TSTP Solution File: MGT034-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT034-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:22:01 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT034-2 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:40:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(greater_or_equal_type, type, (
% 0.13/0.40 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.40 tff(appear_type, type, (
% 0.13/0.40 appear: ( $i * $i ) > $i)).
% 0.13/0.40 tff(sk1_type, type, (
% 0.13/0.40 sk1: $i)).
% 0.13/0.40 tff(efficient_producers_type, type, (
% 0.13/0.40 efficient_producers: $i)).
% 0.13/0.40 tff(greater_type, type, (
% 0.13/0.40 greater: ( $i * $i ) > $o)).
% 0.13/0.40 tff(critical_point_type, type, (
% 0.13/0.40 critical_point: $i > $i)).
% 0.13/0.40 tff(in_environment_type, type, (
% 0.13/0.40 in_environment: ( $i * $i ) > $o)).
% 0.13/0.40 tff(subpopulations_type, type, (
% 0.13/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.40 tff(first_movers_type, type, (
% 0.13/0.40 first_movers: $i)).
% 0.13/0.40 tff(sk2_type, type, (
% 0.13/0.40 sk2: $i)).
% 0.13/0.40 tff(growth_rate_type, type, (
% 0.13/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.40 tff(environment_type, type, (
% 0.13/0.40 environment: $i > $o)).
% 0.13/0.40 tff(selection_favors_type, type, (
% 0.13/0.40 selection_favors: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(zero_type, type, (
% 0.13/0.40 zero: $i)).
% 0.13/0.40 tff(difference_type, type, (
% 0.13/0.40 difference: ( $i * $i ) > $i)).
% 0.13/0.40 tff(decreases_type, type, (
% 0.13/0.40 decreases: $i > $o)).
% 0.13/0.40 tff(disbanding_rate_type, type, (
% 0.13/0.40 disbanding_rate: ( $i * $i ) > $i)).
% 0.13/0.40 tff(founding_rate_type, type, (
% 0.13/0.40 founding_rate: ( $i * $i ) > $i)).
% 0.13/0.40 tff(1,assumption,(critical_point(sk1) = appear(efficient_producers, sk1)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (in_environment(sk1, critical_point(sk1)) <=> in_environment(sk1, appear(efficient_producers, sk1))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (in_environment(sk1, appear(efficient_producers, sk1)) <=> in_environment(sk1, critical_point(sk1))),
% 0.13/0.40 inference(symmetry,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 ((~in_environment(sk1, appear(efficient_producers, sk1))) <=> (~in_environment(sk1, critical_point(sk1)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[3])).
% 0.13/0.40 tff(5,assumption,(subpopulations(first_movers, efficient_producers, sk1, sk2)), introduced(assumption)).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (environment(sk1) <=> environment(sk1)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(7,axiom,(environment(sk1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t3_58')).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (environment(sk1)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(efficient_producers, first_movers, A, B)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(efficient_producers, first_movers, A, B)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.40 tff(14,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(efficient_producers, first_movers, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_symmetry_of_subpopulations_48')).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.40 tff(17,plain,(
% 0.13/0.40 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.40 inference(skolemize,[status(sab)],[16])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | subpopulations(efficient_producers, first_movers, sk1, sk2)) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | subpopulations(efficient_producers, first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | subpopulations(efficient_producers, first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.40 inference(transitivity,[status(thm)],[21, 19])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | subpopulations(efficient_producers, first_movers, A, B))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | subpopulations(efficient_producers, first_movers, sk1, sk2)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (subpopulations(efficient_producers, first_movers, sk1, sk2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[24, 18, 8, 5])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 ((~selection_favors(first_movers, efficient_producers, sk2)) <=> (~selection_favors(first_movers, efficient_producers, sk2))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(27,axiom,(~selection_favors(first_movers, efficient_producers, sk2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t3_62')).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (~selection_favors(first_movers, efficient_producers, sk2)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (^[B: $i, D: $i, A: $i, C: $i] : refl((selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) <=> ![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) <=> ((~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) | selection_favors(C, B, D)) <=> (((~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | selection_favors(C, B, D)))), rewrite((((~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A))) | selection_favors(C, B, D)) <=> (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))), (((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) | selection_favors(C, B, D)) <=> (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) | selection_favors(C, B, D)) <=> ![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.40 tff(34,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulations(B, C, A, D))) | (~greater(growth_rate(C, D), growth_rate(B, D)))) | selection_favors(C, B, D))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp1_high_growth_rates_33')).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.13/0.40 tff(37,plain,(
% 0.13/0.40 ![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[36])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 ((selection_favors(first_movers, efficient_producers, sk2) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)) | (~environment(sk1))) <=> (selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[40])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[41, 39])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | (selection_favors(first_movers, efficient_producers, sk2) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2)) | (~environment(sk1)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 ((~![B: $i, D: $i, A: $i, C: $i] : (selection_favors(C, B, D) | (~greater(growth_rate(C, D), growth_rate(B, D))) | (~subpopulations(B, C, A, D)) | (~environment(A)))) | selection_favors(first_movers, efficient_producers, sk2) | (~environment(sk1)) | (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | (~subpopulations(efficient_producers, first_movers, sk1, sk2))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (~greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[44, 38, 8, 28, 25])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl(((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))))) <=> ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B))))) <=> ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.41 tff(51,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3_34')).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.13/0.41 tff(54,plain,(
% 0.13/0.41 ![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[53])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (((~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1))) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[57])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))) <=> ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[58, 56])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | ((~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : ((~decreases(difference(disbanding_rate(first_movers, B), disbanding_rate(efficient_producers, B)))) | (~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (~decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 55, 8, 5])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.41 tff(68,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a12_57')).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.19/0.41 tff(71,plain,(
% 0.19/0.41 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[75, 73])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, sk2)) | (~environment(sk1)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | decreases(difference(founding_rate(first_movers, B), founding_rate(efficient_producers, B))))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 72, 8, 5])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (^[A: $i] : refl((decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) <=> (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) <=> ![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) <=> ![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (^[A: $i] : trans(monotonicity(rewrite(((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) <=> (decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))), ((((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) <=> ((decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))))), rewrite(((decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A))))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) <=> (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))), ((((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) <=> (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![A: $i] : (((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) <=> ![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.42 tff(85,axiom,(![A: $i] : (((~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A)))) | decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_difference_between_founding_rates_37')).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.42 tff(88,plain,(
% 0.19/0.42 ![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[87])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (((~![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))) | (decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))))) <=> ((~![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))) | decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 ((~![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))) | (decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![A: $i] : (decreases(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) | decreases(difference(disbanding_rate(first_movers, A), disbanding_rate(efficient_producers, A))) | (~decreases(difference(founding_rate(first_movers, A), founding_rate(efficient_producers, A)))))) | decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))) | decreases(difference(disbanding_rate(first_movers, sk2), disbanding_rate(efficient_producers, sk2))) | (~decreases(difference(founding_rate(first_movers, sk2), founding_rate(efficient_producers, sk2))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[92, 89, 79, 62])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (^[B: $i, A: $i] : refl(((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A)))) <=> ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~(B = critical_point(A)))) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))) <=> ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (![B: $i, A: $i] : (((~environment(A)) | (~(B = critical_point(A)))) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.42 tff(99,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~(B = critical_point(A)))) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_54')).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.19/0.42 tff(102,plain,(
% 0.19/0.42 ![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[101])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))) | ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))) | (~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))) | $false) <=> ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((~$true) <=> $false),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((critical_point(sk1) = critical_point(sk1)) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ((~(critical_point(sk1) = critical_point(sk1))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~(critical_point(sk1) = critical_point(sk1))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))) | (~(critical_point(sk1) = critical_point(sk1)))) <=> ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))) | $false)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))) | (~(critical_point(sk1) = critical_point(sk1)))) <=> ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[110, 105])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))) | ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))) | (~(critical_point(sk1) = critical_point(sk1))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))) | ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))) | ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))) | (~(critical_point(sk1) = critical_point(sk1))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))) | (~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[112, 104])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))) | ((~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))) | (~(critical_point(sk1) = critical_point(sk1))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((~environment(A)) | (~greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) | (~(B = critical_point(A))))) | (~environment(sk1)) | (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (~greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[115, 103, 8])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (^[A: $i] : refl(((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) <=> ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) <=> ![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) <=> ![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(120,axiom,(![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_negative_growth_rate_difference_39')).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.43 tff(122,plain,(
% 0.19/0.43 ![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[121])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (((~![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))) | ((~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) | greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))) <=> ((~![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))) | (~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) | greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 ((~![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))) | ((~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) | greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 ((~![A: $i] : ((~greater(zero, difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)))) | (~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) | greater(growth_rate(efficient_producers, critical_point(sk1)), growth_rate(first_movers, critical_point(sk1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (~greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[126, 123, 116])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 (in_environment(sk1, critical_point(sk1)) <=> in_environment(sk1, critical_point(sk1))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(129,axiom,(in_environment(sk1, critical_point(sk1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t3_59')).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (in_environment(sk1, critical_point(sk1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (^[A: $i] : refl((subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))) <=> (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 (^[A: $i] : rewrite((((~environment(A)) | (~in_environment(A, critical_point(A)))) | subpopulations(first_movers, efficient_producers, A, critical_point(A))) <=> (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(135,plain,
% 0.19/0.43 (![A: $i] : (((~environment(A)) | (~in_environment(A, critical_point(A)))) | subpopulations(first_movers, efficient_producers, A, critical_point(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.43 tff(136,axiom,(![A: $i] : (((~environment(A)) | (~in_environment(A, critical_point(A)))) | subpopulations(first_movers, efficient_producers, A, critical_point(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_critical_point_means_FM_and_EP_35')).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.19/0.43 tff(139,plain,(
% 0.19/0.43 ![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[138])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 (((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))) | (subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1)) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)))) <=> ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))) | subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1)) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(142,plain,
% 0.19/0.43 ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))) | (subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1)) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 ((~![A: $i] : (subpopulations(first_movers, efficient_producers, A, critical_point(A)) | (~in_environment(A, critical_point(A))) | (~environment(A)))) | subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1)) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 (subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[143, 140, 8, 130])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[145])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) <=> (((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)))), rewrite((((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.43 tff(150,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)))) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_relationship_of_growth_rates_53')).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.19/0.44 tff(153,plain,(
% 0.19/0.44 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[152])).
% 0.19/0.44 tff(154,plain,
% 0.19/0.44 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.19/0.44 tff(155,plain,
% 0.19/0.44 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(156,plain,
% 0.19/0.44 (((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))) <=> ((~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(157,plain,
% 0.19/0.44 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[156])).
% 0.19/0.44 tff(158,plain,
% 0.19/0.44 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[157, 155])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero) | greater(zero, difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B))))) | (~environment(sk1)) | greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 (greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero) | greater(zero, difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[160, 154, 8, 144])).
% 0.19/0.44 tff(162,plain,
% 0.19/0.44 (greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[161, 127])).
% 0.19/0.44 tff(163,plain,
% 0.19/0.44 (greater(critical_point(sk1), sk2) <=> greater(critical_point(sk1), sk2)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(164,axiom,(greater(critical_point(sk1), sk2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t3_61')).
% 0.19/0.44 tff(165,plain,
% 0.19/0.44 (greater(critical_point(sk1), sk2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.44 tff(166,plain,
% 0.19/0.44 (greater_or_equal(sk2, appear(efficient_producers, sk1)) <=> greater_or_equal(sk2, appear(efficient_producers, sk1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(167,axiom,(greater_or_equal(sk2, appear(efficient_producers, sk1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_t3_60')).
% 0.19/0.44 tff(168,plain,
% 0.19/0.44 (greater_or_equal(sk2, appear(efficient_producers, sk1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) <=> ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(170,plain,
% 0.19/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[169])).
% 0.19/0.44 tff(171,plain,
% 0.19/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(172,plain,
% 0.19/0.44 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) <=> ((~environment(A)) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) <=> (((~environment(A)) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~greater_or_equal(C, appear(efficient_producers, A)))))), rewrite((((~environment(A)) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~greater_or_equal(C, appear(efficient_producers, A)))) <=> ((~environment(A)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) <=> ((~environment(A)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) <=> (((~environment(A)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~greater(B, C))))), rewrite((((~environment(A)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~greater(B, C))) <=> ((~environment(A)) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) <=> ((~environment(A)) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) <=> (((~environment(A)) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))))), rewrite((((~environment(A)) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) <=> ((~environment(A)) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), (((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) <=> ((~environment(A)) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))))), ((((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)) <=> (((~environment(A)) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)))), rewrite((((~environment(A)) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)) <=> ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))), ((((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)) <=> ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 (![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero)) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[172])).
% 0.19/0.45 tff(174,axiom,(![B: $i, A: $i, C: $i] : (((((((~environment(A)) | (~in_environment(A, B))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero))) | (~greater_or_equal(C, appear(efficient_producers, A)))) | (~greater(B, C))) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C))))) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_decreasing_function_38')).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.19/0.45 tff(177,plain,(
% 0.19/0.45 ![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[176])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 (((~environment(sk1)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater(critical_point(sk1), sk2)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)) | (~in_environment(sk1, critical_point(sk1)))) <=> ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater(critical_point(sk1), sk2)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)) | (~in_environment(sk1, critical_point(sk1))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[180])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater(critical_point(sk1), sk2)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)) | (~in_environment(sk1, critical_point(sk1))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[181, 179])).
% 0.19/0.45 tff(183,plain,
% 0.19/0.45 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | ((~environment(sk1)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater(critical_point(sk1), sk2)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero)) | (~in_environment(sk1, critical_point(sk1))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | greater(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)), zero) | (~decreases(difference(growth_rate(first_movers, C), growth_rate(efficient_producers, C)))) | (~greater(B, C)) | (~greater_or_equal(C, appear(efficient_producers, A))) | (~greater_or_equal(difference(growth_rate(first_movers, B), growth_rate(efficient_producers, B)), zero)) | (~in_environment(A, B)))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | (~greater(critical_point(sk1), sk2)) | greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 (greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) | (~greater_or_equal(difference(growth_rate(first_movers, critical_point(sk1)), growth_rate(efficient_producers, critical_point(sk1))), zero))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[184, 178, 8, 130, 168, 165])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 (greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero) | (~decreases(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[185, 162])).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 (greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[186, 93])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (^[A: $i] : refl(((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) <=> ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(189,plain,
% 0.19/0.45 (![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) <=> ![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[188])).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A))) <=> ![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(191,axiom,(![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_positive_growth_rate_difference_41')).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 (![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.45 tff(193,plain,(
% 0.19/0.45 ![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[192])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 (![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.19/0.45 tff(195,plain,
% 0.19/0.45 (((~![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | ((~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))) <=> ((~![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | (~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 ((~![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | ((~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 ((~![A: $i] : ((~greater(difference(growth_rate(first_movers, A), growth_rate(efficient_producers, A)), zero)) | greater(growth_rate(first_movers, A), growth_rate(efficient_producers, A)))) | (~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.19/0.45 tff(198,plain,
% 0.19/0.45 ((~greater(difference(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2)), zero)) | greater(growth_rate(first_movers, sk2), growth_rate(efficient_producers, sk2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[197, 194])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[198, 187, 45])).
% 0.19/0.45 tff(200,plain,(~subpopulations(first_movers, efficient_producers, sk1, sk2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 (^[B: $i, A: $i] : refl(((~greater(A, B)) | greater_or_equal(A, B)) <=> ((~greater(A, B)) | greater_or_equal(A, B)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(202,plain,
% 0.19/0.45 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[201])).
% 0.19/0.45 tff(203,plain,
% 0.19/0.45 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(204,axiom,(![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal_51')).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.45 tff(206,plain,(
% 0.19/0.45 ![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.45 inference(skolemize,[status(sab)],[205])).
% 0.19/0.45 tff(207,plain,
% 0.19/0.45 (![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.19/0.45 tff(208,plain,
% 0.19/0.45 (((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(critical_point(sk1), sk2)) | greater_or_equal(critical_point(sk1), sk2))) <=> ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(critical_point(sk1), sk2)) | greater_or_equal(critical_point(sk1), sk2))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(209,plain,
% 0.19/0.46 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | ((~greater(critical_point(sk1), sk2)) | greater_or_equal(critical_point(sk1), sk2))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(210,plain,
% 0.19/0.46 ((~![B: $i, A: $i] : ((~greater(A, B)) | greater_or_equal(A, B))) | (~greater(critical_point(sk1), sk2)) | greater_or_equal(critical_point(sk1), sk2)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.19/0.46 tff(211,plain,
% 0.19/0.46 (greater_or_equal(critical_point(sk1), sk2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[210, 207, 165])).
% 0.19/0.46 tff(212,plain,
% 0.19/0.46 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(213,plain,
% 0.19/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[212])).
% 0.19/0.46 tff(214,plain,
% 0.19/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(215,plain,
% 0.19/0.46 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) <=> (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(D, B))))), rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(D, B))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) <=> (((~environment(A)) | (~greater_or_equal(D, B)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(C, D))))), rewrite((((~environment(A)) | (~greater_or_equal(D, B)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(C, D))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B)))), ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) | subpopulations(first_movers, efficient_producers, A, D)) <=> (((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(first_movers, efficient_producers, A, D)))), rewrite((((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~subpopulations(first_movers, efficient_producers, A, B))) | subpopulations(first_movers, efficient_producers, A, D)) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) | subpopulations(first_movers, efficient_producers, A, D)) <=> ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(216,plain,
% 0.19/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) | subpopulations(first_movers, efficient_producers, A, D)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[215])).
% 0.19/0.46 tff(217,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater_or_equal(D, B))) | (~greater_or_equal(C, D))) | subpopulations(first_movers, efficient_producers, A, D))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a10_56')).
% 0.19/0.46 tff(218,plain,
% 0.19/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.46 tff(219,plain,
% 0.19/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.19/0.46 tff(220,plain,(
% 0.19/0.46 ![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[219])).
% 0.19/0.46 tff(221,plain,
% 0.19/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.19/0.46 tff(222,plain,
% 0.19/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(223,plain,
% 0.19/0.46 (((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)))) <=> ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(224,plain,
% 0.19/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[223])).
% 0.19/0.46 tff(225,plain,
% 0.19/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[224, 222])).
% 0.19/0.46 tff(226,plain,
% 0.19/0.46 ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(227,plain,
% 0.19/0.46 ((~![B: $i, D: $i, A: $i, C: $i] : ((~environment(A)) | (~greater_or_equal(D, B)) | (~greater_or_equal(C, D)) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, D) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~greater_or_equal(sk2, appear(efficient_producers, sk1))) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~greater_or_equal(critical_point(sk1), sk2)) | subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.46 tff(228,plain,
% 0.19/0.46 (subpopulations(first_movers, efficient_producers, sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[227, 221, 8, 168, 144, 211])).
% 0.19/0.46 tff(229,plain,
% 0.19/0.46 (~subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[228, 200])).
% 0.19/0.46 tff(230,plain,
% 0.19/0.46 (^[A: $i] : refl(((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))) <=> ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(231,plain,
% 0.19/0.46 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))) <=> ![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[230])).
% 0.19/0.46 tff(232,plain,
% 0.19/0.46 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))) <=> ![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(233,plain,
% 0.19/0.46 (^[A: $i] : rewrite((((~environment(A)) | (~in_environment(A, appear(efficient_producers, A)))) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A))) <=> ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(234,plain,
% 0.19/0.46 (![A: $i] : (((~environment(A)) | (~in_environment(A, appear(efficient_producers, A)))) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A))) <=> ![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[233])).
% 0.19/0.46 tff(235,axiom,(![A: $i] : (((~environment(A)) | (~in_environment(A, appear(efficient_producers, A)))) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_FM_and_EP_when_EP_appears_36')).
% 0.19/0.46 tff(236,plain,
% 0.19/0.46 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.19/0.46 tff(237,plain,
% 0.19/0.46 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.19/0.46 tff(238,plain,(
% 0.19/0.46 ![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[237])).
% 0.19/0.46 tff(239,plain,
% 0.19/0.46 (![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[238, 231])).
% 0.19/0.46 tff(240,plain,
% 0.19/0.46 (((~![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))) | ((~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1))))) <=> ((~![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))) | (~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(241,plain,
% 0.19/0.46 ((~![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))) | ((~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(242,plain,
% 0.19/0.46 ((~![A: $i] : ((~environment(A)) | subpopulations(first_movers, efficient_producers, A, appear(efficient_producers, A)) | (~in_environment(A, appear(efficient_producers, A))))) | (~environment(sk1)) | subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.19/0.46 tff(243,plain,
% 0.19/0.46 (subpopulations(first_movers, efficient_producers, sk1, appear(efficient_producers, sk1)) | (~in_environment(sk1, appear(efficient_producers, sk1)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[242, 239, 8])).
% 0.19/0.46 tff(244,plain,
% 0.19/0.46 (~in_environment(sk1, appear(efficient_producers, sk1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[243, 229])).
% 0.19/0.46 tff(245,plain,
% 0.19/0.46 (~in_environment(sk1, critical_point(sk1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[244, 4])).
% 0.19/0.46 tff(246,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[130, 245])).
% 0.19/0.46 tff(247,plain,(~(critical_point(sk1) = appear(efficient_producers, sk1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(248,plain,
% 0.19/0.46 (^[B: $i, A: $i] : refl(((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(249,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[248])).
% 0.19/0.46 tff(250,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(251,plain,
% 0.19/0.46 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, appear(efficient_producers, A))) <=> ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(252,plain,
% 0.19/0.46 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, appear(efficient_producers, A))) <=> ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[251])).
% 0.19/0.46 tff(253,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater_or_equal(B, appear(efficient_producers, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_FM_and_EP_members_EP_appeared_49')).
% 0.19/0.46 tff(254,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.46 tff(255,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.19/0.46 tff(256,plain,(
% 0.19/0.46 ![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[255])).
% 0.19/0.46 tff(257,plain,
% 0.19/0.46 (![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[256, 249])).
% 0.19/0.46 tff(258,plain,
% 0.19/0.46 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(259,plain,
% 0.19/0.47 (((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(260,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[259])).
% 0.19/0.47 tff(261,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))) <=> ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[260, 258])).
% 0.19/0.47 tff(262,plain,
% 0.19/0.47 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | ((~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | (~environment(sk1)) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(263,plain,
% 0.19/0.47 ((~![B: $i, A: $i] : ((~subpopulations(first_movers, efficient_producers, A, B)) | (~environment(A)) | greater_or_equal(B, appear(efficient_producers, A)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, critical_point(sk1))) | greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.47 tff(264,plain,
% 0.19/0.47 (greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[263, 257, 8, 144])).
% 0.19/0.47 tff(265,plain,
% 0.19/0.47 (^[B: $i, A: $i] : refl((greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> (greater(A, B) | (A = B) | (~greater_or_equal(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(266,plain,
% 0.19/0.47 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[265])).
% 0.19/0.47 tff(267,plain,
% 0.19/0.47 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B))) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(268,plain,
% 0.19/0.47 (^[B: $i, A: $i] : rewrite((((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> (greater(A, B) | (A = B) | (~greater_or_equal(A, B))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(269,plain,
% 0.19/0.47 (![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B)) <=> ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[268])).
% 0.19/0.47 tff(270,axiom,(![B: $i, A: $i] : (((~greater_or_equal(A, B)) | greater(A, B)) | (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal_50')).
% 0.19/0.47 tff(271,plain,
% 0.19/0.47 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.19/0.47 tff(272,plain,
% 0.19/0.47 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.19/0.47 tff(273,plain,(
% 0.19/0.47 ![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[272])).
% 0.19/0.47 tff(274,plain,
% 0.19/0.47 (![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.19/0.47 tff(275,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | (greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1)) | (~greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))))) <=> ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1)) | (~greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(276,plain,
% 0.19/0.47 ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | (greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1)) | (~greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(277,plain,
% 0.19/0.47 ((~![B: $i, A: $i] : (greater(A, B) | (A = B) | (~greater_or_equal(A, B)))) | greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1)) | (~greater_or_equal(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.19/0.47 tff(278,plain,
% 0.19/0.47 (greater(critical_point(sk1), appear(efficient_producers, sk1)) | (critical_point(sk1) = appear(efficient_producers, sk1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[277, 274, 264])).
% 0.19/0.47 tff(279,plain,
% 0.19/0.47 (greater(critical_point(sk1), appear(efficient_producers, sk1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[278, 247])).
% 0.19/0.47 tff(280,plain,
% 0.19/0.47 (^[B: $i, A: $i] : refl(((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(281,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[280])).
% 0.19/0.47 tff(282,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(283,plain,
% 0.19/0.47 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A))))), (((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) <=> (((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))))), rewrite((((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))), (((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))))), ((((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) | in_environment(A, B)) <=> (((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | in_environment(A, B)))), rewrite((((~in_environment(A, critical_point(A))) | (~environment(A)) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A)))) | in_environment(A, B)) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))), ((((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) | in_environment(A, B)) <=> ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(284,plain,
% 0.19/0.47 (![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) | in_environment(A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[283])).
% 0.19/0.47 tff(285,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~in_environment(A, critical_point(A)))) | (~greater_or_equal(B, appear(efficient_producers, A)))) | (~greater(critical_point(A), B))) | in_environment(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_critical_time_points_46')).
% 0.19/0.47 tff(286,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.19/0.47 tff(287,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.19/0.47 tff(288,plain,(
% 0.19/0.47 ![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[287])).
% 0.19/0.47 tff(289,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[288, 281])).
% 0.19/0.47 tff(290,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(291,plain,
% 0.19/0.47 (((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))) <=> ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(292,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[291])).
% 0.19/0.47 tff(293,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[292, 290])).
% 0.19/0.47 tff(294,plain,
% 0.19/0.47 ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | ((~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater(critical_point(sk1), appear(efficient_producers, sk1))) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(295,plain,
% 0.19/0.47 ((~![B: $i, A: $i] : ((~in_environment(A, critical_point(A))) | (~environment(A)) | in_environment(A, B) | (~greater(critical_point(A), B)) | (~greater_or_equal(B, appear(efficient_producers, A))))) | (~in_environment(sk1, critical_point(sk1))) | (~environment(sk1)) | in_environment(sk1, appear(efficient_producers, sk1)) | (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.19/0.47 tff(296,plain,
% 0.19/0.47 ((~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) | (~greater(critical_point(sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[295, 289, 8, 130, 244])).
% 0.19/0.47 tff(297,plain,
% 0.19/0.47 (~greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[296, 279])).
% 0.19/0.47 tff(298,plain,
% 0.19/0.47 (^[B: $i, A: $i] : refl(((~(A = B)) | greater_or_equal(A, B)) <=> ((~(A = B)) | greater_or_equal(A, B)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(299,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[298])).
% 0.19/0.47 tff(300,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B)) <=> ![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(301,axiom,(![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_greater_or_equal_52')).
% 0.19/0.47 tff(302,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.19/0.47 tff(303,plain,(
% 0.19/0.47 ![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.19/0.47 inference(skolemize,[status(sab)],[302])).
% 0.19/0.47 tff(304,plain,
% 0.19/0.47 (![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.19/0.47 tff(305,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) <=> ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(306,plain,
% 0.19/0.47 (($false | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) <=> greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(307,plain,
% 0.19/0.47 ((appear(efficient_producers, sk1) = appear(efficient_producers, sk1)) <=> $true),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(308,plain,
% 0.19/0.47 ((~(appear(efficient_producers, sk1) = appear(efficient_producers, sk1))) <=> (~$true)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[307])).
% 0.19/0.47 tff(309,plain,
% 0.19/0.47 ((~(appear(efficient_producers, sk1) = appear(efficient_producers, sk1))) <=> $false),
% 0.19/0.47 inference(transitivity,[status(thm)],[308, 106])).
% 0.19/0.47 tff(310,plain,
% 0.19/0.47 (((~(appear(efficient_producers, sk1) = appear(efficient_producers, sk1))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) <=> ($false | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[309])).
% 0.19/0.47 tff(311,plain,
% 0.19/0.47 (((~(appear(efficient_producers, sk1) = appear(efficient_producers, sk1))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))) <=> greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))),
% 0.19/0.47 inference(transitivity,[status(thm)],[310, 306])).
% 0.19/0.47 tff(312,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | ((~(appear(efficient_producers, sk1) = appear(efficient_producers, sk1))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))) <=> ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[311])).
% 0.19/0.47 tff(313,plain,
% 0.19/0.47 (((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | ((~(appear(efficient_producers, sk1) = appear(efficient_producers, sk1))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))) <=> ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[312, 305])).
% 0.19/0.47 tff(314,plain,
% 0.19/0.47 ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | ((~(appear(efficient_producers, sk1) = appear(efficient_producers, sk1))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(315,plain,
% 0.19/0.47 ((~![B: $i, A: $i] : ((~(A = B)) | greater_or_equal(A, B))) | greater_or_equal(appear(efficient_producers, sk1), appear(efficient_producers, sk1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.19/0.47 tff(316,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[315, 304, 297])).
% 0.19/0.47 % SZS output end Proof
%------------------------------------------------------------------------------