%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT030-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:01 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n009.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 12:19:56 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(greater_type, type, (
% 0.13/0.41 greater: ( $i * $i ) > $o)).
% 0.13/0.41 tff(growth_rate_type, type, (
% 0.13/0.41 growth_rate: ( $i * $i ) > $i)).
% 0.13/0.41 tff(sk1_type, type, (
% 0.13/0.41 sk1: ( $i * $i ) > $i)).
% 0.13/0.41 tff(sk4_type, type, (
% 0.13/0.41 sk4: $i)).
% 0.13/0.41 tff(sk3_type, type, (
% 0.13/0.41 sk3: $i > $i)).
% 0.13/0.41 tff(first_movers_type, type, (
% 0.13/0.41 first_movers: $i)).
% 0.13/0.41 tff(efficient_producers_type, type, (
% 0.13/0.41 efficient_producers: $i)).
% 0.13/0.41 tff(sk2_type, type, (
% 0.13/0.41 sk2: $i > $i)).
% 0.13/0.41 tff(sk5_type, type, (
% 0.13/0.41 sk5: $i > $i)).
% 0.13/0.41 tff(in_environment_type, type, (
% 0.13/0.41 in_environment: ( $i * $i ) > $o)).
% 0.13/0.41 tff(subpopulations_type, type, (
% 0.13/0.41 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.41 tff(stable_type, type, (
% 0.13/0.41 stable: $i > $o)).
% 0.13/0.41 tff(environment_type, type, (
% 0.13/0.41 environment: $i > $o)).
% 0.13/0.41 tff(greater_or_equal_type, type, (
% 0.13/0.41 greater_or_equal: ( $i * $i ) > $o)).
% 0.13/0.41 tff(1,assumption,(~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))), introduced(assumption)).
% 0.13/0.41 tff(2,assumption,(~in_environment(sk4, sk2(sk4))), introduced(assumption)).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (stable(sk4) <=> stable(sk4)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(4,axiom,(stable(sk4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l12_13')).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (stable(sk4)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 (environment(sk4) <=> environment(sk4)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(7,axiom,(environment(sk4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l12_12')).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 (environment(sk4)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (^[A: $i] : refl(((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A))) <=> ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A))) <=> ![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 (![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A))) <=> ![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (^[A: $i] : rewrite((((~environment(A)) | (~stable(A))) | in_environment(A, sk3(A))) <=> ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk3(A))) <=> ![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.41 tff(14,axiom,(![A: $i] : (((~environment(A)) | (~stable(A))) | in_environment(A, sk3(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1_10')).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.41 tff(17,plain,(
% 0.13/0.41 ![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[16])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (((~![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))) | ((~environment(sk4)) | in_environment(sk4, sk3(sk4)) | (~stable(sk4)))) <=> ((~![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))) | (~environment(sk4)) | in_environment(sk4, sk3(sk4)) | (~stable(sk4)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 ((~![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))) | ((~environment(sk4)) | in_environment(sk4, sk3(sk4)) | (~stable(sk4)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 ((~![A: $i] : ((~environment(A)) | in_environment(A, sk3(A)) | (~stable(A)))) | (~environment(sk4)) | in_environment(sk4, sk3(sk4)) | (~stable(sk4))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (in_environment(sk4, sk3(sk4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[21, 18, 8, 5])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl((in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | in_environment(A, sk2(A))) <=> ((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | in_environment(A, sk2(A))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | in_environment(A, sk2(A))) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.41 tff(28,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_1')).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.41 tff(31,plain,(
% 0.13/0.41 ![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[30])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 ((in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[35, 33])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (in_environment(sk4, sk2(sk4)) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[38, 32, 8, 22])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[39, 2])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (^[B: $i, A: $i] : refl((in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))) <=> (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A))) <=> ![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.13/0.41 tff(46,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_2')).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.13/0.41 tff(49,plain,(
% 0.13/0.41 ![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.41 inference(skolemize,[status(sab)],[48])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 ((in_environment(sk4, sk2(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (in_environment(sk4, sk2(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[52])).
% 0.13/0.42 tff(54,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (in_environment(sk4, sk2(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.13/0.42 inference(transitivity,[status(thm)],[53, 51])).
% 0.13/0.42 tff(55,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (in_environment(sk4, sk2(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(56,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : (in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | in_environment(sk4, sk2(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.13/0.42 tff(57,plain,
% 0.13/0.42 (in_environment(sk4, sk2(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[56, 50, 8, 22])).
% 0.13/0.42 tff(58,plain,
% 0.13/0.42 (greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[57, 2])).
% 0.13/0.42 tff(59,plain,
% 0.13/0.42 (^[B: $i, A: $i] : refl(((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(60,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[59])).
% 0.13/0.42 tff(61,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(62,plain,
% 0.13/0.42 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | in_environment(A, sk2(A))) <=> (((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A))) | in_environment(A, sk2(A))))), rewrite((((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A))) | in_environment(A, sk2(A))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | in_environment(A, sk2(A))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(63,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | in_environment(A, sk2(A))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.13/0.42 tff(64,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | in_environment(A, sk2(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_7')).
% 0.13/0.42 tff(65,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.13/0.42 tff(66,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.13/0.42 tff(67,plain,(
% 0.13/0.42 ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[66])).
% 0.13/0.42 tff(68,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.13/0.42 tff(69,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4)))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(70,plain,
% 0.13/0.42 (((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(71,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[70])).
% 0.13/0.42 tff(72,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4)))),
% 0.13/0.42 inference(transitivity,[status(thm)],[71, 69])).
% 0.13/0.42 tff(73,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(74,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | in_environment(A, sk2(A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.13/0.42 tff(75,plain,
% 0.13/0.42 ((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | in_environment(sk4, sk2(sk4))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[74, 68, 8, 22])).
% 0.13/0.42 tff(76,plain,
% 0.13/0.42 (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[75, 2])).
% 0.13/0.42 tff(77,plain,
% 0.13/0.42 (^[B: $i, A: $i] : refl(((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(80,plain,
% 0.13/0.42 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | (~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) <=> (((~environment(A)) | (~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))))), rewrite((((~environment(A)) | (~stable(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) <=> ((~environment(A)) | (~stable(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) <=> ((~environment(A)) | (~stable(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> (((~environment(A)) | (~stable(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))))), rewrite((((~environment(A)) | (~stable(A)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))), ((((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(81,plain,
% 0.13/0.42 (![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.13/0.42 tff(82,axiom,(![B: $i, A: $i] : (((((~environment(A)) | (~stable(A))) | (~subpopulations(first_movers, efficient_producers, A, B))) | (~greater_or_equal(B, sk3(A)))) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1_11')).
% 0.13/0.42 tff(83,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.13/0.42 tff(84,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.13/0.42 tff(85,plain,(
% 0.13/0.42 ![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.42 inference(skolemize,[status(sab)],[84])).
% 0.13/0.42 tff(86,plain,
% 0.13/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.13/0.42 tff(87,plain,
% 0.13/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk4)) | (~stable(sk4)) | greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk4)) | (~stable(sk4)) | greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(88,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk4)) | (~stable(sk4)) | greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(89,plain,
% 0.13/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~stable(A)) | greater(growth_rate(efficient_producers, B), growth_rate(first_movers, B)) | (~greater_or_equal(B, sk3(A))) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk4)) | (~stable(sk4)) | greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.13/0.42 tff(90,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[89, 86, 8, 5, 76, 58, 40])).
% 0.13/0.42 tff(91,plain,(in_environment(sk4, sk2(sk4))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.43 tff(92,plain,
% 0.13/0.43 (^[A: $i] : refl((greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A)) <=> (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A)))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(93,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A)) <=> ![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.13/0.43 tff(94,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A)) <=> ![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(95,plain,
% 0.13/0.43 (^[A: $i] : rewrite((((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | greater(sk5(A), A)) <=> (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A)))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(96,plain,
% 0.13/0.43 (![A: $i] : (((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | greater(sk5(A), A)) <=> ![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.13/0.43 tff(97,axiom,(![A: $i] : (((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | greater(sk5(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l12_15')).
% 0.13/0.43 tff(98,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.13/0.43 tff(99,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.13/0.43 tff(100,plain,(
% 0.13/0.43 ![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))),
% 0.13/0.43 inference(skolemize,[status(sab)],[99])).
% 0.13/0.43 tff(101,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.13/0.43 tff(102,plain,
% 0.13/0.43 (((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))) | greater(sk5(sk2(sk4)), sk2(sk4)))) <=> ((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))) | greater(sk5(sk2(sk4)), sk2(sk4)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(103,plain,
% 0.13/0.43 ((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))) | greater(sk5(sk2(sk4)), sk2(sk4)))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(104,plain,
% 0.13/0.43 ((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | greater(sk5(A), A))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))) | greater(sk5(sk2(sk4)), sk2(sk4))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.13/0.43 tff(105,plain,
% 0.13/0.43 (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | greater(sk5(sk2(sk4)), sk2(sk4))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 0.13/0.43 tff(106,plain,
% 0.13/0.43 (greater(sk5(sk2(sk4)), sk2(sk4))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[105, 1])).
% 0.13/0.43 tff(107,plain,
% 0.13/0.43 (^[A: $i] : refl((subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A))) <=> (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(108,plain,
% 0.13/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.13/0.43 tff(109,plain,
% 0.13/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(110,plain,
% 0.13/0.43 (^[A: $i] : rewrite((((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A))) <=> (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(111,plain,
% 0.13/0.43 (![A: $i] : (((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A))) <=> ![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[110])).
% 0.13/0.43 tff(112,axiom,(![A: $i] : (((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | subpopulations(first_movers, efficient_producers, sk4, sk5(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l12_14')).
% 0.13/0.43 tff(113,plain,
% 0.13/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.13/0.43 tff(114,plain,
% 0.13/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.13/0.43 tff(115,plain,(
% 0.13/0.43 ![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))),
% 0.13/0.43 inference(skolemize,[status(sab)],[114])).
% 0.13/0.43 tff(116,plain,
% 0.13/0.43 (![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.13/0.43 tff(117,plain,
% 0.13/0.43 (((~![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | (~in_environment(sk4, sk2(sk4))))) <=> ((~![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | (~in_environment(sk4, sk2(sk4))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(118,plain,
% 0.13/0.43 ((subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4)))) <=> (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | (~in_environment(sk4, sk2(sk4))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(119,plain,
% 0.13/0.43 (((~![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))) | (subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))))) <=> ((~![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | (~in_environment(sk4, sk2(sk4)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[118])).
% 0.13/0.43 tff(120,plain,
% 0.13/0.43 (((~![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))) | (subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))))) <=> ((~![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | (~in_environment(sk4, sk2(sk4))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[119, 117])).
% 0.13/0.43 tff(121,plain,
% 0.13/0.43 ((~![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))) | (subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(122,plain,
% 0.13/0.43 ((~![A: $i] : (subpopulations(first_movers, efficient_producers, sk4, sk5(A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4))) | (~in_environment(sk4, sk2(sk4)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.13/0.43 tff(123,plain,
% 0.13/0.43 (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[122, 116, 91])).
% 0.13/0.43 tff(124,plain,
% 0.13/0.43 (subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[123, 1])).
% 0.13/0.43 tff(125,plain,
% 0.13/0.43 (^[A: $i] : refl((greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A))))) <=> (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(126,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A))))) <=> ![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[125])).
% 0.13/0.43 tff(127,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A))))) <=> ![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(128,plain,
% 0.13/0.43 (^[A: $i] : rewrite((((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A))))) <=> (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(129,plain,
% 0.13/0.43 (![A: $i] : (((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A))))) <=> ![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[128])).
% 0.13/0.43 tff(130,axiom,(![A: $i] : (((~in_environment(sk4, A)) | greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A))) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l12_16')).
% 0.13/0.43 tff(131,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.13/0.43 tff(132,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.13/0.43 tff(133,plain,(
% 0.13/0.43 ![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))),
% 0.13/0.43 inference(skolemize,[status(sab)],[132])).
% 0.13/0.43 tff(134,plain,
% 0.13/0.43 (![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.13/0.43 tff(135,plain,
% 0.13/0.43 (((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))) | (~in_environment(sk4, sk2(sk4))))) <=> ((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))) | (~in_environment(sk4, sk2(sk4))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(136,plain,
% 0.13/0.43 ((greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))))) <=> (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))) | (~in_environment(sk4, sk2(sk4))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(137,plain,
% 0.13/0.44 (((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))))) <=> ((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))) | (~in_environment(sk4, sk2(sk4)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[136])).
% 0.13/0.44 tff(138,plain,
% 0.13/0.44 (((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))))) <=> ((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))) | (~in_environment(sk4, sk2(sk4))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[137, 135])).
% 0.13/0.44 tff(139,plain,
% 0.13/0.44 ((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))) | (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~in_environment(sk4, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(140,plain,
% 0.13/0.44 ((~![A: $i] : (greater(growth_rate(efficient_producers, A), growth_rate(first_movers, A)) | (~in_environment(sk4, A)) | (~greater(growth_rate(efficient_producers, sk5(A)), growth_rate(first_movers, sk5(A)))))) | greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))) | (~in_environment(sk4, sk2(sk4)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.13/0.44 tff(141,plain,
% 0.13/0.44 (greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))) | (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[140, 134, 91])).
% 0.13/0.44 tff(142,plain,
% 0.13/0.44 (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[141, 1])).
% 0.13/0.44 tff(143,plain,
% 0.13/0.44 (^[B: $i, A: $i, C: $i] : refl((greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(144,plain,
% 0.13/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[143])).
% 0.13/0.44 tff(145,plain,
% 0.13/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(146,plain,
% 0.13/0.44 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> (((~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))))), rewrite((((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(147,plain,
% 0.13/0.44 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.13/0.44 tff(148,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_9')).
% 0.13/0.44 tff(149,plain,
% 0.13/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.13/0.44 tff(150,plain,
% 0.13/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.13/0.44 tff(151,plain,(
% 0.13/0.44 ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.13/0.44 inference(skolemize,[status(sab)],[150])).
% 0.13/0.44 tff(152,plain,
% 0.13/0.44 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.13/0.44 tff(153,plain,
% 0.13/0.44 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(154,plain,
% 0.13/0.44 ((greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4))))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(155,plain,
% 0.13/0.44 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[154])).
% 0.13/0.44 tff(156,plain,
% 0.13/0.44 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[155, 153])).
% 0.13/0.44 tff(157,plain,
% 0.13/0.44 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(158,plain,
% 0.13/0.44 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4)))),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.13/0.45 tff(159,plain,
% 0.13/0.45 (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[158, 152, 8, 22, 142, 124, 106])).
% 0.13/0.45 tff(160,plain,
% 0.13/0.45 (^[B: $i, A: $i, C: $i] : refl((greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(161,plain,
% 0.13/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[160])).
% 0.13/0.45 tff(162,plain,
% 0.13/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(163,plain,
% 0.13/0.45 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))))), ((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~greater(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), ((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))))), (((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))))), rewrite((((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(164,plain,
% 0.13/0.45 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[163])).
% 0.13/0.45 tff(165,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_4')).
% 0.13/0.45 tff(166,plain,
% 0.13/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.13/0.45 tff(167,plain,
% 0.13/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.13/0.45 tff(168,plain,(
% 0.13/0.45 ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.45 inference(skolemize,[status(sab)],[167])).
% 0.13/0.45 tff(169,plain,
% 0.13/0.45 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.13/0.45 tff(170,plain,
% 0.13/0.45 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(171,plain,
% 0.13/0.45 ((greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(172,plain,
% 0.13/0.45 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[171])).
% 0.13/0.45 tff(173,plain,
% 0.13/0.45 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[172, 170])).
% 0.13/0.45 tff(174,plain,
% 0.13/0.45 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)))),
% 0.13/0.45 inference(quant_inst,[status(thm)],[])).
% 0.13/0.45 tff(175,plain,
% 0.13/0.45 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4)))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.13/0.45 tff(176,plain,
% 0.13/0.45 (subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.13/0.45 inference(unit_resolution,[status(thm)],[175, 169, 8, 22, 142, 124, 106])).
% 0.13/0.45 tff(177,assumption,(~greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))), introduced(assumption)).
% 0.13/0.45 tff(178,plain,
% 0.13/0.45 (^[B: $i, A: $i] : refl(((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(179,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[178])).
% 0.13/0.45 tff(180,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(181,plain,
% 0.13/0.45 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(182,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[181])).
% 0.13/0.45 tff(183,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_5')).
% 0.13/0.45 tff(184,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.13/0.45 tff(185,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.13/0.45 tff(186,plain,(
% 0.13/0.45 ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.13/0.45 inference(skolemize,[status(sab)],[185])).
% 0.13/0.45 tff(187,plain,
% 0.13/0.45 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.13/0.45 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.13/0.45 tff(188,plain,
% 0.13/0.45 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(189,plain,
% 0.13/0.46 (((~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(190,plain,
% 0.13/0.46 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))))),
% 0.13/0.46 inference(monotonicity,[status(thm)],[189])).
% 0.13/0.46 tff(191,plain,
% 0.13/0.46 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.13/0.46 inference(transitivity,[status(thm)],[190, 188])).
% 0.13/0.46 tff(192,plain,
% 0.13/0.46 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))),
% 0.13/0.46 inference(quant_inst,[status(thm)],[])).
% 0.13/0.46 tff(193,plain,
% 0.13/0.46 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.13/0.46 tff(194,plain,
% 0.13/0.46 ((~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[193, 187, 8, 22])).
% 0.13/0.46 tff(195,plain,
% 0.13/0.46 (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[194, 177])).
% 0.13/0.46 tff(196,plain,
% 0.13/0.46 (greater(sk5(sk2(sk4)), sk2(sk4))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[105, 195])).
% 0.13/0.46 tff(197,plain,
% 0.13/0.46 (subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[123, 195])).
% 0.13/0.46 tff(198,plain,
% 0.13/0.46 (~greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4))))),
% 0.13/0.46 inference(unit_resolution,[status(thm)],[141, 195])).
% 0.13/0.46 tff(199,plain,
% 0.13/0.46 (^[B: $i, A: $i, C: $i] : refl((greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))),
% 0.13/0.46 inference(bind,[status(th)],[])).
% 0.13/0.46 tff(200,plain,
% 0.13/0.46 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.46 inference(quant_intro,[status(thm)],[199])).
% 0.13/0.46 tff(201,plain,
% 0.13/0.46 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.46 inference(rewrite,[status(thm)],[])).
% 0.13/0.46 tff(202,plain,
% 0.13/0.46 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) <=> ((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> (((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))))), rewrite((((~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) <=> ((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))), ((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> (((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater(C, sk2(A)))))), rewrite((((~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), ((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) <=> ((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)))), (((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))))), rewrite((((~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B)) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))), (((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))))),
% 0.13/0.46 inference(bind,[status(th)],[])).
% 0.13/0.46 tff(203,plain,
% 0.13/0.46 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C))) <=> ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.46 inference(quant_intro,[status(thm)],[202])).
% 0.13/0.46 tff(204,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | greater_or_equal(sk1(B, A), B)) | (~subpopulations(first_movers, efficient_producers, A, C))) | (~greater(C, sk2(A)))) | greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_6')).
% 0.13/0.46 tff(205,plain,
% 0.13/0.46 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.13/0.46 tff(206,plain,
% 0.13/0.46 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.46 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.13/0.46 tff(207,plain,(
% 0.13/0.46 ![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.13/0.46 inference(skolemize,[status(sab)],[206])).
% 0.13/0.46 tff(208,plain,
% 0.13/0.46 (![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.22/0.46 tff(209,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(210,plain,
% 0.22/0.46 ((greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(211,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[210])).
% 0.22/0.46 tff(212,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))) <=> ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[211, 209])).
% 0.22/0.46 tff(213,plain,
% 0.22/0.46 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(214,plain,
% 0.22/0.46 ((~![B: $i, A: $i, C: $i] : (greater(growth_rate(efficient_producers, C), growth_rate(first_movers, C)) | (~greater(C, sk2(A))) | (~subpopulations(first_movers, efficient_producers, A, C)) | (~in_environment(A, B)) | (~environment(A)) | greater_or_equal(sk1(B, A), B))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4)) | greater(growth_rate(efficient_producers, sk5(sk2(sk4))), growth_rate(first_movers, sk5(sk2(sk4)))) | (~subpopulations(first_movers, efficient_producers, sk4, sk5(sk2(sk4)))) | (~greater(sk5(sk2(sk4)), sk2(sk4)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.22/0.46 tff(215,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[214, 208, 8, 22, 177, 198, 197, 196])).
% 0.22/0.46 tff(216,plain,(greater_or_equal(sk1(sk3(sk4), sk4), sk3(sk4))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(217,plain,
% 0.22/0.46 (greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4))) | (~subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[89, 86, 8, 5, 216])).
% 0.22/0.46 tff(218,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[217, 176, 159])).
% 0.22/0.46 tff(219,plain,(greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(220,plain,
% 0.22/0.46 (^[B: $i, A: $i] : refl(((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(221,plain,
% 0.22/0.46 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[220])).
% 0.22/0.46 tff(222,plain,
% 0.22/0.46 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(223,plain,
% 0.22/0.47 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))), rewrite((((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), (((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(224,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[223])).
% 0.22/0.47 tff(225,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | (~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A))))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_8')).
% 0.22/0.47 tff(226,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.22/0.47 tff(227,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.22/0.47 tff(228,plain,(
% 0.22/0.47 ![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[227])).
% 0.22/0.47 tff(229,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.22/0.47 tff(230,plain,
% 0.22/0.47 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(231,plain,
% 0.22/0.47 (((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(232,plain,
% 0.22/0.47 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[231])).
% 0.22/0.47 tff(233,plain,
% 0.22/0.47 (((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))) <=> ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[232, 230])).
% 0.22/0.47 tff(234,plain,
% 0.22/0.47 ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(235,plain,
% 0.22/0.47 ((~![B: $i, A: $i] : ((~greater(growth_rate(efficient_producers, sk1(B, A)), growth_rate(first_movers, sk1(B, A)))) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.22/0.47 tff(236,plain,
% 0.22/0.47 ((~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[235, 229, 8, 22])).
% 0.22/0.47 tff(237,plain,
% 0.22/0.47 (~greater(growth_rate(efficient_producers, sk1(sk3(sk4), sk4)), growth_rate(first_movers, sk1(sk3(sk4), sk4)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[236, 219])).
% 0.22/0.47 tff(238,plain,
% 0.22/0.47 (^[B: $i, A: $i] : refl((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(239,plain,
% 0.22/0.47 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[238])).
% 0.22/0.47 tff(240,plain,
% 0.22/0.47 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(241,plain,
% 0.22/0.47 (^[B: $i, A: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))))), rewrite(((subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), (((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(242,plain,
% 0.22/0.47 (![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A))))) <=> ![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[241])).
% 0.22/0.47 tff(243,axiom,(![B: $i, A: $i] : ((((~environment(A)) | (~in_environment(A, B))) | subpopulations(first_movers, efficient_producers, A, sk1(B, A))) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_earliest_time_growth_rate_exceeds_3')).
% 0.22/0.47 tff(244,plain,
% 0.22/0.47 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.22/0.47 tff(245,plain,
% 0.22/0.47 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.22/0.47 tff(246,plain,(
% 0.22/0.47 ![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[245])).
% 0.22/0.47 tff(247,plain,
% 0.22/0.47 (![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[246, 239])).
% 0.22/0.47 tff(248,plain,
% 0.22/0.47 (((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))) <=> ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(249,plain,
% 0.22/0.47 ((subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4))))) <=> ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(250,plain,
% 0.22/0.48 (((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))) <=> ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | ((~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[249])).
% 0.22/0.48 tff(251,plain,
% 0.22/0.48 (((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))) <=> ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[250, 248])).
% 0.22/0.48 tff(252,plain,
% 0.22/0.48 ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4)) | (~in_environment(sk4, sk3(sk4))) | (~environment(sk4)) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(253,plain,
% 0.22/0.48 ((~![B: $i, A: $i] : (subpopulations(first_movers, efficient_producers, A, sk1(B, A)) | (~in_environment(A, B)) | (~environment(A)) | (~greater(growth_rate(efficient_producers, sk2(A)), growth_rate(first_movers, sk2(A)))))) | (~environment(sk4)) | (~in_environment(sk4, sk3(sk4))) | (~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.22/0.48 tff(254,plain,
% 0.22/0.48 ((~greater(growth_rate(efficient_producers, sk2(sk4)), growth_rate(first_movers, sk2(sk4)))) | subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[253, 247, 8, 22])).
% 0.22/0.48 tff(255,plain,
% 0.22/0.48 (subpopulations(first_movers, efficient_producers, sk4, sk1(sk3(sk4), sk4))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[254, 219])).
% 0.22/0.48 tff(256,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[217, 255, 237])).
% 0.22/0.48 % SZS output end Proof
% 0.22/0.48 % E exiting
%------------------------------------------------------------------------------