_1(E!2), first_movers) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))) <=> ((~![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))) | (~environment(E!2)) | (~stable(E!2)) | contracts_from(tptp_fun_To_1(E!2), first_movers) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(118,plain,
% 0.18/0.42 ((contracts_from(tptp_fun_To_1(E!2), first_movers) | (~stable(E!2)) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))))) <=> ((~environment(E!2)) | (~stable(E!2)) | contracts_from(tptp_fun_To_1(E!2), first_movers) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(119,plain,
% 0.18/0.42 ((~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))) <=> (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(120,plain,
% 0.18/0.42 ((contracts_from(tptp_fun_To_1(E!2), first_movers) | (~stable(E!2)) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))))) <=> (contracts_from(tptp_fun_To_1(E!2), first_movers) | (~stable(E!2)) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[119])).
% 0.18/0.42 tff(121,plain,
% 0.18/0.42 ((contracts_from(tptp_fun_To_1(E!2), first_movers) | (~stable(E!2)) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))))) <=> ((~environment(E!2)) | (~stable(E!2)) | contracts_from(tptp_fun_To_1(E!2), first_movers) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[120, 118])).
% 0.18/0.42 tff(122,plain,
% 0.18/0.42 (((~![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))) | (contracts_from(tptp_fun_To_1(E!2), first_movers) | (~stable(E!2)) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))) <=> ((~![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))) | ((~environment(E!2)) | (~stable(E!2)) | contracts_from(tptp_fun_To_1(E!2), first_movers) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[121])).
% 0.18/0.42 tff(123,plain,
% 0.18/0.42 (((~![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))) | (contracts_from(tptp_fun_To_1(E!2), first_movers) | (~stable(E!2)) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))) <=> ((~![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))) | (~environment(E!2)) | (~stable(E!2)) | contracts_from(tptp_fun_To_1(E!2), first_movers) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[122, 117])).
% 0.18/0.42 tff(124,plain,
% 0.18/0.42 ((~![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))) | (contracts_from(tptp_fun_To_1(E!2), first_movers) | (~stable(E!2)) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(125,plain,
% 0.18/0.42 ((~![E: $i, To: $i] : (contracts_from(To, first_movers) | (~stable(E)) | (~environment(E)) | (~in_environment(E, To)) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(To))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(To)), zero)) | (~greater_or_equal(tptp_fun_T_0(To), To)))))) | (~environment(E!2)) | (~stable(E!2)) | contracts_from(tptp_fun_To_1(E!2), first_movers) | (~in_environment(E!2, tptp_fun_To_1(E!2))) | (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.42 tff(126,plain,
% 0.18/0.42 (~(greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[125, 116, 19, 18, 100, 89])).
% 0.18/0.42 tff(127,plain,
% 0.18/0.42 ((greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))) | greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(128,plain,
% 0.18/0.42 (greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.18/0.42 tff(129,plain,
% 0.18/0.42 ((greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))) | (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(130,plain,
% 0.18/0.42 (~greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.18/0.42 tff(131,plain,
% 0.18/0.42 (((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2)))))) | ![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(132,plain,
% 0.18/0.42 (![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[131, 79])).
% 0.18/0.42 tff(133,plain,
% 0.18/0.42 (((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))))) <=> ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(134,plain,
% 0.18/0.42 ((greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))) <=> (greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(135,plain,
% 0.18/0.42 (((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))) <=> ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[134])).
% 0.18/0.42 tff(136,plain,
% 0.18/0.42 (((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))) <=> ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[135, 133])).
% 0.18/0.42 tff(137,plain,
% 0.18/0.42 ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))) | (greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(138,plain,
% 0.18/0.42 ((~![T: $i] : (greater(zero, growth_rate(first_movers, T)) | (~subpopulations(first_movers, efficient_producers, E!2, T)) | (~greater_or_equal(T, tptp_fun_To_1(E!2))))) | greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.18/0.42 tff(139,plain,
% 0.18/0.42 (~subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[138, 132, 130, 128])).
% 0.18/0.43 tff(140,plain,
% 0.18/0.43 ((greater(zero, growth_rate(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))) | greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(141,plain,
% 0.18/0.43 (greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[140, 126])).
% 0.18/0.43 tff(142,plain,
% 0.18/0.43 (^[E: $i, T: $i] : refl((subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(143,plain,
% 0.18/0.43 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) <=> ![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[142])).
% 0.18/0.43 tff(144,plain,
% 0.18/0.43 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))), ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))), ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))))), (((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))), (((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(145,plain,
% 0.18/0.43 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[144])).
% 0.18/0.43 tff(146,plain,
% 0.18/0.43 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(147,plain,
% 0.18/0.43 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) <=> (environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)))), (((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)))), rewrite(((environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))), (((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(148,plain,
% 0.18/0.43 (![E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[147])).
% 0.18/0.43 tff(149,axiom,(![E: $i, T: $i] : ((((environment(E) & in_environment(E, T)) & greater(cardinality_at_time(first_movers, T), zero)) & greater(cardinality_at_time(efficient_producers, T), zero)) => subpopulations(first_movers, efficient_producers, E, T))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_non_empty_fm_and_ep')).
% 0.18/0.43 tff(150,plain,
% 0.18/0.43 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.18/0.43 tff(151,plain,
% 0.18/0.43 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.18/0.43 tff(152,plain,(
% 0.18/0.43 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater(cardinality_at_time(first_movers, T), zero) & greater(cardinality_at_time(efficient_producers, T), zero))) | subpopulations(first_movers, efficient_producers, E, T))),
% 0.18/0.43 inference(skolemize,[status(sab)],[151])).
% 0.18/0.43 tff(153,plain,
% 0.18/0.43 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.18/0.43 tff(154,plain,
% 0.18/0.43 (![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[153, 143])).
% 0.18/0.43 tff(155,plain,
% 0.18/0.43 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | ((~environment(E!2)) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!2)) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(156,plain,
% 0.18/0.43 ((subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero))) <=> ((~environment(E!2)) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(157,plain,
% 0.18/0.43 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | ((~environment(E!2)) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[156])).
% 0.18/0.43 tff(158,plain,
% 0.18/0.43 (((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)))) <=> ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!2)) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[157, 155])).
% 0.18/0.43 tff(159,plain,
% 0.18/0.43 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(160,plain,
% 0.18/0.43 ((~![E: $i, T: $i] : (subpopulations(first_movers, efficient_producers, E, T) | (~environment(E)) | (~in_environment(E, T)) | (~greater(cardinality_at_time(first_movers, T), zero)) | (~greater(cardinality_at_time(efficient_producers, T), zero)))) | (~environment(E!2)) | (~greater(cardinality_at_time(first_movers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)) | subpopulations(first_movers, efficient_producers, E!2, tptp_fun_T_0(tptp_fun_To_1(E!2))) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.18/0.44 tff(161,plain,
% 0.18/0.44 ((~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[160, 154, 19, 141, 139])).
% 0.18/0.44 tff(162,plain,
% 0.18/0.44 (~greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[161, 58])).
% 0.18/0.44 tff(163,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : refl((greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(164,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[163])).
% 0.18/0.44 tff(165,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(166,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : rewrite((greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(167,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[166])).
% 0.18/0.44 tff(168,axiom,(![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> (greater(X, Y) | (X = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal')).
% 0.18/0.44 tff(169,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.18/0.44 tff(170,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.18/0.44 tff(171,plain,(
% 0.18/0.44 ![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[170])).
% 0.18/0.44 tff(172,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.18/0.44 tff(173,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) <=> ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = appear(efficient_producers, E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(174,plain,
% 0.18/0.44 (greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) <=> ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = appear(efficient_producers, E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.18/0.44 tff(175,plain,
% 0.18/0.44 (((tptp_fun_T_0(tptp_fun_To_1(E!2)) = appear(efficient_producers, E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(176,plain,
% 0.18/0.44 ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = appear(efficient_producers, E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[175, 1])).
% 0.18/0.44 tff(177,plain,
% 0.18/0.44 ((~(greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) <=> ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = appear(efficient_producers, E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))) | greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) | (~((tptp_fun_T_0(tptp_fun_To_1(E!2)) = appear(efficient_producers, E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(178,plain,
% 0.18/0.44 ((~(greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) <=> ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = appear(efficient_producers, E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))) | greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.18/0.44 tff(179,plain,
% 0.18/0.44 (greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[178, 174])).
% 0.18/0.44 tff(180,plain,
% 0.18/0.44 (^[E: $i, T: $i] : refl((greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(181,plain,
% 0.18/0.44 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) <=> ![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[180])).
% 0.18/0.44 tff(182,plain,
% 0.18/0.44 (^[E: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) <=> (~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) <=> (~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))))), rewrite((~(~((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))), ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) <=> ((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite((((~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))), (((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(183,plain,
% 0.18/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[182])).
% 0.18/0.44 tff(184,plain,
% 0.18/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(185,plain,
% 0.18/0.44 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) <=> (environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)))), rewrite(((environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))), ((((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(186,plain,
% 0.18/0.44 (![E: $i, T: $i] : (((environment(E) & in_environment(E, T)) & greater_or_equal(T, appear(efficient_producers, E))) => greater(cardinality_at_time(efficient_producers, T), zero)) <=> ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[185])).
% 0.18/0.44 tff(187,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','t6')).
% 0.18/0.44 tff(188,plain,
% 0.18/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.18/0.44 tff(189,plain,
% 0.18/0.44 (![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.18/0.44 tff(190,plain,(
% 0.18/0.44 ![E: $i, T: $i] : ((~(environment(E) & in_environment(E, T) & greater_or_equal(T, appear(efficient_producers, E)))) | greater(cardinality_at_time(efficient_producers, T), zero))),
% 0.18/0.44 inference(skolemize,[status(sab)],[189])).
% 0.18/0.44 tff(191,plain,
% 0.18/0.44 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.18/0.44 tff(192,plain,
% 0.18/0.44 (![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[191, 181])).
% 0.18/0.44 tff(193,plain,
% 0.18/0.44 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | ((~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))) <=> ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(194,plain,
% 0.18/0.44 ((greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))) <=> ((~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(195,plain,
% 0.18/0.44 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))) <=> ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | ((~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[194])).
% 0.18/0.44 tff(196,plain,
% 0.18/0.44 (((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))) <=> ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[195, 193])).
% 0.18/0.44 tff(197,plain,
% 0.18/0.44 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(198,plain,
% 0.18/0.44 ((~![E: $i, T: $i] : (greater(cardinality_at_time(efficient_producers, T), zero) | (~environment(E)) | (~in_environment(E, T)) | (~greater_or_equal(T, appear(efficient_producers, E))))) | (~environment(E!2)) | (~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.18/0.45 tff(199,plain,
% 0.18/0.45 ((~in_environment(E!2, tptp_fun_T_0(tptp_fun_To_1(E!2)))) | greater(cardinality_at_time(efficient_producers, tptp_fun_T_0(tptp_fun_To_1(E!2))), zero)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[198, 192, 19, 179])).
% 0.18/0.45 tff(200,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[199, 162, 58])).
% 0.18/0.45 tff(201,plain,(~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(202,assumption,(greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))), introduced(assumption)).
% 0.18/0.45 tff(203,plain,
% 0.18/0.45 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(204,plain,
% 0.18/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(X, Y) & greater(Y, Z)) <=> (~((~greater(X, Y)) | (~greater(Y, Z))))), ((~(greater(X, Y) & greater(Y, Z))) <=> (~(~((~greater(X, Y)) | (~greater(Y, Z))))))), rewrite((~(~((~greater(X, Y)) | (~greater(Y, Z))))) <=> ((~greater(X, Y)) | (~greater(Y, Z)))), ((~(greater(X, Y) & greater(Y, Z))) <=> ((~greater(X, Y)) | (~greater(Y, Z))))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)))), rewrite((((~greater(X, Y)) | (~greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))), (((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(205,plain,
% 0.18/0.45 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[204])).
% 0.18/0.45 tff(206,plain,
% 0.18/0.45 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(207,plain,
% 0.18/0.45 (^[X: $i, Y: $i, Z: $i] : rewrite(((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z)))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(208,plain,
% 0.18/0.45 (![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[207])).
% 0.18/0.45 tff(209,axiom,(![X: $i, Y: $i, Z: $i] : ((greater(X, Y) & greater(Y, Z)) => greater(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_transitivity')).
% 0.18/0.45 tff(210,plain,
% 0.18/0.45 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.18/0.45 tff(211,plain,
% 0.18/0.45 (![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.18/0.45 tff(212,plain,(
% 0.18/0.45 ![X: $i, Y: $i, Z: $i] : ((~(greater(X, Y) & greater(Y, Z))) | greater(X, Z))),
% 0.18/0.45 inference(skolemize,[status(sab)],[211])).
% 0.18/0.45 tff(213,plain,
% 0.18/0.45 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.18/0.45 tff(214,plain,
% 0.18/0.45 (![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[213, 203])).
% 0.18/0.45 tff(215,plain,
% 0.18/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(216,plain,
% 0.18/0.45 ((greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2)))) <=> ((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(217,plain,
% 0.18/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | ((~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[216])).
% 0.18/0.45 tff(218,plain,
% 0.18/0.45 (((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[217, 215])).
% 0.18/0.45 tff(219,plain,
% 0.18/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(220,plain,
% 0.18/0.45 ((~![X: $i, Y: $i, Z: $i] : (greater(X, Z) | (~greater(X, Y)) | (~greater(Y, Z)))) | (~greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))) | (~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.18/0.45 tff(221,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[220, 214, 81, 202, 201])).
% 0.18/0.45 tff(222,plain,(~greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(223,plain,
% 0.18/0.45 ((~![X: $i, Y: $i] : (greater_or_equal(X, Y) <=> ((X = Y) | greater(X, Y)))) | (greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)) <=> ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(224,plain,
% 0.18/0.45 (greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)) <=> ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[223, 172])).
% 0.18/0.45 tff(225,plain,
% 0.18/0.45 ((~(greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)) <=> ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))) | (~greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))) | ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(226,plain,
% 0.18/0.45 ((~(greater_or_equal(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)) <=> ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))))) | ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[225, 128])).
% 0.18/0.45 tff(227,plain,
% 0.18/0.45 ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[226, 224])).
% 0.18/0.45 tff(228,plain,
% 0.18/0.45 ((~((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2)))) | (tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(229,plain,
% 0.18/0.45 ((tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)) | greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), tptp_fun_To_1(E!2))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.18/0.45 tff(230,plain,
% 0.18/0.45 (tptp_fun_T_0(tptp_fun_To_1(E!2)) = tptp_fun_To_1(E!2)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[229, 222])).
% 0.18/0.45 tff(231,plain,
% 0.18/0.45 (greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2)) <=> greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[230])).
% 0.18/0.45 tff(232,plain,
% 0.18/0.45 (greater(tptp_fun_To_1(E!2), appear(efficient_producers, E!2)) <=> greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))),
% 0.18/0.45 inference(symmetry,[status(thm)],[231])).
% 0.18/0.45 tff(233,plain,
% 0.18/0.45 (greater(tptp_fun_T_0(tptp_fun_To_1(E!2)), appear(efficient_producers, E!2))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[81, 232])).
% 0.18/0.45 tff(234,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[201, 233])).
% 0.18/0.45 % SZS output end Proof
%------------------------------------------------------------------------------